Log24

Friday, October 3, 2025

A Unifying Framework

Filed under: General — Tags: , , , , — m759 @ 1:15 am
 

Finite Geometry: A Unifying Framework
for Art and Mathematics

"In essence, finite geometry, exemplified by the Cullinane diamond theorem, acts as a 'portal' that unveils profound mathematical structures underlying seemingly simple patterns, demonstrating the interconnectedness of geometry, algebra, combinatorics, and visual art, with significant implications for fields ranging from error-correcting codes to experimental design and signal processing."

— NotebookLM AI on 18 September 2025

See as well a dies natalis  on 18 September 2025 —

Sunday, September 28, 2025

Fundamental Structure: “(7, 3, 1)”

Filed under: General — Tags: , , , — m759 @ 4:02 pm

Update on Monday morning, Sept. 29, 2025  —

Related reading . . . Jack Edmonds in Wikipedia and . . .

Edmonds, Jack (1991), "A Glimpse of Heaven,"
in J.K. Lenstra; A.H.G. Rinnooy Kan; A. Schrijver (eds.),
History of Mathematical Programming – A Collection of
Personal Reminiscences, CWI, Amsterdam and North-Holland,
Amsterdam, pp. 32–54

Monday, September 15, 2025

For Word Collectors . . . “Once in a Lullaby”

Filed under: General — Tags: , , , — m759 @ 11:47 pm

Monday, February 7, 2022

Science News

Filed under: General — Tags: , , — m759 @ 3:06 pm

See the above science adviser in this  journal —

"Non-Chaos Non-Magic," Feb. 26, 2021.

Tuesday, March 23, 2021

The Fano Hallows

Filed under: General — Tags: , — m759 @ 4:39 pm

From a Log24 post of Friday, February 26, 2021 —

( Not to be confused with The Tin Man’s Hat. )

This image may be regarded as memorializing a photographer
who died at 80 on Feb. 26 and who

“captured Warhol’s self-designed mythology in the making”
— Alex Vadukul in The New York Times  today

Sunday, March 21, 2021

Mathematics and Narrative: The Unity

Filed under: General — Tags: , , , — m759 @ 10:25 pm

“To conquer, three boxes* have to synchronize and join together into the Unity.”

―Wonder Woman in Zack Snyder’s Justice League

See also The Unity of Combinatorics  and The Miracle Octad Generator.

* Cf.  Aitchison’s Octads —

Friday, February 26, 2021

Non-Chaos Non-Magic

Filed under: General — Tags: , — m759 @ 12:21 pm

For fans of “WandaVision” —

“1978 was perhaps the seminal year in the origin of chaos magic. . . .”

— Wikipedia article on Chaos Magic

Non-Chaos Non-Magic from Halloween 1978 —

The Cullinane diamond theorem, AMS Notices, Feb. 1979, pp. A-193-194

Related material —

A doctoral student of a different  Peter Cameron —

( Not to be confused with The Tin Man’s Hat. )

Thursday, May 28, 2020

Unity Game

Filed under: General — Tags: , , — m759 @ 11:59 pm

“Old men ought to be explorers.” — T. S. Eliot

“Everybody’s lost but me!” — Young Indiana Jones, quoted
in a book review (“Knox Peden on Martin Hägglund”) in
Sydney Review of Books  on May 26 . . .

” Here I am reminded of the words of
the young Indiana Jones alone in the desert,
decades before the Last Crusade:
‘Everybody’s lost but me.’ “

 Related remarks — Now You See It, Now You Don’t.

Finite Geometry at GitHub

Filed under: General — Tags: , , — m759 @ 5:04 pm

My website on finite geometry is now available
on GitHub at http://m759.github.io/ . The part
of greatest interest to coders is also at
https://repl.it/@m759/View-4x4x4#index.html .

Wednesday, May 20, 2020

Raiders of the Lost Unity

Filed under: General — Tags: — m759 @ 2:21 pm

Mathematics as a Black Art

Filed under: General — Tags: , , — m759 @ 11:34 am

Thursday, May 7, 2020

Now You See It, Now You Don’t

Filed under: General — Tags: , , , — m759 @ 11:00 pm

“Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to explain
how art fits into our subject and what we mean by beauty.”

— Sir Michael Atiyah, quoted here on April 4, 2016

 

Illustrations, from the American Mathematical Society Spring
2020 book sale, of a book scheduled to be published May 28.

Kant as Diamond Cutter

Filed under: General — Tags: , , , — m759 @ 4:26 am

"He wished Kant were alive. Kant would have appreciated it.
That master diamond cutter."

— Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance , Part III.

Kant's  "category theory" —

"In the Transcendental Analytic, Kant deduces the table of twelve categories, or pure concepts of the understanding….

The categories must be 'schematized' because their non-empirical origin in pure understanding prevents their having the sort of sensible content that would connect them immediately to the objects of experience; transcendental schemata are mediating representations that are meant to establish the connection between pure concepts and appearances in a rule-governed way. Mathematical concepts are discussed in this context since they are unique in being pure but also sensible concepts: they are pure because they are strictly a priori  in origin, and yet they are sensible since they are constructed in concreto . "

— Shabel, Lisa, "Kant's Philosophy of Mathematics", The Stanford Encyclopedia of Philosophy  (Spring 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2016/entries/kant-mathematics/>.

See also The Diamond Theorem and Octad.us.

Wednesday, May 6, 2020

“The Ship of Theseus”…

Filed under: General — Tags: , — m759 @ 2:17 pm

is a philosophical conundrum  discussed this morning  in the weblog of
David Justice.

A related statement of this “problem of identity,” from posts
in this  weblog tagged “For Banff 2009” yesterday afternoon—

Remarks related to the ship of Theseus —

Sunday, April 26, 2020

The Triangle of Art

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

This post was suggested by yesterday morning's link to  The Fano Hallows.

"Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to explain
how art fits into our subject and what we mean by beauty."

— Sir Michael Atiyah, quoted here on April 4, 2016

A symbol related to  The Fano Hallows —

Thursday, April 26, 2018

Defining Form

Filed under: General — Tags: , — m759 @ 7:00 pm

Images related to the previous post —

Wednesday, April 25, 2018

A Deathly Triangle

Filed under: General,Geometry — Tags: , , , — m759 @ 11:27 pm

'Imprisoned in a Tesseract,' a study of novelist James Blish

Tuesday, December 27, 2011

Getting with the Program

Filed under: General,Geometry — Tags: , , , , — m759 @ 4:28 am

Stanley Fish in The New York Times  yesterday evening—

IMAGE- Stanley Fish, 'The Old Order Changeth,' Boxing Day, 2011

From the MLA program Fish discussed—

IMAGE- MLA session, 'Defining Form,' chaired by Colleen Rosenfeld of Pomona College

Above: An MLA session, “Defining Form,” led
by Colleen Rosenfeld of Pomona College

An example from Pomona College in 1968—

IMAGE- Triangular models of small affine and projective finite geometries

The same underlying geometries (i.e., “form”) may be modeled with
a square figure and a cubical figure rather than with the triangular
figures of 1968 shown above.

See Finite Geometry of the Square and Cube.

Those who prefer a literary approach to form may enjoy the recent post As Is.
(For some context, see Game of Shadows.)

Thursday, May 5, 2011

On Art and Magic

Filed under: General,Geometry — Tags: , , — m759 @ 10:30 pm

Two Blocks Short of a Design:

A sequel to this morning's post on Douglas Hofstadter

http://www.log24.com/log/pix11A/110505-ThemeAndVariations-Hofstadter.jpg

 

Photo of Hofstadter by Mike McGrath taken May 13, 2006

Related material — See Lyche's  "Theme and Variations" in this journal
and Hofstadter's "Variations on a Theme as the Essence of Imagination"
— Scientific American  October 1982

A quotation from a 1985 book by Hofstadter—

"… we need to entice people with the beauties of clarity, simplicity, precision,
elegance, balance, symmetry, and so on.

Those artistic qualities… are the things that I have tried to explore and even
to celebrate in Metamagical Themas .  (It is not for nothing that the word
'magic' appears inside the title!)"

The artistic qualities Hofstadter lists are best sought in mathematics, not in magic.

An example from Wikipedia —

http://www.log24.com/log/pix11A/110505-BlockDesignTheory.jpg

Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

The Deathly Hallows  symbol—
Two blocks short of  a design.

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