Tuesday, August 31, 2021

Summer Knowledge

Filed under: General — Tags: — m759 @ 11:00 PM

The title is that of a book of poems by Delmore Schwartz.

From "Searching for God in the Next Apartment,"
by Stanley Moss, New York Times Book Review ,
Sunday, October 19, 1986 —

Throughout Schwartz's poetry a question of belief is central. He thought we could not live without an interpretation of the whole of life, and that modern social orders were inevitably deficient in satisfying this need. He wrote studies and poetry explicitly concerned with the decline of Christian belief and the impossibility of any belief whatsoever. He read Rimbaud's ''Season in Hell,'' Valery's ''Cimetiere Marin,'' Arnold's ''Dover Beach,'' Hardy's ''Oxen,'' Stevens' ''Sunday Morning'' as poems forged in just such a dilemma. His own preferred poem, ''Starlight Like Intuition Pierced the Twelve,'' continued this argument.

See also Log24 posts tagged Central Myth, and the following image:

Matrix Reloaded

Filed under: General — Tags: — m759 @ 6:01 PM

In today's online New York Times , Kathryn Harrison reviews a new novel:

By Lauren Groff

From the online New York Times Book Review  on May 24, 2018 —

From this  journal on May 24, 2018 —

Further remarks by Lauren Groff on May 24, 2018 —

"Something invisible and pernicious seems to be preventing
even good literary men from either reaching for books with
women’s names on the spines, or from summoning women’s
books to mind when asked to list their influences. I wonder
what such a thing could possibly be."

Quentin Tarantino?


"It seems no coincidence that all of these titles
are written by women, for a primary angle of 
Gunpowder Milkshake  is one that tries its best
to promote 'feminism' in a Quentin Tarantino
sort of way." 

Or Lévi-Strauss?

See Log24 posts on The Matrix of Lévi-Strauss

Annals of Geometry

Filed under: General — Tags: , — m759 @ 2:21 PM

A passage by Max Jammer quoted in yesterday's post
A Brief Introduction to Ideas suggests further remarks:

There are geometries in which lengths are not invariant 
because they are not  relevant — for instance, projective 
geometry,  finite  geometry, and of course finite projective 

See the annus mirabilis  introduction to that subject 
cited by Jammer in yesterday's Brief Introduction —

Monday, August 30, 2021

In Search of Beauty Bare

Filed under: General — Tags: — m759 @ 4:11 PM

Wikipedia illustrates Euclid —

Many will prefer a different rendition of the above color scheme:


A Brief Introduction to Ideas

Filed under: General — Tags: , — m759 @ 1:06 PM

"The Greek hodos , path . . . ."  — Max Jammer, 1954

Down, or: A Black Box for Didion

Filed under: General — Tags: , — m759 @ 12:28 PM

From "Why I Write," by Joan Didion —

"I am not a scholar. I am not in the least an intellectual, which is not to say that when I hear the word 'intellectual' I reach for my gun, but only to say that I do not think in abstracts. During the years when I was an undergraduate at Berkeley I tried, with a kind of hopeless late-adolescent energy, to buy some temporary visa into the world of ideas, to forge for myself a mind that could deal with the abstract.

All I knew then was what I wasn’t, and it took me some years to discover what I was.

In short I tried to think. I failed. My attention veered inexorably back to the specific, to the tangible, to what was generally considered, by everyone I knew then and for that matter have known since, the peripheral. I would try to contemplate the Hegelian dialectic and would find myself concentrating instead on a flowering pear tree outside my window and the particular way the petals fell on my floor. I would try to read linguistic theory and would find myself wondering instead if the lights were on in the Bevatron up the hill. When I say that I was wondering if the lights were on in the Bevatron you might immediately suspect, if you deal in ideas at all, that I was registering the Bevatron as a political symbol, thinking in shorthand about the military-industrial complex and its role in the university community, but you would be wrong. I was only wondering if the lights were on in the Bevatron, and how they looked. A physical fact.

I had trouble graduating from Berkeley, not because of this inability to deal with ideas—I was majoring in English, and I could locate the house-and-garden imagery in The Portrait of a Lady  as well as the next person, 'imagery' being by definition the kind of specific that got my attention—but simply because I had neglected to take a course in Milton. For reasons which now sound baroque I needed a degree by the end of that summer, and the English department finally agreed, if I would come down from Sacramento every Friday and talk about the cosmology of Paradise Lost , to certify me proficient in Milton. I did this. Some Fridays I took the Greyhound bus, other Fridays I caught the Southern Pacific’s City of San Francisco on the last leg of its transcontinental trip. I can no longer tell you whether Milton put the sun or the earth at the center of his universe in Paradise Lost , the central question of at least one century and a topic about which I wrote ten thousand words that summer, but I can still recall the exact rancidity of the butter in the City of San Francisco’s dining car, and the way the tinted windows on the Greyhound bus cast the oil refineries around Carquinez Strait into a grayed and obscurely sinister light. In short my attention was always on the periphery, on what I could see and taste and touch, on the butter, and the Greyhound bus. During those years I was traveling on what I knew to be a very shaky passport, forged papers: I knew that I was no legitimate resident in any world of ideas. I knew I couldn’t think. All I knew then was what I couldn’t do. All I knew then was what I wasn’t, and it took me some years to discover what I was."

"I knew that I was no legitimate resident in any world of ideas."
— Joan Didion, December 5, 1976

"In the 1988 interview with Scripps Howard, Mr. Poynter mused
about the device he wanted to invent for his own tombstone.

'When you walked up to it,' he said, 'you’d activate
an electronic voice. And it would say, "Come on down."’”

New York Times  obituary yesterday

And add, "We all float down here"?

For other, better, remarks about ideas by Didion
see "Freeze the shifting phantasmagoria," a phrase
from her 1979 book The White Album.

Sunday, August 29, 2021


Filed under: General — Tags: — m759 @ 10:52 PM

"As within, so without" — Mystic phrase from the previous post.

Ed Asner in Studio 60 S1E11, Dec. 4, 2006

Memento Mori : 1:47

Filed under: General — Tags: — m759 @ 2:35 PM

The above is from a New York Times  1:47 report of an August 13 death.

From this  journal on August 13Euclid's  1.47 —

“Before Time Began . . .” — Optimus Prime

Filed under: General — Tags: — m759 @ 1:01 PM

Concepts of Space — 

(From the March 2019 post Back to the Annus Mirabilis , 1905 )


Concepts of Space and  Time — 

Saturday, August 28, 2021

Solomon’s Super*  Cube…

Filed under: General — Tags: — m759 @ 1:33 PM

Geometry for Jews  continues.

210828-Golomb-2x2x2-Super_Cube.jpg (500×373)

The conclusion of Solomon Golomb's
"Rubik's Cube and Quarks,"
American Scientist , May-June 1982 —

Related geometric meditation —
Archimedes at Hiroshima
in posts tagged Aitchison.


* As opposed to Solomon's Cube .

Crimson Peak: Only the Dead

Filed under: General — m759 @ 12:25 PM

A title adaptation for Drunkspeare:

"Only the Dead Know Brooklyn Square."

For St. Augustine’s Day

Filed under: General — m759 @ 11:43 AM

From a Harvardwood page footer —

. . . Should we choose to accept it . . .

Scenes from… The Seventh Sausage

Filed under: General — Tags: — m759 @ 10:37 AM

A cinematic meditation for Harvardwood.

"Another opening, another show."

Friday, August 27, 2021

Special for the National Comedy Center

Filed under: General — Tags: — m759 @ 12:57 PM

Newlove grew up in Jamestown, NY, a city which
appeared in his fiction. He reportedly died on Aug. 17.
Synchronology check: "Little Museum of Horrors."

From Mike’s Marbleopolis: Repeating the Hook

Filed under: General — m759 @ 9:42 AM


"The hook is repeated seven times in 'Borderline.' "

 — An April 1999 article on music theory.

The authors of the above article have perhaps more respect for
marble columns than do Scarlett, Madonna, and the current
pandering leadership of the American Mathematical Society.

Thursday, August 26, 2021

The Usual Suspects

Filed under: General — m759 @ 11:58 AM


A prequel: The Coffee Detective 

Related images —

A logo for Stephen King . . .

… and an earlier version of that logo
    for Quentin Tarantino —

Another Opening, Another Show

Filed under: General — Tags: — m759 @ 10:24 AM


Filed under: General — Tags: — m759 @ 9:58 AM

 Related remarks for mattress dancers
This  journal on the above Instagram date.

Introibo for Buck Mulligan

Filed under: General — Tags: , — m759 @ 8:23 AM

. . . And then there is . . .

For fans of "Inherent Vice" —


Wednesday, August 25, 2021

Einstein Revelado

Filed under: General — Tags: , , — m759 @ 1:36 PM

For those too young to remember the 20th century . . .

Related illustrations —

Space Symbol

Filed under: General — Tags: , — m759 @ 12:28 PM

I prefer Kirsch's "Space Babel" (Tablet , Dec. 4, 2020).

An image we may regard as illustrating 
the group-identity symbol "e" for "Einheit"

Some context:

Tuesday, August 24, 2021

Stones’ Bedrock

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


Filed under: General — Tags: , — m759 @ 10:13 AM

Monday, August 23, 2021

Turning a Corner on the Street of Dreams

Filed under: General — Tags: , — m759 @ 1:26 PM

The previous post  suggests a review . . .

Sharpening the Corners of the World

Filed under: General — Tags: — m759 @ 11:15 AM

"This is the purpose of being alive, to find someone
who sharpens the corners of the world for you and
allows you to peer into the souls of your fellow man!"

[“Corners” link added.]

Rosa Lyster two hours ago at

For  instance —

Back to the Future

Filed under: General — Tags: — m759 @ 3:36 AM

A recent view of the approximate former location of Morrell's Bar
in Warren, Pa. (See the previous post, Sunday morning's Bar Exam) —

See too remarks on a fictional  Tim Horton here and in a 2012
film review from a publication at the University of Cambridge

"Although the use of their work for good versus evil
was the concern for three of the main protagonists,
for one character – Dr Tim Horton – the bigger question
was one of academic and intellectual morality."

See as well this  journal on the above article's date — November 20, 2012.

Sunday, August 22, 2021

Bar Exam

Filed under: General — Tags: — m759 @ 10:16 AM

"Looking for what was, where it used to be"
— Wallace Stevens

A search for Morrell's Bar, Warren, Pa., yields a newspaper page
from January 21, 1954.  Some law-related stories appear on
the same page.

"So we beat on, boats against the current . . . ."
— F. Scott Fitzgerald

A Link for Don Everly …

Filed under: General — m759 @ 9:29 AM

… that was posted here in 2014 in memory of his brother —

http://www.log24.com/log/pix14/140104-For_Phil_Everly.jpg .

Saturday, August 21, 2021

Depth and Insight

Filed under: General — m759 @ 11:35 AM

A Calendar for Witch Wannabes

Filed under: General — Tags: — m759 @ 11:09 AM

A visual framework to adapt for the above calendar —

Elemental square by John Opsopaus from 'The Rotation of the Elements'

A related geometric illustration 
from a New Yorker  article

"Here's a quarter, call someone who cares."
— Country song lyric


Filed under: General — m759 @ 10:05 AM

A Bon Jovi "Stripped" video released May 1, 2007 —

Synchronology check —

This  journal in the early morning of the above release date —


to put one's back
into something
bei etwas
Einsatz zeigen
to up the ante den Einsatz erhöhen
to debrief den Einsatz
nachher besprechen
to be on duty im Einsatz sein
mil. to be in action im Einsatz sein
to play for
high stakes
mit hohem
Einsatz spielen

"Nine is a very
powerful Nordic number
— Katherine Neville,
The Magic Circle

Happy Walpurgisnacht.

Friday, August 20, 2021

Space Note

Filed under: General — Tags: — m759 @ 7:50 PM

"Consider the six-dimensional vector space ( 𝔽2 )6
over the two-element field 𝔽2 ."

— Page 23 of "The Universal Kummer Threefold,"
arXiv:1208.1229v3, 12 June 2013, by Qingchun Ren,
Steven V. Sam, Gus Schrader, and Bernd Sturmfels.

An illustration of that space from 1981 —

IMAGE- 'Solid Symmetry' by Steven H. Cullinane, Dec. 24, 1981

The above recollection of the Kummer Threefold  remark was suggested by
recent posts now tagged Smallfield . . .

"Third Man – an elderly American railway bum,
a schizophrenic, speaks with a Southern drawl"

"Art to which I fix my celebrated signature."

— "Third Man" in Victor Snaith's play "Changing Stations"

If we read the above "art" as  a scythe blade to which the "signature" —
Snaith ("the crooked handle or shaft of a scythe") — is attached,
an image of the late art critic Robert Hughes comes to mind:

That image of Hughes appeared here in a post of June 17, 2015 —
"Slow Art, Continued" — that also referenced the Kummer Threefold
paper above.

Diamond Brackets*

Filed under: General — Tags: — m759 @ 9:57 AM

For more on the phrase "diamond brackets," see the post
Artistic Style of July 24, 2018.

This was the dies natalis  (in the Catholic sense) of philosophy
professor Garth L. Kemerling.

From Kemerling's internet "Philosophy Pages" —

"First, it must be possible in principle to arrange and organize
the chaos of our many individual sensory images by tracing
the connections that hold among them. This Kant called
the synthetic unity of the sensory manifold.

Second, it must be possible in principle for a single subject
to perform this organization by discovering the connections
among perceived images. This is satisfied by what Kant called
the transcendental unity of apperception."

Related Log24 phrases —

"Intake Manifold" and "Bulk Apperception."

* See also Bracketing (phenomenology) in Wikipedia.

Symbols and Mysteries

Filed under: General — Tags: , — m759 @ 8:40 AM

Japanese Steel

Filed under: General — Tags: — m759 @ 12:00 AM

“Character and action, you brought together” —
Keanu Reeves to the late Sonny Chiba.

Thursday, August 19, 2021

A Scalpel for Einstein

Filed under: General — Tags: — m759 @ 2:08 PM

(A sequel to this morning's post A Subtle Knife for Sean.)

Exhibit A —

Einstein in The Saturday Review, 1949

"In any case it was quite sufficient for me 
if I could peg proofs upon propositions
the validity of which did not seem to me to be dubious.
For example, I remember that an uncle told me
the Pythagorean theorem before the holy geometry booklet
had come into my hands. After much effort I succeeded
in 'proving' this theorem on the basis of the similarity
of triangles
in doing so it seemed to me 'evident' that
the relations of the sides of the right-angled triangles
would have to be completely determined by one of the
acute angles. Only something which did not in similar fashion
seem to be 'evident' appeared to me to be in need of any proof
at all. Also, the objects with which geometry deals seemed to
be of no different type than the objects of sensory perception,
'which can be seen and touched.' This primitive idea, which
probably also lies at the bottom of the well-known Kantian
problematic concerning the possibility of 'synthetic judgments
a priori' rests obviously upon the fact that the relation of
geometrical concepts to objects of direct experience
(rigid rod, finite interval, etc.) was unconsciously present."

Exhibit B —

Strogatz in The New Yorker, 2015

"Einstein, unfortunately, left no … record of his childhood proof.
In his Saturday Review essay, he described it in general terms,
mentioning only that it relied on 'the similarity of triangles.' 
The consensus among Einstein’s biographers is that he probably
discovered, on his own, a standard textbook proof in which similar
triangles (meaning triangles that are like photographic reductions
or enlargements of one another) do indeed play a starring role.
Walter Isaacson, Jeremy Bernstein, and Banesh Hoffman all come
to this deflating conclusion, and each of them describes the steps
that Einstein would have followed as he unwittingly reinvented
a well-known proof."

Exhibit C —

Schroeder in a book, 1991

Schroeder presents an elegant and memorable proof. He attributes
the proof to Einstein, citing purely hearsay evidence in a footnote.

The only other evidence for Einstein's connection with the proof
is his 1949 Saturday Review  remarks.  If Einstein did  come up with
the proof at age 11 and discuss it with others later, as Schroeder
claims, it seems he might have felt a certain pride and been more
specific in 1949, instead of merely mentioning the theorem in passing
before he discussed Kantian philosophy relating concepts to objects.

Strogatz says that . . .

"What we’re seeing here is a quintessential use of
a symmetry argument… scaling….

Throughout his career, Einstein would continue to
deploy symmetry arguments like a scalpel, getting to
the hidden heart of things." 

Connoisseurs of bullshit may prefer a faux-Chinese approach to
"the hidden heart of things." See Log24 on August 16, 2021 —

http://m759.net/wordpress/?p=96023 —
In a Nutshell: The Core of Everything .


Filed under: General — m759 @ 12:31 PM

"The subject of -theory takes its name from a 1957 construction of 
Alexander Grothendieck which appeared in the 
Grothendieck–Riemann–Roch theorem, his generalization of
Hirzebruch's theorem.[2] Let X  be a smooth algebraic variety.
To each vector bundle on , Grothendieck associates an invariant, its class .
The set of all classes on X  was called K(X from the German Klasse ."

— Wikipedia, Algebraic -theory

In memory of a mathematician who reportedly died on July 3rd, 2021 —

For a somewhat simpler K , see Aesthetic Distance.

A Subtle Knife for Sean

Filed under: General — Tags: — m759 @ 11:34 AM

From yesterday morning's post "What's in a Name?" —

"Third Man – an elderly American railway bum,
a schizophrenic, speaks with a Southern drawl"

"Art to which I fix my celebrated signature."

— "Third Man" in Victor Snaith's play "Changing Stations"

In the above Facebook post, a dead person speaks —

"You and I are separated by a thin piece of silk
which neither the strongest man could tear,
nor the sharpest tool could pierce.
Nothing can cross this membrane that divides us
except art, music, poetry and love."

Try a subtle knife, Sean.

Related material —

Wednesday, August 18, 2021

Art’s Bedfellows

Filed under: General — m759 @ 11:43 AM

What’s in a Name?

Filed under: General — Tags: — m759 @ 10:38 AM

"Third Man – an elderly American railway bum,
a schizophrenic, speaks with a Southern drawl"

"Art to which I fix my celebrated signature."

— "Third Man" in Victor Snaith's play "Changing Stations"

"Snaithing  may thus be Smallfield . . . ."

Eight the Great

Filed under: General — m759 @ 9:03 AM

Starring J. J. Abrams as Leonhard Euler?

Related material —

The Cornell cap in the recent HBO "White Lotus" —

  "I'm just playing the hand I was dealt."

Tuesday, August 17, 2021

Class Dance

Filed under: General — m759 @ 11:05 PM

From Under the Volcano , Chapter II—

Hotel Bella Vista
Gran Baile Noviembre 1938
a Beneficio de la Cruz Roja.
Los Mejores Artistas del radio en accion.
No falte Vd.

In Search of . . . E!

Filed under: General — m759 @ 9:23 PM

From the above  Essays on the Plays  

"In the first short play of 365 Days  . . . ."

Some will prefer film  with the same title —

A Question for Solomon

Filed under: General — m759 @ 1:20 PM

The previous post, Mythical Figure, suggests a review of posts
tagged Solomon Marcus.

See as well . . .

Mythical Figure

Filed under: General — Tags: — m759 @ 12:55 PM

A phrase from the previous post : "modern society's mythical figures."

A mythical figure from Claude Lévi-Strauss

The above image is from a study of Lévi-Strauss's "Canonical Formula" …

Little Museum of Horrors

Filed under: General — m759 @ 11:58 AM

Synchronology check — See LA Scenes tag.

Science and Science Entertainment

Filed under: General — m759 @ 11:38 AM

Google News today — Science:

Google News today — Entertainment:

Science Entertainment

See "Dark Matter" in this  journal.

Escape from the Grid

Filed under: General — Tags: — m759 @ 5:57 AM

Related material:  Dance of the Numbers  (Log24, Dec. 15, 2005).

Monday, August 16, 2021

At McDonald’s

Filed under: General — m759 @ 12:30 PM

Click for a webpage on McDonald.

See also . . .



In a Nutshell: The Core of Everything

Filed under: General — m759 @ 11:32 AM

“The great Confucius guided China spiritually for over 2,000 years.
The main doctrine is ' 仁 ' pronounced 'ren', meaning two people,
i.e., human relationship. Modern science has been highly competitive.
I think an injection of the human element will make our subject more
healthy and enjoyable." 

Geometer Shiing-Shen Chern in a Wikipedia article

See the "ren" character in Wiktionary.  See as well . . .

"The development of ren  ( 仁 )  in early Chinese philosophy,"
By Robin Elliott Curtis, U. of B.C. Master's thesis, 2016

Thus, we can conclude that several different forms of
the character ren , were in existence during the
Warring States period. This shows that etymological analyses
focusing exclusively on the combination of 人 and 二 are inadequate.
It should also serve as a warning against “
character fetishization,”
or giving “exaggerated status to Chinese characters in the interpretation
of Chinese language, thought, and culture.” 46

46  Edward McDonald 2009, p. 1194.

McDonald, Edward. 2009. “Getting over the Walls of
Discourse: 'Character Fetishization' in Chinese Studies.”
The Journal of Asian Studies  68 (4): 1189 – 1213.

Wikipedia article on Ren  in Confucianism:

人 + 二  =  仁  (Rén)
man on left two on right,
the relationship between two human beings,
means co-humanity. Originally the character
was just written as丨二  [citation needed] 
representing yin yang,
the vertical line is yang
(bright, traditionally masculine, heaven, odd numbers),
the two horizontal lines are yin
(dark, traditionally feminine, earth, even numbers),
仁 is the core of everything. 

"The core of everything" . . . Citation needed ?

The Space of Possibilities

Filed under: General — Tags: , — m759 @ 3:57 AM

The title is from "Federico Ardila on Math, Music and
the Space of Possibilities
," a podcast from Steven Strogatz's
Quanta Magazine  series. The transcript is dated March 29, 2021.

Ardila: … in a nutshell, what combinatorics is about is just
the study of possibilities and how do you organize them,
given that there’s too many of them to list them.

Strogatz:  So, I love it. Combinatorics is not just
the art of the possible, but the enumeration of the possible,
the counting of the possible and the organizing of the possible.

Strogatz:  It’s such a poetic image, actually: the space of possibilities.

This  journal on the podcast date, March 29, 2021 —

A more precise approach to the space of possibilities:

Sunday, August 15, 2021

Simple Similarity

Filed under: General — Tags: , — m759 @ 1:05 PM

The following image (click to enlarge) is now the target of
a link on the phrase "similarly divided" in Friday's post
"The Divided Square."

Related material —

A version of the above Schroeder pages, dumbed down for
readers of The New Yorker

Note  that the proof under discussion has nothing to do with 
the New Yorker 's rubric "Annals of Technology."

Note also the statement by Strogatz that 

"Einstein’s proof reveals why the Pythagorean theorem
applies only to right triangles: they’re the only kind
made up of smaller copies of themselves." 

Exercise:  Discuss the truth or falsity of the Strogatz statement
after reviewing the webpage Triangles Are Square.

For approaches to geometry that are more advanced, see
this  journal on the above New Yorker  date — Nov. 19, 2015 —

Highlights of the Dirac-Mathieu Connection.


Saturday, August 14, 2021

North of Big Snake

Filed under: General — m759 @ 11:18 AM

The title refers to a Log24 post of Feb. 8, 2021.

Detail from an image in that post:

 By groping toward the light we are made to realize
 how deep the darkness is around us." — Arthur Koestler

Related Hollywood remark:

"You've blown communication
…as we've known it… right out of
the water. You know that, don't you?"

— Cliff Robertson in Brainstorm  (1983)

Ave Atque Vale

Filed under: General — Tags: — m759 @ 2:42 AM


A letter in The Mathematical Intelligencer , January 1988  




A farewell lecture at Yale, April 2013

Kagan's obituary in the online New York Times  tonight
says that he died at 89 on August 6, 2021.

The above farewell lecture of Kagan was on Thursday, April 25, 2013
From this  journal on Kagan's "born yesterday" date — April 24, 2013

"By groping toward the light we are made to realize
 how deep the darkness is around us."

— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118

Friday, August 13, 2021

The Divided Square

Filed under: General — Tags: , — m759 @ 12:19 AM

Compare and contrast —

Update of 2:25 PM ET on Friday, August 13th, 2021 —

Plato's alleged motto, "Let no one ignorant of geometry enter,"
seems to have been of little use to those attempting to make sense
of his "divided line" analogy in the Republic.

Some related geometry —

    The Divided Square :

Three Similarly Divided Squares :

The image “http://www.log24.com/log/pix06A/Pythagorean_Theorem.jpg” cannot be displayed, because it contains errors.

Scholium —

Thursday, August 12, 2021

Unsocratic Method

Filed under: General — Tags: , — m759 @ 11:42 AM

"One, two, three . . . but where is the fourth?" — Socrates

Update of 4:40 AM ET the next morning —

    For students of metaphor —

"four major pillars
   of the reality-based community" —

Update at 6:32 AM ET Friday the 13th — Cross-examination

A Square Crystal Paperweight

Filed under: General — Tags: — m759 @ 9:21 AM

Friday March 31, 2006

Filed under: GeneralGeometry —
Tags:  —
m759 @ 12:00 PM 

Women's History Month continues…
Ontology Alignment

"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally.  To understand who Michael Laski is you must have a feeling for that kind of compulsion."

— Joan Didion in the Saturday Evening Post,
Nov. 18, 1967 (reprinted in Slouching Towards Bethlehem)

"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.

— Joan Didion in The Last Thing He Wanted, Knopf, 1996

"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….

Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real."

— Rebecca Goldstein, 
Mathematics and the Character of Tragedy

Wednesday, August 11, 2021

Expanding the Ulysses  Spielraum

Filed under: General — Tags: — m759 @ 12:07 PM

For Stephen King and the Club Dumas

Related perceptive remarks by Juliane Ungänz —

Zweig was the author of Schachnovelle .

Synchronology Check

Filed under: General — Tags: — m759 @ 10:53 AM

From the previous post . . .

"This review was filed from the 2020 Sundance Film Festival
on January 30th."

Meanwhile . . .

Click the above image for posts on "Expanding the Spielraum."

See as well . . .

Pause and Rewind

Filed under: General — Tags: — m759 @ 2:14 AM

A well in the opening scenes of the 2020 film version of Joan Didion's
1996 novel The Last Thing He Wanted


From a link in the previous post

Sorvino in “The Last Templar
at the Church of the Lost Well:

Mira Sorvino at the Church of the Lost Well in 'The Last Templar'

Consider the source.


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

An online New York Times  obituary today
of a scholar who reportedly died on August 1 —

"In a career that took him to Hong Kong and Taiwan,
as well as a succession of Ivy League universities,
Professor Yu often returned to the theme that China’s
long traditions could be a wellspring, not an enemy,
of enlightenment, individual dignity and democracy."

— Chris Buckley

Cf.  Hexagram 48 in this  journal and some synonyms:

Tuesday, August 10, 2021


Filed under: General — m759 @ 11:28 AM

The structure in the previous post (three trios), though historically significant,
offers less opportunity for contrapuntal variation than . . .

Related remarks for Pleasantly Discursive Day

Ex Fano Apollinis

Filed under: General — Tags: — m759 @ 9:41 AM

Margaret Atwood on Lewis Hyde's 
Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

"As a Chinese jar . . . ."
     — Four Quartets


Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
  the field of Reason…."
– John Outram, architect    

The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.




The Lo Shu as a Finite Space


IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Monday, August 9, 2021

Harvard Elegy

Filed under: General — Tags: — m759 @ 10:41 AM

Bryan Marquard in The Boston Globe  yesterday 
on a professor who died on 7 July, 2021 —

" A Harvard Medical School professor emeritus in psychiatry,
Dr. Hobson told the Globe in 2011 that he didn’t 'feel bad about
taking on Sigmund Freud. I think Sigmund Freud has become
politically correct. Psychoanalysis has become the bible, and
I think that’s crazy.'

He also forcefully set aside the theories of Carl Jung, the Swiss
psychiatrist who analyzed dreams and saw them as important
messages sent from the psyche.

'If you’re a pure scientist, Jung is just deadly,' Dr. Hobson said
in [a] 2005 interview. 'The collective unconscious, the anima
these are literary constructs. You can’t do any science on that
kind of stuff.' ”

See as well this  journal on 7 July 2021 —

Art Criticism for the Chateau Marmont

Filed under: General — m759 @ 10:00 AM

"Nice work if you can get it." — Classic song lyric

Photo credit: Peter Lindbergh

See also . . . Sunset Boulevard Revisited  and . . .

“Do not block intersection.” — City of Los Angeles

The Tune  (Suggested by “Hum: Seek the Void”)

Filed under: General — Tags: , , , , — m759 @ 1:43 AM

"Two years ago . . . ." — Synopsis of the August 3 film "Hum"

Two years ago on August 3 . . .

The Eightfold Cube

What is going on in this picture?

The above is an image from
the August 3, 2019,
post "Butterfield's Eight."

"Within the week . . . ."
— The above synopsis of "Hum"

This suggests a review of a post
from August 5, 2019, that might
be retitled . . .

"The void she knows,
  the tune she hums."

Sunday, August 8, 2021

Requiem for a Showman

Filed under: General — m759 @ 8:15 AM

"Bowden applied what he viewed as the lessons of the battlefield
to the football field. While bedridden with rheumatic fever at age 13,
he had listened to radio broadcasts telling of World War II battles,
and he later studied the campaigns of Patton, MacArthur and
Germany’s Erwin Rommel.

'They all demonstrate discipline,' Bowden once said, 'and that you
need reserves so that if you’re getting annihilated on one front, you
can attack somewhere else.' ” — Richard Goldstein


See as well "Geometry Battlefield" in this morning's previous post.


Filed under: General — m759 @ 7:48 AM

Remarks by Roberta Smith in the print version of The New York Times
on Friday, August 6, suggest a review . . .

Smith's remarks concerned a show that first opened in 2019
at the Los Angeles Museum of Contemporary Art (MOCA).

A MOCA-related post in this  journal —

The Nachtmantel  above is a painting by Jörg Immendorff,
who reportedly died at 61 in 2007 —

A 'painter with provocative themes'

A less provocative theme from Log24 on the date of Immendorff's death:

The image “http://www.log24.com/log/pix07/070528-Quadric.jpg” cannot be displayed, because it contains errors.

"The form, the pattern" — T. S. Eliot

Saturday, August 7, 2021

Art Angles

Filed under: General — Tags: , — m759 @ 9:53 AM

And then there is Bardo  College . . .

"Katz approaches her subject from every angle,

its relationship to feminism, multiculturalism and
the counterculture, as well as its (now questionable)
cultural appropriation and even its underlying debt
to Minimalism (the use of repetition and the grid)."

This is from a Roberta Smith piece yesterday morning
in The New York Times  print version:

"A version of this article appears in print on Aug. 6, 2021,
Section C, Page 6 of the New York edition with the headline: 
Celebrating a Riotous Decor That Keeps Eyes Moving."

Well, perhaps not every  angle.

Friday, August 6, 2021

Strong Curtain

Filed under: General — m759 @ 10:20 PM

"Drop me a line."

Thursday, August 5, 2021

Music for Bobos

Filed under: General — Tags: , — m759 @ 9:49 PM

A play by George Bernard Shaw is the source of the book title at 
the end of the previous post  — "Music is the brandy of the damned ." 
This suggests a corresponding song  title . . .

From the album "The Time of the Assassins."
The above image is not of the singer's own  background.

The Dumbing-Down

Filed under: General — Tags: , — m759 @ 10:45 AM

"How old is  the 'Big Spider Beck' joke?"

From "Blackboard Jungle" (1955) —


– You see, music is based on mathematics,
and it's just that the next class … 
s a little more advanced.


– We're advanced, teach. 
– Two times two is four.
– Are  four. 

See also Damnation Morning  in this journal and . . .

Wednesday, August 4, 2021

The Pink Lotus

Filed under: General — m759 @ 11:59 PM

The Jewel in Venn's Lotus (photo by Gerry Gantt)

The Mondegreen Correction:  “That’s on the green, my dear.”

Filed under: General — Tags: , — m759 @ 11:22 PM

In memory of  a former St. Bonaventure student

A sequel to . . . 

The Cross of Lady Mondegreen

Filed under: General — Tags: — m759 @ 2:35 PM

“They’re gonna put me in the movies…” — Johnny Russell

Filed under: General — Tags: — m759 @ 1:49 PM

Bobos in Paradise  Reconsidered

Filed under: General — Tags: , — m759 @ 1:04 PM

"You're gonna need an ocean/
  of calamine lotion" — "Poison Ivy"

In Memory of Louise Fishman*

Filed under: General — m759 @ 12:22 PM

"One, two, three . . . but where is the fourth?"


Click for Daimon Theory  posts.

* Fishman, an abstract expressionist painter,
reportedly died in Manhattan at 82 on July 26.

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

Filed under: General — Tags: — m759 @ 2:38 AM

My own lucubrations from April 12, 2012 include . . .

From the target of the above link —

Image of MOMA Chess Set cover.

"Here's to efficient packing.

Tuesday, August 3, 2021


Filed under: General — m759 @ 4:47 PM

See also July 27 in this  journal.

Other religious remarks:

The Algebra Project

Filed under: General — m759 @ 4:19 PM

(Continued from Math Rights, July 25.)

For Bob Moses, see the July 25 post Math Rights.

For Math in the Media, see the remarks below.

For another perspective on rings, see Square Space.


Filed under: General — Tags: — m759 @ 2:26 AM

A scene for Nietzsche's Sils Maria

A midrash for Freud, from Kate Beckinsale tonight —

Risin' Up to the Challenge of Her Rival

Pacific Rimming: The Joy of X

Filed under: General — Tags: — m759 @ 1:14 AM

An older generation's Rimmer

The torch is passed to a new generation —

Then there is the X of Paul Fussell —

Mature  adults  only —

For a more realistic (and straight ) X-scene, search for 
ph5dadfa97d2cc1 . (See esp. the 10 seconds starting at 07:04).

Monday, August 2, 2021

The Dinner Party

Filed under: General — Tags: — m759 @ 1:28 PM

For Darkinbad the Brightdayler

Savage Stevens

Filed under: General — m759 @ 11:22 AM



Your query matched 15 lines
An Ordinary Evening in New Haven (iv)
Stanza: 61; Line Number: 7
     They only know a savage assuagement cries
Stanza: 62; Line Number: 8
     With a savage voice; and in that cry they hear
Stanza: 64; Line Number: 10
     In a savage and subtle and simple harmony,
Credences of Summer (vii)
Stanza: 101; Line Number: 11
     The object, grips it in savage scrutiny,
Examination of the Hero in a Time of War (ii)
Stanza: 26; Line Number: 12
     And rainbow sortilege, the savage weapon
Exposition of the Contents of a Cab (OP)
Line Number: 12
     And savage blooms;
From the Journal of Crispin (II) (OP)
Stanza: 114; Line Number: 20
     Into a savage color he goes on.
Line Number: 9
     That savage of fire,
Less and Less Human, O Savage Spirit
     Less and Less Human, O Savage Spirit
Page from a Tale
Line Number: 20
     They looked back at Hans’ look with savage faces.
Sunday Morning (vii)
Stanza: 95; Line Number: 5
     Naked among them, like a savage source.
The Comedian as the Letter C, ii: Concerning the Thunderstorms of Yucatan
Stanza: 14; Line Number: 14
     Into a savage color he went on.
The Man with the Blue Guitar (iii)
Stanza: 29; Line Number: 9
     To bang it from a savage blue,
The Pediment of Appearance
Line Number: 10
     The savage transparence. They go crying
The World as Meditation
Line Number: 6
     Whose mere savage presence awakens the world in which she dwells.
Online Concordance to Wallace Stevens’s Poetry

Sunday, August 1, 2021

Blackboard Jungle Cruise

Filed under: General — Tags: , — m759 @ 11:25 PM

See also Big Time in this  journal.

The Jazz Me Blues

Filed under: General — Tags: — m759 @ 10:19 PM

The title refers to a record played during math class
in the 1955 film "Blackboard Jungle."

Related posts:  Bix and Mira. See as well . . .

The Savage Sixteens

Filed under: General — Tags: — m759 @ 3:51 PM

"Savage ('wild,' 'undomesticated') modes of thought are primary
in human mentality. They are what we all have in common."

— "The Cerebral Savage: On the Work of Claude Lévi-Strauss,"
by Clifford Geertz (Encounter, vol. 28 no. 4, April 1967, pp. 25-32)

For more Geertz and some related art, see The Kaleidoscope Puzzle
which lets you picture twin sixteens .

"Can you imagine the mathematical possibilities?"

— Line from "Annie Hall" (1977)

Devil’s Arithmetic:  26+26=52

Filed under: General — Tags: — m759 @ 12:42 PM

From a search in this journal for Ronna.

"It’ll drive you crazy or make you sane
Moment by moment
It’s a brand new game
The more I learn
The less I understand about love"

— Ronna Reeves, 1992

Old Joke

Filed under: General — Tags: , — m759 @ 11:48 AM

"Can you imagine the mathematical possibilities?"
Line from "Annie Hall"

Related joke —

The Catherine Hardwicke version —

More fun . . . A 26-year old Cara Delevingne.

Consider the Source.

Filed under: General — m759 @ 10:18 AM

Click for the source.

Freudenthal vs. Weyl

Filed under: General — m759 @ 2:10 AM

Hans Freudenthal in 1962 on the axiomatic approach to geometry
of Fano and Hilbert —

"The bond with reality is cut."

Some philosophical background —

For Weyl's "few isolated relational concepts," see (for instance)
Projective Geometries over Finite Fields , by
J. W. P. Hirschfeld (first published by Oxford University Press in 1979).

Weyl in 1932 —

Mathematics is the science of the infinite , its goal the symbolic comprehension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. The intuitive feeling for, the quiet unquestioning acceptance of the infinite, is peculiar to the Orient; but it remains merely an abstract consciousness, which is indifferent to the concrete manifold of reality and leaves it unformed, unpenetrated. Coming from the Orient, the religious intuition of the infinite, the apeiron , takes hold of the Greek soul in the Dionysiac-Orphic epoch which precedes the Persian wars. Also in this respect the Persian wars mark the separation of the Occident from the Orient. This tension between the finite and the infinite and its conciliation now become the driving motive of Greek investigation; but every synthesis, when it has hardly been accomplished, causes the old contrast to break through anew and in a deepened sense. In this way it determines the history of theoretical cognition to our day. 

— "The Open World: Three Lectures on the Metaphysical Implications of Science," 1932

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