Saturday, November 17, 2018


Filed under: Uncategorized — Tags: — m759 @ 7:00 AM

See as well . . .

. . . and posts tagged Alperin.

On its current homepage, the American Mathematical Society  
links to a Nov. 15 blog post illustrating the Stan Lee approach
to mathematics:

Stories: "Math needs more stories. All kinds of stories…" 

See too Mathematics and Narrative in this  journal.

Friday, November 16, 2018

The Transposed Squares

Filed under: Uncategorized — m759 @ 9:12 PM

I.e. (click to enlarge) —


Parable of India

Filed under: Uncategorized — m759 @ 12:42 PM

See too  "When thou seekest me, seek towards India."

William Goldman

Filed under: Uncategorized — Tags: — m759 @ 10:30 AM

From the above source —

See as well the author Les Daniels in this  journal.

On All Souls’ Day 2018

Filed under: Uncategorized — m759 @ 2:40 AM

See as well Under the Volcano  and All Souls in this  journal.

Related material —

Thursday, November 15, 2018

Mathematics and Narrative

Filed under: Uncategorized — m759 @ 9:08 PM

Mathematics —

See (for instance) a research group at Ghent University.

For those who prefer narrative . . .

See also . . .


Filed under: Uncategorized — m759 @ 8:15 AM

"I need a photo opportunity, I want a shot at redemption.
Don't want to end up a cartoon in a cartoon graveyard."
– Paul Simon

From the previous post

From a cartoon graveyard —

See also, in this  journal, Smallest Perfect and Nocciolo .

Wednesday, November 14, 2018

Phase Space

Filed under: Uncategorized — m759 @ 3:33 AM

"Open the pod bay doors, Bernard."

Tuesday, November 13, 2018

Blackboard Jungle Continues.

Filed under: Uncategorized — m759 @ 6:19 PM

From the 1955 film "Blackboard Jungle" —

From a trailer for the recent film version of A Wrinkle in Time

Detail of the phrase "quantum tesseract theorem":

From the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Related mathematics from Koen Thas that some might call a
"quantum tesseract theorem" —

Some background —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also posts tagged Dirac and Geometry. For more
background on finite  geometry, see a web page
at Thas's institution, Ghent University.

Monday, November 12, 2018

Half Crazy

Filed under: Uncategorized — m759 @ 10:42 PM

Douglas Rain, the voice of HAL in Kubrick's 2001 , reportedly
died at 90 on Sunday, Nov. 11, 2018. A piece from the Sunday,
April 1, 2018, print  edition of The New York Times  recalls that . . .

When HAL says, “I know I’ve made some very poor decisions recently, but I can give you my complete assurance that my work will be back to normal,” Mr. Rain somehow manages to sound both sincere and not reassuring. And his delivery of the line “I think you know what the problem is just as well as I do” has the sarcastic drip of a drawing-room melodrama and also carries the disinterested vibe of a polite sociopath.

Kubrick had Mr. Rain sing the 1892 love song “Daisy Bell” (“I’m half crazy, all for the love of you”) almost 50 times, in uneven tempos, in monotone, at different pitches and even just by humming it. In the end, he used the very first take. Sung as HAL’s brain is being disconnected, it’s from his early programming days, his computer childhood. It brings to an end the most affecting scene in the entire film.

— Gerry Flahive in the online New York Times 

"A version of this article appears in print on , on Page AR13 of the New York edition with the headline: HAL 9000 Wasn’t Always So Eerily Calm."

This  journal on the above online date, March 30, 2018 —

"Program or be programmed."
— A saying by Douglas Rushkoff

See as well the following link from this journal
on Armistice Day, the reported date of Mr. Rain's death —

"Halmos + Tombstone."

Raum und Zwischenraum*

Filed under: Uncategorized — m759 @ 8:42 AM

An Internet search for "Raum und Zwischenraum " this morning
led to a Munich artist who reportedly died on Nov. 11, 2012.

Related material —

Desert Cross, in Log24 on that date, and . . .

* See Zwischenraum  in this journal.

Sunday, November 11, 2018


Filed under: Uncategorized — m759 @ 11:00 PM

Warburg at Cornell U. Press

See also Warburg + Cornell in this journal.

"Yet if this Denkraum ,  this 'twilight region,'  is where the artist and
emblem-maker invent, then, as Gombrich well knew, Warburg also
constantly regrets the 'loss' of this 'thought-space,' which he also
dubs the Zwischenraum  and Wunschraum ."

Memory, Metaphor, and Aby Warburg's Atlas of Images ,
     Christopher D. Johnson, Cornell University Press, 2012, p. 56


Filed under: Uncategorized — m759 @ 3:33 AM

See also this journal on the above Catch-22 date — July 16, 2014 —
and a search in this journal for "Halmos + Tombstone."

Thursday, November 8, 2018

Reality vs. Axiomatic Thinking

Filed under: Uncategorized — m759 @ 11:16 PM

From https://blogs.scientificamerican.com/…

A  Few  of  My  Favorite  Spaces:
The Fano Plane

The intuition-challenging Fano plane may be
the smallest interesting configuration
of points and lines.

By Evelyn Lamb on October 24, 2015

"…finite projective planes seem like
a triumph of purely axiomatic thinking
over any hint of reality. . . ."

For Fano's axiomatic  approach, see the Nov. 3 Log24 post
"Foundations of Geometry."

For the Fano plane's basis in reality , see the eightfold cube
at finitegeometry.org/sc/ and in this journal.

See as well "Two Views of Finite Space" (in this journal on the date 
of Lamb's remarks — Oct. 24, 2015).

Some context:  Gödel's Platonic realism vs. Hilbert's axiomatics
in remarks by Manuel Alfonseca on June 7, 2018. (See too remarks
in this journal on that date, in posts tagged "Road to Hell.")

Geometry Lesson

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

From "The Trials of Device" (April 24, 2017) —

Wittgenstein's pentagram and 4x4 'counting-pattern'

Pentagon with pentagram    

See also Wittgenstein in a search for "Ein Kampf " in this journal.

Wednesday, November 7, 2018

The Fact-Checker

Filed under: Uncategorized — m759 @ 9:43 PM


In memory of Christopher Lehmann-Haupt, who reportedly died
today (Wed., Nov. 7, 2018) at 84 —

See Lehmann-Haupt in this journal on May 23, 2012:

On author Paul Fussell, who died today —

"Vincent B. Sherry, writing in The Cambridge Companion to the Literature of the First World War , called Mr. Fussell’s book 'the fork in the road for Great War criticism.'"  — Christopher Lehmann-Haupt in The New York Times

Actually, the writing was by James Campbell. Sherry was the book's editor. See Campbell's "Interpreting the War," pp. 261-279 of the 2005 (first) printing. The fork is on page 267.

Update of 9:26 PM— In the latest  version of Lehmann-Haupt's article, the fork has disappeared. But Campbell's writing is still misidentified as Sherry's.

Defense Against the Dark Arts

Filed under: Uncategorized — m759 @ 6:19 AM

"What is the Necropastoral?" was published on April 29th, 2014.
Also on April 29th, 2014 —

See as well Christianity and Culture  by T. S. Eliot.

Tuesday, November 6, 2018

Four Quartets Prize

Filed under: Uncategorized — m759 @ 9:00 PM

On a poem sequence that won this year's Four Quartets Prize —

"Decomposing and reconstituting bodies and landforms
feed the evolution of Smith’s afrofuturist necropastoral."

Bait and Tackle

Filed under: Uncategorized — Tags: — m759 @ 1:13 PM

The Bait —

For the tackle, see a 1988 album from The Residents.

Settings and Tools

Filed under: Uncategorized — m759 @ 11:02 AM

Desert Notes*

Filed under: Uncategorized — Tags: — m759 @ 3:13 AM

A November 1 LA Times  article about a book to be published today —

Why did Jonathan Lethem
turn toward the desert
in 'The Feral Detective'?

See also searches in this  journal for Desert and, more particularly,
Point Omega and Mojave.

* The title of a book by Barry Holstun Lopez.

On Mathematical Beauty

Filed under: Uncategorized — Tags: — m759 @ 2:18 AM

A phrase from the previous post —
"a size-eight dame in a size-six dress" —
suggests a review . . .

See as well the diamond-theorem correlation and . . .

Why PSL(2,7) is isomorphic to GL(3.2)

Monday, November 5, 2018

Eyes on the Prize

Filed under: Uncategorized — Tags: , — m759 @ 7:04 PM

High Life at Sils Maria

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

Related art —

Sunday, November 4, 2018

Kristen vs. the Space Witch*

Filed under: Uncategorized — Tags: — m759 @ 11:59 PM

* We know the former. There is no shortage of candidates for the latter.

“Look Up” — The Breakthrough Prize* Theme This Evening

Filed under: Uncategorized — Tags: — m759 @ 10:45 PM

Looking up images for "The Space Theory of Truth" this evening —

Detail  (from the post "Logos" of Oct. 14)


Dead Poet

Filed under: Uncategorized — Tags: — m759 @ 2:01 PM

The New York Times  today on a poet, Judith Kazantzis,
"who died on Sept. 18 at 78" —

"Judith’s oldest sister is Antonia Fraser, the biographer
and novelist and widow of the playwright Harold Pinter."

"Her [Judith’s] death was confirmed by Andy Croft, who runs
Smokestack Books, the publisher of 'Sister Intervention' [sic* ]
(2014), Ms. Kazantzis’ last collection of poetry. He did not
specify the cause or where she died."

Notable lines from that book's poem "In the Garden" —

Two trees of life, not in the woods,
but in the garden.

See also the post "Death Day" in this  journal on Sept. 18.

* The title is actually "Sister Invention ."

Saturday, November 3, 2018

For St. Anselm

Filed under: Uncategorized — Tags: , , — m759 @ 11:00 PM

"… at his home in San Anselmo . . . ."

See also Anselm in this journal, as well as the Devil's Night post Ojos.

The Space Theory of Truth

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM

Earlier posts have discussed the "story theory of truth"
versus the "diamond theory of truth," as defined by 
Richard Trudeau in his 1987 book The Non-Euclidean Revolution.

In a New York Times  opinion piece for tomorrow's print edition,*
novelist Dara Horn touched on what might be called 
"the space theory of truth."

When they return to synagogue, mourners will be greeted
with more ancient words: “May God comfort you
among the mourners of Zion and Jerusalem.”
In that verse, the word used for God is hamakom 
literally, “the place.” May the place comfort you.

[Link added.]

The Source —

See Dara Horn in this  journal, as well as Makom.

* "A version of this article appears in print on ,
on Page A23 of the New York edition with the headline: 
American Jews Know This Story."

Foundations of Geometry

Filed under: Uncategorized — m759 @ 1:40 PM

"costruire (o, dirò meglio immaginare) un ente" — Fano, 1892

"o, dirò meglio, costruire" — Cullinane, 2018

Friday, November 2, 2018

Day of the Dead

Filed under: Uncategorized — m759 @ 9:00 AM

From Wikipedia

Day of the Dead
Observed by Mexico, and regions with large Hispanic populations
Type Cultural 
Syncretic Christian
Significance Prayer and remembrance of friends and family members who have died
Celebrations Creation of altars to remember the dead, traditional dishes for the Day of the Dead
Begins October 31
Ends November 2
Date October 31
Next time 31 October 2019
Frequency Annual
Related to All Saints' Day

"The Day of the Dead (Spanish: Día de Muertos ) is
a Mexican holiday celebrated throughout Mexico,
in particular the Central and South regions,
and by people of Mexican heritage elsewhere.
The multi-day holiday focuses on gatherings
of family and friends to pray for and remember
friends and family members who have died, and
help support their spiritual journey. . . .

The holiday is sometimes called Día de los Muertos 
in Anglophone countries, a back-translation of its
original name, Día de Muertos .

Gradually, it was associated with October 31,
November 1, and November 2 to coincide with the
Western Christianity triduum of Allhallowtide: 
All Saints' EveAll Saints' Day, and All Souls' Day."


The previous post concerned a poet who reportedly
died on October 23, 2018.  This journal on that date —

Elevation of the Hostess

Filed under: Uncategorized — m759 @ 1:27 AM

Or:  Netflix and Chill on All Souls' Day

Midrash from Huffington Post  (click to enlarge) —

Thursday, November 1, 2018

Formation, Transformation . . . . Solution, Dissolution

Filed under: Uncategorized — m759 @ 8:40 PM

Literary Doodles

Filed under: Uncategorized — m759 @ 11:59 AM

The Great Doodle of Northrop Frye —

Shown below is a "Story Circle" based on the work of Joseph Campbell.
The author of this particular version is unknown.  

Note that there are 12 steps in the above Story Circle. This suggests
some dialogue from a recent film . . .

Donnie —"We can't ask for help if we don't think there's anyone out there to give it. You have to grasp this concept. And that doesn't have to be fucking Jesus Christ or Buddha or Vanna White."
John — "So, can I choose the genitalia of Raquel Welch?"
Donnie — "I would advise against that, Callahan."
John — "Why?"
Donnie — "'Cause it's not a fucking joke. If you can't look outside yourself and you can't find a higher power, you're fucked."

Read more: https://www.springfieldspringfield.co.uk/movie_script.php?movie=dont-worry-he-wont-get-far-on-foot

The Albee Box

Filed under: Uncategorized — m759 @ 3:00 AM

See also Albee + Box in this  journal.

Wednesday, October 31, 2018

The Crucible of Death

Filed under: Uncategorized — m759 @ 7:00 PM

This journal yesterday

On a new Netflix series:

We don’t yet have a story structure that allows witches to be powerful for long stretches of time without men holding them back. And what makes the new Sabrina  so exciting is that it seems to be trying to build that story structure itself, in real time, to find a way to let Sabrina have her power and her freedom.

It might fail. But if it does, it will be a glorious and worthwhile failure — the type that comes with trying to pioneer a new kind of story.

—  Constance Grady at Vox, the morning before
      Devil's Night (Oct. 30-31), 2018

A playwright who reportedly died yesterday

"Attention must be paid."

Tuesday, October 30, 2018


Filed under: Uncategorized — Tags: — m759 @ 11:11 PM

From the Hulu series 'The Path,' the Eye logo

A better term than "phase space" might be "story space."

The Quantum Space Story

Filed under: Uncategorized — m759 @ 2:00 PM

Finkelstein reportedly died on Sunday, January 24, 2016.

"A Serious Man  kicks off with a Yiddish-language frame story that takes place in a 19th-century Eastern European shtetl, where a married couple has an enigmatic encounter with an old acquaintance who may be a dybbuk , or malevolent spirit (and who's played by the Yiddish theater actor Fyvush Finkel). The import of this parable is cryptic to the point of inscrutability, making it a perfect introduction to the rest of the movie."

— Dana Stevens at Slate.com on Oct. 1, 2009

See also Finkelstein in this  journal.

See as well posts now tagged Oct. 4, 2018,
in the context of today's previous post.

Story Structure, Story Space

Filed under: Uncategorized — m759 @ 1:00 PM

Constance Grady at Vox  today on a new Netflix series —

We don’t yet have a story structure that allows witches to be powerful for long stretches of time without men holding them back. And what makes the new Sabrina  so exciting is that it seems to be trying to build that story structure itself, in real time, to find a way to let Sabrina have her power and her freedom.

It might fail. But if it does, it will be a glorious and worthwhile failure — the type that comes with trying to pioneer a new kind of story.

See also Story Space  in this  journal.

Monday, October 29, 2018

For the Church of Synchronology*

Filed under: Uncategorized — m759 @ 9:21 PM

* See that term in this journal.

Sunday, October 28, 2018

Commonwealth Tales, or “Lost in Physics”

Filed under: Uncategorized — m759 @ 11:00 PM

From Ulysses , by James Joyce —

John Eglinton, frowning, said, waxing wroth:

—Upon my word it makes my blood boil to hear anyone compare Aristotle with Plato.

—Which of the two, Stephen asked, would have banished me from his commonwealth?

Compare and contrast:

Plato's diamond in Jowett's version of the Meno dialogue

Fans of Plato might enjoy tales of Narnia, but fans of
James Joyce and Edgar Allan Poe might prefer
a tale by Michael Chabon from April 2001 about a
"doleful little corner of western Pennsylvania."


Filed under: Uncategorized — m759 @ 4:56 PM

From a New York Times  obituary today —

“Centering prayer is all about heartfulness, which
is a little different from mindfulness,” the Rev. Carl Arico,
a co-founder of Contemplative Outreach, said in a
telephone interview. “It goes to the relationship with God,
who is already there. It’s not sitting in a void.”

Windows 10 lockscreen image

For the Sabine Women

Filed under: Uncategorized — m759 @ 3:12 PM

Sunday Dinner

Filed under: Uncategorized — m759 @ 2:11 PM

History 101

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

 181028-Interrobang-Wikipedia.jpg (229×524)

'Pinter's hallmark,' according to Harlan Ellison

Friday, October 26, 2018

Saying More: Pathmark, Hallmark, Waymark

Filed under: Uncategorized — m759 @ 2:11 PM

The previous post (Pathmark Meets Hallmark) suggests
a review of the Waymark Prize in mathematics.

Pathmark Meets Hallmark

Filed under: Uncategorized — Tags: — m759 @ 2:03 PM

From earlier posts now tagged Pathmark

From earlier posts tagged Black Diamond

A source for the above Ellison quote —

'Pinter's hallmark,' according to Harlan Ellison

See also A Christmas Carol.

Thursday, October 25, 2018

Breaking the Stranglehold

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

George Soros


When I wrote this article I was troubled by drawing an overly sharp distinction between the natural and social sciences. Beinhocker’s (2013) article in this symposium and a workshop at the Central European University on 8 October 2013 led me to modify my views on separating the two. I still think that the methodological convention I proposed is needed in the near term in order to break the stranglehold of rational choice theory, but . . . .

The above postscript is from . . .

See also this  journal on 8 October 2013 —


Filed under: Uncategorized — Tags: , — m759 @ 1:18 PM

Two images from a post of April 11, 2014

Tom Cruise at the Vatican in MI3


Michelle Monaghan, star of "The Path," in MI3 —

Hickory Dickory.

Aesthetic Requiem

Filed under: Uncategorized — Tags: , — m759 @ 12:01 AM

See also Aesthetics (Oct. 17, 2018).

Wednesday, October 24, 2018

Raiders of the Lost Crucible Continues

Filed under: Uncategorized — Tags: , — m759 @ 10:22 PM

Mystery Box

Filed under: Uncategorized — Tags: — m759 @ 3:38 PM

". . . humanity battling an unseen force . . . ." —

Quantum Space Elements?

The Cracked Potter

Filed under: Uncategorized — Tags: — m759 @ 1:52 PM

See also an embedded ad in The Atlantic  magazine, Sept. 2017.


Filed under: Uncategorized — Tags: , — m759 @ 4:38 AM

The previous post suggests a review.

Following the above reference to March 30, 2016 —

Following the above reference to Lovasz —

The Path of Logic

Filed under: Uncategorized — Tags: , — m759 @ 3:05 AM

Ay Que Bonito

Filed under: Uncategorized — m759 @ 2:00 AM


"Ay que bonito es bailar
a las dos de la mañana"

— Adapted from a song lyric

See also . . .

Shadi Bartsch-Zimmer, Helen A. Regenstein
Distinguished Service Professor of Classics
at the University of Chicago,

"currently the lead editor of the journal 
KNOW: A Journal on the Formation of Knowledge."

Tuesday, October 23, 2018

Simplicity Versus Complexity

Filed under: Uncategorized — m759 @ 7:13 PM

Simplicity  (Click for some complexity.)

Complexity  (Click for some simplicity.)

A passage from the 2011 book Idea Man  that was suggested by
a recent New Yorker  article on the book's author, the late Paul Allen —

Left-click image to enlarge.

Plan 9 from Inner Space

Filed under: Uncategorized — m759 @ 9:57 AM

Click the image for some context.

Monday, October 22, 2018

Story Space

Filed under: Uncategorized — m759 @ 4:48 PM

A better term than "phase space" might be "story space."

See as well Expanding the Spielraum.

For Connoisseurs of Conceptual Art

Filed under: Uncategorized — Tags: — m759 @ 1:32 PM

In related news . . .

Sunday, October 21, 2018

For Connoisseurs of Bad Art

Filed under: Uncategorized — Tags: — m759 @ 7:00 PM

Yesterday afternoon's post "Study in Blue and Pink" featured 
an image related to the "Blade and Chalice" of Dan Brown 

Requiem for a comics character known as "The Blue Blade" —


"We all float down here."

About the corresponding "Pink Chalice," the less said the better.


Filed under: Uncategorized — m759 @ 11:00 AM


Saturday, October 20, 2018


Filed under: Uncategorized — m759 @ 10:30 PM

See also Stella Octangula.

Study in Blue and Pink

Filed under: Uncategorized — Tags: — m759 @ 3:00 PM

Related Log24 posts — See Blade + Chalice.


Filed under: Uncategorized — m759 @ 2:30 PM

This  post was suggested by the date of a photograph.

Friday, October 19, 2018

A Tale of Two Naked Cities

Filed under: Uncategorized — m759 @ 2:03 PM

News from Hell's Kitchen, New York —

A view of Broadway and Columbus, San Francisco —

See as well actor Bruce Gordon's film debut —


Kaleidoscope and Old Lace

Filed under: Uncategorized — m759 @ 12:31 PM

See posts now tagged "Kaleidoscope Society" and, more generally,
a search in this journal for "Kaleidoscope."

Related material —

Photo caption in a news story today:

"Father Gary Thomas attends the premiere of Warner Brothers’
'The Rite' at Grauman’s Chinese Theatre, in Los Angeles,
on January 26, 2011. Thomas is holding a special Mass
on Thursday and Saturday [Oct. 18 and 20] to counter
a planned hex on Supreme Court Justice Brett Kavanaugh."

See as well posts tagged "Rubik Exorcism."

IMAGE- Anthony Hopkins exorcises a Rubik cube

Thursday, October 18, 2018

Bicoastal Delights

Filed under: Uncategorized — m759 @ 11:22 PM

East Coast — See the previous post.

West Coast — See . . .

"Show all" — Yes!

Studio 54: Putting the Hell in Hell’s Kitchen

Filed under: Uncategorized — m759 @ 10:38 PM

The previous post suggests a New York Times  review from today:

The Quick and the Dirty

Filed under: Uncategorized — Tags: — m759 @ 2:32 PM

Two stars of the 2016 film "Urge"

See also other posts tagged QDOS (Quick and Dirty Operating System).

“Break on through” — The Doors

Filed under: Uncategorized — Tags: — m759 @ 1:38 PM

Wednesday, October 17, 2018

Breakthrough Prize

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

181017-Breakthrough_Prize-news.jpg (500×212)

"…  what once seemed pure abstractions have turned out to
      underlie real physical processes."

— https://breakthroughprize.org/Prize/3

Related material from the current New Yorker


Filed under: Uncategorized — Tags: — m759 @ 11:22 AM

From "The Phenomenology of Mathematical Beauty,"
by Gian-Carlo Rota —

The Lightbulb Mistake

. . . . Despite the fact that most proofs are long, and despite our need for extensive background, we think back to instances of appreciating mathematical beauty as if they had been perceived in a moment of bliss, in a sudden flash like a lightbulb suddenly being lit. The effort put into understanding the proof, the background material, the difficulties encountered in unraveling an intricate sequence of inferences fade and magically disappear the moment we become aware of the beauty of a theorem. The painful process of learning fades from memory, and only the flash of insight remains.

We would like  mathematical beauty to consist of this flash; mathematical beauty should  be appreciated with the instantaneousness of a lightbulb being lit. However, it would be an error to pretend that the appreciation of mathematical beauty is what we vaingloriously feel it should be, namely, an instantaneous flash. Yet this very denial of the truth occurs much too frequently.

The lightbulb mistake is often taken as a paradigm in teaching mathematics. Forgetful of our learning pains, we demand that our students display a flash of understanding with every argument we present. Worse yet, we mislead our students by trying to convince them that such flashes of understanding are the core of mathematical appreciation.

Attempts have been made to string together beautiful mathematical results and to present them in books bearing such attractive titles as The One Hundred Most Beautiful Theorems of Mathematics . Such anthologies are seldom found on a mathematician’s bookshelf. The beauty of a theorem is best observed when the theorem is presented as the crown jewel within the context of a theory. But when mathematical theorems from disparate areas are strung together and presented as “pearls,” they are likely to be appreciated only by those who are already familiar with them.

The Concept of Mathematical Beauty

The lightbulb mistake is our clue to understanding the hidden sense of mathematical beauty. The stark contrast between the effort required for the appreciation of mathematical beauty and the imaginary view mathematicians cherish of a flashlike perception of beauty is the Leitfaden  that leads us to discover what mathematical beauty is.

Mathematicians are concerned with the truth. In mathematics, however, there is an ambiguity in the use of the word “truth.” This ambiguity can be observed whenever mathematicians claim that beauty is the raison d’être of mathematics, or that mathematical beauty is what gives mathematics a unique standing among the sciences. These claims are as old as mathematics and lead us to suspect that mathematical truth and mathematical beauty may be related.

Mathematical beauty and mathematical truth share one important property. Neither of them admits degrees. Mathematicians are annoyed by the graded truth they observe in other sciences.

Mathematicians ask “What is this good for?” when they are puzzled by some mathematical assertion, not because they are unable to follow the proof or the applications. Quite the contrary. Mathematicians have been able to verify its truth in the logical sense of the term, but something is still missing. The mathematician who is baffled and asks “What is this good for?” is missing the sense  of the statement that has been verified to be true. Verification alone does not give us a clue as to the role of a statement within the theory; it does not explain the relevance  of the statement. In short, the logical truth of a statement does not enlighten us as to the sense of the statement. Enlightenment , not truth, is what the mathematician seeks when asking, “What is this good for?” Enlightenment is a feature of mathematics about which very little has been written.

The property of being enlightening is objectively attributed to certain mathematical statements and denied to others. Whether a mathematical statement is enlightening or not may be the subject of discussion among mathematicians. Every teacher of mathematics knows that students will not learn by merely grasping the formal truth of a statement. Students must be given some enlightenment as to the sense  of the statement or they will quit. Enlightenment is a quality of mathematical statements that one sometimes gets and sometimes misses, like truth. A mathematical theorem may be enlightening or not, just as it may be true or false.

If the statements of mathematics were formally true but in no way enlightening, mathematics would be a curious game played by weird people. Enlightenment is what keeps the mathematical enterprise alive and what gives mathematics a high standing among scientific disciplines.

Mathematics seldom explicitly acknowledges the phenomenon of enlightenment for at least two reasons. First, unlike truth, enlightenment is not easily formalized. Second, enlightenment admits degrees: some statements are more enlightening than others. Mathematicians dislike concepts admitting degrees and will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in its place, how it sheds light around itself, like Lichtung — a clearing in the woods. We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved. The term “mathematical beauty,” together with the lightbulb mistake, is a trick mathematicians have devised to avoid facing up to the messy phenomenon of enlightenment. The comfortable one-shot idea of mathematical beauty saves us from having to deal with a concept that comes in degrees. Talk of mathematical beauty is a cop-out to avoid confronting enlightenment, a cop-out intended to keep our description of mathematics as close as possible to the description of a mechanism. This cop-out is one step in a cherished activity of mathematicians, that of building a perfect world immune to the messiness of the ordinary world, a world where what we think should be true turns out to be true, a world that is free from the disappointments, ambiguities, and failures of that other world in which we live.

How many mathematicians does  it take to screw in a lightbulb?

Tuesday, October 16, 2018


Filed under: Uncategorized — Tags: — m759 @ 9:11 PM

For the title, see the Wikipedia article on the late Paul Allen.

See also . . .

Related material — the late Patrick Swayze in Ghost and King Solomon's Mines.

"Please wait as your operating system is initiated."


Literary Relations

Filed under: Uncategorized — m759 @ 2:03 PM

See also Log24 on November 7, 2016.

Hen Scratches

Filed under: Uncategorized — Tags: — m759 @ 1:18 PM

Robert M. Adams on Finnegans Wake 
in The New York Times 
on Sunday, January 18, 1987:

"There is a great passage in the 'Wake' where Joyce — if he was not
just a phantasm in the mind of HCE — appears to address his reader
directly, jocularly and sympathetically:

'You is feeling like you was lost in the bush, boy? You says:
It is a puling sample jungle of woods. You most shouts out:
Bethicket me for a stump of a beech if I have the poultriest
notions what the farest he all means. Gee up, girly!'

For there's a bird in the case, and if we follow her hen scratches,
we may be able to 'pick a peck of kindlings yet from the sack of
auld hensyne.' That's what keeps the 'Wake' fellowship awake at night . . . ."

Not to mention "skreaking and skrittering" —

Monday, October 15, 2018

History at Bellevue

Filed under: Uncategorized — Tags: , — m759 @ 9:38 PM

The previous post, "Tesserae for a Tesseract," contains the following
passage from a 1987 review of a book about Finnegans Wake

"Basically, Mr. Bishop sees the text from above
and as a whole — less as a sequential story than
as a box of pied type or tesserae for a mosaic,
materials for a pattern to be made."

A set of 16 of the Wechsler cubes below are tesserae that 
may be used to make patterns in the Galois tesseract.

Another Bellevue story —

“History, Stephen said, is a nightmare
from which I am trying to awake.”

— James Joyce, Ulysses

Tesserae for a Tesseract

Filed under: Uncategorized — Tags: , — m759 @ 8:22 PM

The source —

The Other Side

Filed under: Uncategorized — Tags: , — m759 @ 1:00 PM

"As far as I know, there is no escape for mortal beings from time.
But experimental ideas of practical access to eternity
exerted tremendous sway on educated, intelligent, and forward-
looking people in the late nineteenth and early twentieth centuries,
with a cutoff that was roughly coincident with the First World War.
William James died in 1910 without having ceased to urge
an open-minded respect for occult convictions."

New Yorker  art critic Peter Schjeldahl in the Oct. 22, 2018, issue.

Also in that issue —

For Zingari Shoolerim*

Filed under: Uncategorized — Tags: , — m759 @ 12:19 PM

IMAGE- Site with keywords 'Galois space, Galois geometry, finite geometry' at DiamondSpace.net

The structure at top right is that of the
in the previous post.

* "Zingari shoolerim" is from
    Finnegans Wake .

Daily Maro

Filed under: Uncategorized — Tags: — m759 @ 12:08 AM

From a post of May 21, 2004

A comment on that post —

"Oh yeah – MARO means bread in Romani – pretty cool, huh?" 

See also a New Yorker  piece from the Oct. 15, 2018, issue —


Sunday, October 14, 2018


Filed under: Uncategorized — m759 @ 10:00 AM

New and old AMS logos —

I prefer the old.  Related material —

For an old Crosswicks curse, see that phrase in this journal.

For a new curse, see . . .

    "Unsheathe your dagger definitions." — James Joyce.

Saturday, October 13, 2018

Corinthian Style

Filed under: Uncategorized — m759 @ 3:20 PM

The previous two posts discussed the Twitter account of
the author of a New York Times  opinion column published
online today. From a rather different Twitter —

Location: Endor

Filed under: Uncategorized — Tags: — m759 @ 2:26 PM

See also Space Writer in this  journal.

Space 101

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

Screenshot of a tweet by space writer Shannon Stirone
posted at 10:57 PM ET October 12 —

See also NASA + Wiig.

Stirone has an opinion piece in today's online New York Times  promoting NASA.

Discussing the Hubble Space Telescope, she claims that . . .

"Hubble peers deep into space, patiently collecting the universe’s traveling light,
then delivering it to us in never before seen images: galaxies, supernovas and
nebulae. It is a time machine. And without it we wouldn’t know we are inside
a galaxy that is just one of possibly trillions."


Filed under: Uncategorized — m759 @ 12:00 PM

Monday, January 8, 2018


Filed under: Uncategorized — m759 @ 12:00 AM 

See also the previous post.

Particular Values

Filed under: Uncategorized — m759 @ 11:01 AM

See also Hobsbawm in this journal.

Friday, October 12, 2018

Spooky Moonrise

Filed under: Uncategorized — m759 @ 7:31 PM

Kristen Wiig leaving bookstore in 
"Comedians in Cars Getting Coffee," S9E1 —

A Windows 10 lockscreen image — "Spooky Moonrise Over Lake":

Thursday, October 11, 2018

Bum Tip

Filed under: Uncategorized — m759 @ 10:10 PM

For a more academic meditation, see University Diaries  today.


Filed under: Uncategorized — m759 @ 2:07 PM

The word "adcraft" in the previous post suggests adman Cary Grant
in "North by Northwest," which in turn suggests a Log 24 post from 
Tuesday, March 4, 2014:


"Mr. Kaplan, you are quite the performer."

That  post was suggested by . . .

See also Log24 posts of Sunday, March 2, 2014 — Oscar Day.


Filed under: Uncategorized — m759 @ 1:00 PM

Related adcraft — "Harry Potter and the Philosopher's Stone"
became, for the U.S. market, "… and the Sorcerer's Stone."

Wednesday, October 10, 2018

Witch Luck *

Filed under: Uncategorized — m759 @ 7:35 PM

*  And Omensetter's  * . . .

Quoted here on Dec. 14, 2017

— Justin E. H. Smith


“Crossword Omen” Continues.

Filed under: Uncategorized — m759 @ 12:14 PM

An image from earlier Log24 posts tagged Crossword Omen

Portrait, in the 2013 film Oblivion , of  a 2005 graduate
of London's Royal Academy of Dramatic Art —

London derrière.


Filed under: Uncategorized — m759 @ 10:17 AM

On the answers to the puzzle discussed here last night

"Look, this is a complicated theme, but it was no help to me
while solving and feels like an elaborate joke that the teller
has to explain, where you're like 'Oh … yeah, that's clever.'
But you didn't laugh."

— Today's "Rex Parker Does the NYT Crossword Puzzle"

A Stitch in Time

Filed under: Uncategorized — m759 @ 9:00 AM

The above October 7th screenshot is of a New York Times  ad in the
"Business Day" section that accompanied a story with the headline 

"Pret a Manager . . . ." [sic ].

The error was corrected:

Tuesday, October 9, 2018

Nicht Spielerei

Filed under: Uncategorized — m759 @ 10:48 PM


A YouTube description —

"Walter Klien performing Mozart's 12 Variations in C Major
on the French Song: "Ah vous dirai-je, Maman" K.265 on
the piano. Used in Twinkle Twinkle Little Star, Baa Baa
Black Sheep, and the Alphabet Song."


"Published on May 23, 2010"

See also this  journal on May 23, 2010 —

Posts now tagged Death Story.

Related material —


Filed under: Uncategorized — m759 @ 12:00 PM

Breadcrumbs for Sophia

Filed under: Uncategorized — m759 @ 12:08 AM

"Spiel ist nicht Spielerei." — Fröbel

See also Gretel in posts from January 24, 2013.

Monday, October 8, 2018

Four Slashes

Filed under: Uncategorized — m759 @ 9:17 PM

"Four slashes of one size fits all.
It should not fit you."

— Alyssa Milano, "A Survivor's Prayer"

Milano's reference was to the hashtag symbol.

For another view of this symbol, see Pound Sign.

Some less popular "four slashes" art from Milan —

The Milano Fork

Filed under: Uncategorized — m759 @ 10:41 AM

"When you come to a fork in the road…"

IMAGE- Alyssa Milano as a child, with fork


Filed under: Uncategorized — m759 @ 12:38 AM

IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

Note that some have to stop and some don't.

This  journal on the above date, 5 July 2008 —

"Review by Charles Isherwood in today’s New York Times :

A god deserves a great entrance. And Dionysus, the god of wine
and party boy of Mount Olympus, whose celebratory rituals got
the whole drama thing rolling in the first place, surely merits a
spectacular one….”

Sunday, October 7, 2018

In the Bag

Filed under: Uncategorized — m759 @ 7:55 AM

"Skip the preface, and it's in the bag!" — Nabokov

See also Shattuck in this journal and . . .

Saturday, October 6, 2018

Smart Drug

Filed under: Uncategorized — m759 @ 10:00 PM

For Shoshana

Filed under: Uncategorized — m759 @ 8:45 PM

See Shoshana, Frame Tale, and Artistic Vision.

Au Revoir, Cosette

Filed under: Uncategorized — m759 @ 2:56 PM

Mary Stewart, 'The Little Broomstick'


Filed under: Uncategorized — m759 @ 1:00 PM

Friday, October 5, 2018

The “Ignotiles” of Paul Hertz

Filed under: Uncategorized — m759 @ 3:09 PM

The above figure illustrating 24 permutations is dated "2007."

An earlier permutations figure, archived on June 17, 2006 —

An illustration of the above title "I Want To Be a Mathematician" —

Wanting does not make it so.

Thursday, October 4, 2018

Mage Studies: Art vs. Bullshit

Filed under: Uncategorized — m759 @ 10:32 PM


From an October 3 post


From an academic's website —


Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

The previous post suggests a review of . . .

Broomsday 2004.

The image “http://www.log24.com/log/pix04B/041016-Poster2.jpg” cannot be displayed, because it contains errors.

Art Trail

Filed under: Uncategorized — Tags: — m759 @ 12:13 PM

“There’s always a place at the edge of our knowledge,
where what’s beyond is unimaginable, and that edge,
of course, moves.” — Physicist Leon Lederman in
The New York Times  yesterday afternoon.

An image from Florence, SC

Click image for related material.

Wednesday, October 3, 2018

Nobel Literature Prize

Filed under: Uncategorized — m759 @ 9:20 PM

The New York Times  today —

Leon Lederman, 96, Explorer (and Explainer) of
the Subatomic World, Dies

By George Johnson

Oct. 3, 2018

Leon Lederman, whose ingenious experiments with particle accelerators
deepened science’s understanding of the subatomic world, died
early Wednesday in Rexburg, Idaho. He was 96.

His wife, Ellen Carr Lederman, confirmed the death, at a care facility.
She and Dr. Lederman, who had long directed the Fermi National Accelerator
Laboratory outside Chicago, had retired to eastern Idaho.

"… novelist, poet and minister George MacDonald . . . ."

See as well Jess Lederman, Investment Banker.

"I have three children with my first wife, Florence Gordon.
Daughter Rena is an anthropologist,
son Jesse is an investment banker
and daughter Rachel a lawyer."

— Leon Lederman at nobelprize.org.

Adamantine Meditation

Filed under: Uncategorized — m759 @ 12:24 PM


A Catholic philosopher —

Related art —

Image result for mog miracle octad bricks

Tuesday, October 2, 2018

Raiders of the Lost Crucible

Filed under: Uncategorized — Tags: — m759 @ 11:22 AM

See other posts now tagged Crucible Raiders.

Related entertainment —

From YouTube:

From NBC:

For more from the above date,
Oct. 8, 2016, click "seriously" below.

But seriously

Sunday, September 30, 2018


Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

Click the above for an example.

Iconology of the Eightfold Cube

Filed under: Uncategorized — Tags: — m759 @ 11:13 AM

Found today in an Internet image search, from the website of
an anonymous amateur mathematics enthusiast

Forming Gray codes in the eightfold cube with the eight
I Ching  trigrams (bagua ) —

Forming Gray codes in the eightfold cube with the eight I Ching trigrams (bagua)

This  journal on Nov. 7, 2016

A different sort of cube, from the makers of the recent
Netflix miniseries "Maniac" —

See also Rubik in this  journal.

Saturday, September 29, 2018

“Ikonologie des Zwischenraums”

Filed under: Uncategorized — Tags: , — m759 @ 9:29 AM

The title is from Warburg. The Zwischenraum  lines and shaded "cuts"
below are to be added together in characteristic two, i.e., via the
set-theoretic symmetric difference  operator.

Some small Galois spaces (the Cullinane models)

Friday, September 28, 2018


Filed under: Uncategorized — m759 @ 4:48 PM

ART WARS Midrash

Filed under: Uncategorized — m759 @ 9:00 AM

"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"

"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'"

— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks
on the "story theory" of truth as opposed to the "diamond theory"
of truth in The Non-Euclidean Revolution  (1987)

The deaths of Roth and Grünbaum on September 14th,
The Feast of the Holy Cross, along with Douthat's column
today titled "Only the Truth Can Save Us Now," suggest a
review of

Elements of Number Theory, by Vinogradov .

Thursday, September 27, 2018

Branko Grünbaum, 1929-2018

Filed under: Uncategorized — m759 @ 7:59 PM

See an American Mathematical Society obituary
and a Seattle Times  obituary.

Cube Meditation

Filed under: Uncategorized — m759 @ 1:12 PM

See also "Eternal Recreation" (Christmas Eve, 2012).

Older Posts »

Powered by WordPress