Tuesday, May 27, 2025
Thursday, May 8, 2025
Geometric Theology
From a post of April 17, 2025 —
Some may interpret this as a chessboard, with the white bishops on
their home squares 39 and 36 and the black bishops on 33 and 30.
"I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another."
– Vladimir Nabokov in Speak, Memory
Comments Off on Geometric Theology
Thursday, March 27, 2025
A Tale for Holland, Michigan:
Red Sails in the Sunset
Comments Off on A Tale for Holland, Michigan:
Red Sails in the Sunset
Red Sails in the Sunset
Thursday, August 29, 2024
Fearful Symmetry
Peter Woit this afternoon on "The Terrifying Power of Mathematics" —
"… the quantum field theory of fields satisfying the Dirac equation.
Here there’s a standard apparatus of how to calculate given in
every quantum field theory textbook. These standard calculations
involving Dirac gamma-matrices fit well with Feynman’s 'physicists
finding they have the correct equations without understanding them
have been so terrified they give up trying to understand them'."
For a definition of these matrices, see . . .
Weisstein, Eric W. "Dirac Matrices."
From MathWorld — A Wolfram Web Resource.
https://mathworld.wolfram.com/DiracMatrices.html —
"The Dirac matrices are a class of 4×4 matrices which arise
in quantum electrodynamics. There are a variety of different
symbols used, and Dirac matrices are also known as
gamma matrices or Dirac gamma matrices."
For related religious remarks, see "Physics for Poets"
( Log24, April 20, 2022 ).
Comments Off on Fearful Symmetry
Wednesday, August 21, 2024
“Triangle of Sadness” Conspiracy?
|
Headline from The Independent —
Why we don’t let compassion get in
The Sicilian superyacht disaster proves one thing – Tuesday 20 August 2024 14:12 BST |
Related reading . . . Other posts now tagged "Original Conspiracy."
Comments Off on “Triangle of Sadness” Conspiracy?
Wednesday, August 14, 2024
Midnight Not in Paris
"Before time began . . . ." — Optimus Prime
Comments Off on Midnight Not in Paris
Thursday, April 25, 2024
Time and Chance
As for time … See this journal on the above Sting date.
A professional hallucinator that
some will find more entertaining:
Comments Off on Time and Chance
Wednesday, April 24, 2024
Plan 9 for Helen Vendler
Comments Off on Plan 9 for Helen Vendler
Tuesday, June 13, 2023
Inquisitive Minds Want to Know
"Does the expression 'generative pre-trained transformer'
mean anything to you?"
Comments Off on Inquisitive Minds Want to Know
Sunday, March 5, 2023
Geometry and Death Continued* —
The Case of Richard Brautigan
* Continued from the previous post.
Comments Off on Geometry and Death Continued* —
The Case of Richard Brautigan
The Case of Richard Brautigan
Wednesday, August 17, 2022
Cold Comfort Dam
"And, as with all retold tales that are in people's hearts,
there are only good and bad things and black and white
things and good and evil things and no in-between anywhere."
— John Steinbeck, author's epigraph to The Pearl
From the Season 4 finale of Westworld :
uploading Dolores's pearl at Hoover Dam —
For those who prefer greater theological simplicity . . .
Optimus Prime on a different Hoover Dam figure, that of
the AllSpark: "Before time began, there was the Cube."
Simplifying even more . . .
“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”
– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art , Cornell U. Press, 1975
As above, Black's theology forms a cube.
Comments Off on Cold Comfort Dam
Thursday, July 14, 2022
For Dark Jokester*
Also on April 1, 2015 —
From the essay cited above —
For the formula of building blocks , see Walsh series.
* See Google.
Comments Off on For Dark Jokester*
Wednesday, July 13, 2022
Annals of Comparative Linguistics
Comments Off on Annals of Comparative Linguistics
A New Yorker Child’s Progress
A New Yorker writer on why he wanted to
learn mathematics at an advanced age —
|
"The challenge, of course, especially in light of the collapsing horizon, since I was sixty-five when I started. Also, I wanted especially to study calculus because I never had. I didn’t even know what it was—I quit math after feeling that with Algebra II I had pressed my luck as far as I dared. Moreover, I wanted to study calculus because Amie told me that when she was a girl William Maxwell had asked her what she was studying, and when she said calculus he said, 'I loved calculus.' Maxwell would have been about the age I am now. He would have recently retired after forty years as an editor of fiction at The New Yorker , where he had handled such writers as Vladimir Nabokov, Eudora Welty, John Cheever, John Updike, Shirley Hazzard, and J. D. Salinger. When Salinger finished Catcher in the Rye , he drove to the Maxwells’ country house and read it to them on their porch. I grew up in a house on the same country road that Maxwell and his wife, Emily, lived on, and Maxwell was my father’s closest friend."
— Wilkinson, Alec. A Divine Language (p. 5). Published |
See as well two versions of
a very short story, "Turning Nine."
Wilkinson's title is of course deplorable.
Related material: "Night Hunt" in a
Log24 search for the phrase "Good Question."
Comments Off on A New Yorker Child’s Progress
Tuesday, July 12, 2022
“Tell it Skewb” continues.
Previously on Log24:
"Tell it Skewb." — Motto adapted from Emily Dickinson.
On further investigation . . .
From the above Sanfilippo date —
Comments Off on “Tell it Skewb” continues.
Object Lesson: The Quelling
"The successful artist shares with the politician
a recurrent temptation to indulge in emotional claptrap.
Bernard Bosanquet in Three Lectures on Aesthetic (1915)
proposed that this urge to chase after tears or laughter
could be quelled by attaching the art-emotion to a particular object
and not a set of reactions. His consequent definition of art was
'feeling expressed for expression’s sake.' Notice, however, that
this is something only the deranged would dream of wanting in
real life. Our everyday expressions of feeling are spontaneous and
practical; they are never 'for expression’s sake.' By contrast,
aesthetic feeling is self-sufficient."
— David Bromwich in The Nation, July 11, 2022
A Particular Object —
"Tell it Skewb." — Motto adapted from Emily Dickinson.
Comments Off on Object Lesson: The Quelling
Monday, July 11, 2022
Wednesday, June 29, 2022
Techie Wordplay: “Lynx”
"As of 2022, it is the oldest web browser still being maintained,,,,"
"The speed benefits of text-only browsing are most apparent
when using low bandwidth internet connections, or older computer
hardware that may be slow to render image-heavy content."
— Wikipedia [“Older” link added.]
And then there is . . .
See as well the LYNX of Oslo artist Josefine Lyche.
Update of June 30, 2022 —
Lyche, whose art often incorporates mathematical notions,
has not yet, as far as I know, explored the Borromean link
(three rings, linked mutually but not pairwise) in her art.
Remarks by a different math fan, Evelyn Lamb —
"I have had a thing for the Borromean rings for years now.
There’s something so poetic about them. The three rings
are strong together, but they fall apart if any one of them
is removed. Alternatively, the three rings are trapped together
until one of them leaves and sets the others free. I’m kind of
surprised there isn’t a Wisława Szymborska poem or
Tom Stoppard play that explores the metaphorical possibilities
in the Borromean rings." — Scientific American , Sept. 30, 2016.
See also the Lamb date Sept. 30, 2016, as well as work
by Lyche, in Log24 posts tagged Star Cube.
Related material — The Log24 post Borromean Generators.
Comments Off on Techie Wordplay: “Lynx”
Wednesday, February 23, 2022
The Unity of Mathematics
https://en.wikisource.org/wiki/
A_History_of_Mathematics/
Recent_Times/Theory_of_Functions —
See also Gopel in this journal.
Comments Off on The Unity of Mathematics
Monday, February 21, 2022
Stimulus
"The class is objectively characterized, but not
the individual coordinate assignment."
Tell it to Watchduck, Hermann.
See a related remark by Quack5quack in Raiders of the Lost Coordinates.
Comments Off on Stimulus
Wednesday, February 16, 2022
Tuesday, February 15, 2022
“… Then We Take Berlin” — Leonard Cohen
"Stories are the only way people can absorb information
in any depth" — Stephen Lussier, retired De Beers executive
Related story — De Beer's Consolidated Mine
“Nothing Lasts Forever” will screen at Berlinale
on February 12th at 9 pm at Cubix 7, February 17th
at 9 pm at Cubix 5 and 6, and February 18th at 6 pm
at Cubix 5 and 6. — https://moveablefest.com
See as well "Story Theory of Truth" in this journal.
Comments Off on “… Then We Take Berlin” — Leonard Cohen
Monday, February 14, 2022
Artbusters: Cubism
" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."
"Before time began, there was the Cube." — Optimus Prime
|
Comments Off on Artbusters: Cubism
Saturday, February 12, 2022
Das Geheimnis der Einheit
Thomas Mann on "the mystery of the unity" —
"Denn um zu wiederholen, was ich anfangs sagte:
in dem Geheimnis der Einheit von Ich und Welt,
Sein und Geschehen, in der Durchschauung des
scheinbar Objectiven und Akzidentellen als
Veranstaltung der Seele glaube ich den innersten Kern
der analytischen Lehre zu erkennen." (GW IX 488)
An Einheit-Geheimnis that is perhaps* more closely related
to pure mathematics** —
"What is the nature of the original unity
that throws itself apart in this separation,
and in what sense are the separated ones
here as the essence of the abyss?
Here it cannot be a question of any kind of 'dialectic,'
but only of the essence of the ground
(that is, of truth) itself." [Tr. by Google]
" Welcher Art ist die ursprüngliche Einheit,
daß sie sich in diese Scheidung auseinanderwirft,
und in welchem Sinn sind die Geschiedenen
hier als Wesung der Ab-gründigkeit gerade einig?
Hier kann es sich nicht um irgend eine »Dialektik«
handeln, sondern nur um die Wesung des Grundes
(der Wahrheit also) selbst."
* Or perhaps not .
** For a relevant Scheidung , see Eightfold Cube.
Comments Off on Das Geheimnis der Einheit
Friday, February 11, 2022
De Beer’s Consolidated Mine
The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel
Many Dimensions published in 1993 by Wm. B. Eerdmans.
But seriously . . .
Comments Off on De Beer’s Consolidated Mine
Thursday, February 10, 2022
Block Design Subtest:
Psycoloquy Meets Psycho Loki
Related illustration from a search in this journal for Wechsler —
|
|
Above: Dr. Harrison Pope, Harvard professor of psychiatry,
demonstrates the use of the Wechsler Adult Intelligence Scale (WAIS)
“block design” subtest.
— From a Log24 search for “Harrison Pope.”
Comments Off on Block Design Subtest:
Psycoloquy Meets Psycho Loki
Psycoloquy Meets Psycho Loki
Saturday, February 5, 2022
Mathieu Cube Labeling
Shown below is an illustration from "The Puzzle Layout Problem" —
- September 2003
-
Lecture Notes in Computer Science 2912:500-501
DOI:10.1007/978-3-540-24595-7_50 - Source: DBLP
-
Conference: Graph Drawing, 11th International Symposium,
GD 2003, Perugia, Italy, September 21-24, 2003, Revised Papers - Authors: Kozo Sugiyama, Seok-Hee Hong, Atsuhiko Maeda
Exercise: Using the above numerals 1 through 24
(with 23 as 0 and 24 as ∞) to represent the points
∞, 0, 1, 2, 3 … 22 of the projective line over GF(23),
reposition the labels 1 through 24 in the above illustration
so that they appropriately* illustrate the cube-parts discussed
by Iain Aitchison in his March 2018 Hiroshima slides on
cube-part permutations by the Mathieu group M24.
A note for Northrop Frye —
Interpenetration in the eightfold cube — the three midplanes —
A deeper example of interpenetration:
Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.
* "Appropriately" — I.e. , so that the Aitchison cube octads correspond
exactly, via the projective-point labels, to the Curtis MOG octads.
Comments Off on Mathieu Cube Labeling
Saturday, March 13, 2021
Eternal Spark
According to Lt. Col. Wayne M. McDonnell in June 1983 —
“… it is accurate to observe that when a person experiences
the out-of- body state he is, in fact, projecting that eternal spark
of consciousness and memory which constitutes the ultimate
source of his identity….”
— Section 27, “Consciousness in Perspective,” of
“Analysis and Assessment of Gateway Process.”
A related quotation —
“In truth, the physical AllSpark is but a shell….”
— https://tfwiki.net/wiki/AllSpark
From the post Ghost in the Shell (Feb. 26, 2019) —
See also, from posts tagged Ogdoad Space —
“Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye’s formal interest lay in
the ‘schematosis’ and fearful symmetries of his own presentations.”
— From p. 61 of James C. Nohrnberg’s “The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye,”
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterly, January 2001)
— as well as . . .
Related illustration from posts tagged with
the quilt term Yankee Puzzle —
Comments Off on Eternal Spark
Wednesday, August 26, 2020
Wednesday, July 22, 2020
Card
“The pattern of the thing precedes the thing.
I fill in the gaps of the crossword at any spot
I happen to choose. These bits I write on
index cards until the novel is done.”
— Vladimir Nabokov, interview,
Paris Review No. 41 (Summer-Fall 1967).
Another story —
Related material: Mathematics as a Black Art.
Comments Off on Card