Log24

Monday, August 4, 2025

Commedia dell’Arte:  Comedy vs. Art

Filed under: General — Tags: — m759 @ 5:15 am

Thanks for the warning. Other news for Thursday, August 7th —

Sunday, May 25, 2025

Tiger Art

Filed under: General — Tags: — m759 @ 4:17 am

Wednesday, October 23, 2024

The Delta Transform

Filed under: General — Tags: , , , , — m759 @ 7:04 am

Rothko — "… the elimination of all obstacles between the painter and
the idea, and between the idea and the observer."

Walker Percy has similarly discussed elimination of obstacles between
the speaker and the word, and between the word and the hearer.

Walker Percy's chapter on 'The Delta Factor' from 'Message in the Bottle'

Click images to enlarge.

Related mathematics —

The source: http://finitegeometry.org/sc/gen/typednotes.html.

A document from the above image —

AN INVARIANCE OF SYMMETRY

BY STEVEN H. CULLINANE

We present a simple, surprising, and beautiful combinatorial
invariance of geometric symmetry, in an algebraic setting.

DEFINITION. A delta transform of a square array over a 4-set is
any pattern obtained from the array by a 1-to-1 substitution of the
four diagonally-divided two-color unit squares for the 4-set elements.

THEOREM. Every delta transform of the Klein group table has
ordinary or color-interchange symmetry, and remains symmetric under
the group G of 322,560 transformations generated by combining
permutations of rows and colums with permutations of quadrants.

PROOF (Sketch). The Klein group is the additive group of GF (4);
this suggests we regard the group's table  T as a matrix over that
field. So regarded, T is a linear combination of three (0,1)-matrices
that indicate the locations, in  T, of the 2-subsets of field elements.
The structural symmetry of these matrices accounts for the symmetry
of the delta transforms of  T, and is invariant under G.

All delta transforms of the 45 matrices in the algebra generated by
the images of  T under G are symmetric; there are many such algebras. 

THEOREM. If 1 m ≤ n2+2, there is an algebra of 4m
2n x 2n matrices over GF(4) with all delta transforms symmetric.

An induction proof constructs sets of basis matrices that yield
the desired symmetry and ensure closure under multiplication.

REFERENCE

S. H. Cullinane, Diamond theory (preprint).

Update of 1:12 AM ET on Friday, Oct. 25, 2024 —

The above "invariance of symmetry" document was written in 1978
for submission to the "Research Announcements" section of the
Bulletin of the American Mathematical Society .  This pro forma 
submission was, of course, rejected.  Though written before
I learned of similar underlying structures in the 1974 work of
R. T. Curtis on his "Miracle Octad Generator," it is not without
relevance to his work.

Tuesday, October 22, 2024

Tiger Symmetry

Filed under: General — Tags: , , — m759 @ 3:23 am

Thursday, September 19, 2024

Miss Princeton

Filed under: General — Tags: , — m759 @ 1:07 pm

Wednesday, August 28, 2024

Forms

Filed under: General — Tags: , — m759 @ 10:59 pm

'In the wide realm of the world
there are ancient forms,
incorruptible and eternal forms —
any one of them might be
the symbol that I sought."

— "The Writing of the God," by Jorge Luis Borges

"The governor showed him a cell
whose floor, walls, and vaulted ceiling
were covered by a drawing (in barbaric colors
that time, before obliterating, had refined)
of an infinite tiger. It was a tiger composed of
many tigers, in the most dizzying of ways;
it was crisscrossed with tigers, striped with tigers,
and contained seas and Himalayas and armies
that resembled other tigers."

— "The Zahir," by Jorge Luis Borges

Related art:

https://www.instagram.com/miapensa/.

Saturday, May 4, 2024

The Showalter Letter

Filed under: General — Tags: — m759 @ 2:24 am

Wikipedia on the director of Anne Hathaway's new film "The Idea of You" —

"[Michael] Showalter was born in Princeton, New Jersey, the son of
Elaine Showalter (née Cottler), an author, feminist literary critic,
and professor of English, and English Showalter, a Yale-educated
professor of 18th century French literature. His father is Episcopalian
and his mother is Jewish."

See also Elaine  Showalter in this journal on "O for Ophelia."

"But the tigers come at night . . ." — Anne Hathaway as Fantine

Saturday, March 23, 2024

Annals of Deceptive Fiction: Life of Pi

Filed under: General — Tags: — m759 @ 10:58 am

The image of a mathematician reading Life of Pi  in today's 8:36 AM ET post
suggests some further reading, not  about a fictional tiger —

As for the tiger . . .

"Liars prosper."

Wednesday, September 4, 2019

Tiger Leap

Filed under: General — Tags: , — m759 @ 7:18 am

(Continued)

Walter Benjamin on 'a tiger's leap into the past'

See also RIP: The Peace of Pi —

Wednesday, August 28, 2019

Tiger’s Leap  to 1905

Filed under: General — Tags: , , — m759 @ 3:03 pm

Walter Benjamin on 'a tiger's leap into the past'

See other posts
now tagged
Crosswicks Curse.

 

Click to enlarge:

Block Designs?

Tuesday, August 27, 2019

Tiger Leaps

Filed under: General — Tags: , , — m759 @ 10:33 am

Walter Benjamin on 'a tiger's leap into the past'

See also Tiger in this journal, esp.

The image “http://www.log24.com/log/pix05/050123-Tiger.JPG” cannot be displayed, because it contains errors.   and . . .

other "Death and the Spirit" posts.

Saturday, March 25, 2017

Like Decorations in a Cartoon Graveyard

Filed under: General,Geometry — Tags: , , , — m759 @ 4:00 am

Continued from April 11, 2016, and from

A tribute to Rothko suggested by the previous post

For the idea  of Rothko's obstacles, see Hexagram 39 in this journal.

Friday, December 16, 2016

Rothko’s Swamps

Filed under: General,Geometry — Tags: , , — m759 @ 2:45 am

“… you don’t write off an aging loved one
just because he or she becomes cranky.”

— Peter Schjeldahl on Rothko in The New Yorker ,
issue dated December 19 & 26, 2016, page 27

He was cranky in his forties too —

See Rothko + Swamp in this journal.

Related attitude —

From Subway Art for Times Square Church , Nov. 7

Saturday, March 2, 2013

Life of Pi

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

Earlier

Princeton Harvard Eating —

Harvard Math Department Pi Day event

"But the tigers come at night,
With their voices soft as thunder."

Les Miserables

Sunday, January 30, 2011

Sermon

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

Today's sermon, suggested by yesterday's New York midday and evening lottery— "6/18 and 4/18."

Background for 6/18— Go Tigers!

6/18

Background for 4/18— Requiem for an Editor*

4/18

* See "Sally Menke, Tarantino's Editor, Dies."

Friday, July 3, 2009

Friday July 3, 2009

Filed under: General — Tags: , , — m759 @ 6:00 am
Damnation Morning
continued

“The tigers of wrath are wiser
    than the horses of instruction.”

Blake

“… the moment is not
properly an atom of time
 but an atom of eternity.
 It is the first reflection
 of eternity in time, its first
attempt, as it were, at
       stopping time….”
 
Kierkegaard

Symmetry Axes
of the Square:

Symmetry axes of the square

(Damnation Morning)

From the cover of the
 Martin Cruz Smith novel
Stallion Gate:

Image of an atom from the cover of the novel 'Stallion Gate'

A Monolith
for Kierkegaard:


Images of time and eternity in memory of Michelangelo


Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

Rubén Darío

Related material:

The deaths of
 Ernest Hemingway
on the morning of
Sunday, July 2, 1961,
and of Alexis Arguello
on the morning of
Wednesday, July 1, 2009.
See also philosophy professor
Clancy Martin in the
London Review of Books
(issue dated July 9, 2009)
 on AA members as losers
“the ‘last men,’ the nihilists,
 the hopeless ones.”

Thursday, January 3, 2008

Thursday January 3, 2008

Filed under: General — Tags: — m759 @ 1:01 pm
Context-Sensitive Theology
continued:

The Revelation Game 
 
New Year’s reading for
the tigers of Princeton

 
Two reviews from the February 2008 Notices of the American Mathematical Society:

From a review of

A Certain Ambiguity
(A Mathematical Novel)

by Gaurav Suri and Hartosh Singh Bal
Princeton University Press
Hardcover, US$27.95, 281 pages —

“From the Habermas-Lyotard debate (see [1] for an introduction) to the Sokal hoax ([4]), to recent atheist manifestos on the bestseller lists (e.g., [2]) the question of foundations for intellectual thought and especially for intellectual debate has never been more critical or urgent.”

[1] M. Bérubé, What’s Liberal about the Liberal Arts? Classroom Politics and “Bias” in Higher Education, W. W. Norton, 2006.
[2] S. Harris, Letter to a Christian Nation, Knopf, 2006.
[4] A. Sokal and P. Bricmont, Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science, Picador, 1999.

Danny Calegari of Caltech

Also in the February Notices– a review of a book, Superior Beings: If They Exist, How Would We Know?, in which the author

“.. uses elementary ideas from game theory to create situations between a Person (P) and God (Supreme Being, SB) and discusses how each reacts to the other in these model scenarios….

In the ‘Revelation Game,’ for example,
the Person (P) has two options:
1) P can believe in SB’s existence
2) P can not believe in SB’s existence
The Supreme Being also has two options:
1) SB can reveal Himself
2) SB can not reveal Himself….

… [and] goals allow us to rank all the outcomes for each player from best… to worst…. The question we must answer is: what is the Nash equilibrium in this case?”

The answer is what one might expect from the American Mathematical Society:

“… the dominant strategy for both is when SB does not reveal Himself and P does not believe in His existence.”

Other strategies are, of course, possible. See last year’s entries.

See also
the life of John Nash,

http://www.log24.com/log/pix08/080103-BeautifulMind.jpg

for whom the above
equilibrium is named.

Sunday, December 30, 2007

Sunday December 30, 2007

Filed under: General — Tags: , — m759 @ 1:00 pm
The Christmas Tiger

Part I:
The Gauntlet

On Jonah Goldberg's new book Liberal Fascism– an attack on, among others, Woodrow Wilson:

"'… at some point,' Goldberg writes, 'it is necessary to throw down the gauntlet, to draw a line in the sand, to set a boundary, to cry at long last, "Enough is enough."'"

The Goldberg declaration is from a review in today's New York Times titled "Heil Woodrow!"

Part II:
Uncle Duke
Goes to Washington

Today's Doonesbury:

http://www.log24.com/log/pix07A/071230-Doonesbury2.jpg


Part III:
A Holiday Tradition

Dialogue from the classic Capra film "Mr. Smith Goes to Washington"–

SUMMERS: When the country needs men up there who know and have courage as it never did before, he's just gonna decorate a chair and get himself honored.

DARRELL: Oh, but he'll vote! Sure. Just like his colleague tells him to.

DIZ: "Yes, sir," like a Christmas tiger. He'll nod his head and vote…

REPORTERS: "Yes."

DIZ: You're not a Senator! You're an honorary stooge! You ought to be shown up!

The film starred
James Stewart,
Princeton
Class of 1932.

Part IV:
The Tigers of Princeton

The Christmas evening Pennsylvania Lottery 4-digit number was 0666, the Christian "number of the beast." For the beast itself, see the Dec. 3 Log24 entry "Santa's Polar Opposite?" with its link to a discussion of a metaphorical tiger at the South Pole. A more realistic version of the beast appeared in the news on Christmas evening.

The Christmas number may also be interpreted as a reference to 6/6/6, the graduation date of the Class of 2006 at Princeton University.


Part V:
"Heil Woodrow!"

 

As noted above, this title from a book review in today's New York Times refers to Woodrow Wilson, President of the United States (1913-1921) and President of Princeton University (1902-1910).

A suitable heraldic emblem
to accompany the Goldberg Heil:

http://www.log24.com/log/pix07A/071230-Shield.jpg

The Princeton Shield

For another heraldic emblem
related, if only in this journal,
to Princeton, see
Religious Symbolism
at Princeton:

Goldberg might prefer,
for his Heil,
the following variation:

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

Click on the Fahne (flag)
for further details.

Goldberg might also enjoy

An Unsuitable Santa:

The image “http://www.log24.com/log/pix07/070628-Santa.jpg” cannot be displayed, because it contains errors.
Santa from Aaron Sorkin's
Studio 60 on the Sunset Strip

Related material:

Taking Christ to Studio 60

Monday, August 6, 2007

Monday August 6, 2007

Filed under: General — Tags: , — m759 @ 8:00 am
The Divine Universals

"The tigers of wrath          
 are wiser than                
 the horses of instruction."

— William Blake,
Proverbs of Hell

From Shining Forth:

  The Place of the Lion, by Charles Williams, 1931, Chapter Eight:

"Besides, if this fellow were right, what harm would the Divine Universals do us? I mean, aren't the angels supposed to be rather gentle and helpful and all that?"

"You're doing what Marcellus warned you against… judging them by English pictures. All nightgowns and body and a kind of flacculent sweetness. As in cemeteries, with broken bits of marble. These are Angels– not a bit the same thing. These are the principles of the tiger and the volcano and the flaming suns of space."

 Under the Volcano, Chapter Two:

"But if you look at that sunlight there, then perhaps you'll get the answer, see, look at the way it falls through the window: what beauty can compare to that of a cantina in the early morning? Your volcanoes outside? Your stars– Ras Algethi? Antares raging south southeast? Forgive me, no." 

 A Spanish-English dictionary:

lucero m.
morning or evening star:
any bright star….
hole in a window panel
     for the admission of light….

Look at the way it
falls through the window….

— Malcolm Lowry

How art thou fallen from heaven,
O Lucifer, son of the morning!
— Isaiah 14:12

For more on Spanish
and the evening star,
see Plato, Pegasus, and
the Evening Star.

 Symmetry axes
of the square:

Symmetry axes of the square

(See Damnation Morning.)

From the cover of the
 Martin Cruz Smith novel
Stallion Gate:

Atom on cover of Stallion

"That old Jew
gave me this here."

Dialogue from the
Robert Stone novel
A Flag for Sunrise.

Related material:

A Mass for Lucero,

Log24, Sept. 13, 2006

Mathematics, Religion, Art

— and this morning's online
New York Times obituaries:

Cardinal Lustiger of Paris and jazz pianist Sal Mosca, New York Times obituaries on August 6, 2007

The above image contains summary obituaries for Cardinal Lustiger, Archbishop of Paris, 1981-2005, and for Sal Mosca, jazz pianist and teacher. In memory of the former, see all of the remarks preceding the image above. In memory of the latter, the remarks of a character in Martin Cruz Smith's Stallion Gate on jazz piano may have some relevance:

"I hate arguments. I'm a coward. Arguments are full of words, and each person is sure he's the only one who knows what the words mean. Each word is a basket of eels, as far as I'm concerned. Everybody gets to grab just one eel and that's his interpretation and he'll fight to the death for it…. Which is why I love music. You hit a C and it's a C and that's all it is. Like speaking clearly for the first time. Like being intelligent. Like understanding. A Mozart or an Art Tatum sits at the piano and picks out the undeniable truth."

Wednesday, July 18, 2007

Wednesday July 18, 2007

Filed under: General — Tags: — m759 @ 7:03 am
Burning Bright

“What is real?”
Pope Benedict XVI
in Brazil on May 13

Yesterday in
the Keystone State:

PA Lottery July 17, 2007: Mid-day 853, Evening 856

This suggests– via a search on “853-856” + “universals”– that we consult pages 853-856 in The Library of America’s William James: Writings 1902-1910.

Beginning on page 853 in this book, and ending on page 856, is an excerpt from a James address that the editor has titled…

The Tigers in India

“There are two ways of knowing things, knowing them immediately or intuitively, and knowing them conceptually or representatively.  Altho such things as the white paper before our eyes can be known intuitively, most of the things we know, the tigers now in India, for example, or the scholastic system of philosophy, are known only representatively or symbolically.

Suppose, to fix our ideas, that we take first a case of conceptual knowledge, and let it be our knowledge of the tigers in India, as we sit here.  Exactly what do we mean by saying that we here know the tigers? ….

Most men would answer that what we mean by knowing the tigers is having them, however absent in body, become in some way present to our thought…. At the very least, people would say that what we mean by knowing the tigers is mentally pointing towards them as we sit here….

… The pointing of our thought to the tigers is known simply and solely as a procession of mental associates and motor consequences that follow on the thought, and that would lead harmoniously, if followed out, into some ideal or real context, or even into the immediate presence, of the tigers….

… In all this there is no self-transcendency in our mental images taken by themselves. They are one phenomenal fact; the tigers are another; and their pointing to the tigers is a perfectly commonplace intra-experiential relation, if you once grant a connecting world to be there.  In short, the ideas and the tigers are in themselves as loose and separate, to use Hume’s language, as any two things can be, and pointing means here an operation as external and adventitious as any that nature yields.

I hope you may agree with me now that in representative knowledge there is no special inner mystery, but only an outer chain of physical or mental intermediaries connecting thought and thing. To know an object is here to lead to it through a context which the world supplies….

Let us next pass on to the case of immediate or intuitive acquaintance with an object, and let the object be the white paper before our eyes…. What now do we mean by ‘knowing’ such a sort of object as this?  For this is also the way in which we should know the tiger if our conceptual idea of him were to terminate by having led us to his lair?

… the paper seen and the seeing of it are only two names for one indivisible fact which, properly named, is the datum, the phenomenon, or the experience. The paper is in the mind and the mind is around the paper, because paper and mind are only two names that are given later to the one experience, when, taken in a larger world of which it forms a part, its connections are traced in different directions.1

James, Writings 1902-1910, page 856

The same volume also contains
James’s The Varieties of
Religious Experience.

“The Tigers in India” is
only a part of a 20-page
James address originally titled
The Knowing of Things Together
(my emphasis).

Sunday, October 22, 2006

Sunday October 22, 2006

Filed under: General — Tags: — m759 @ 5:01 pm
Go Tigers!

Brooke Shields

On this date:

“In 1746,
Princeton University
in New Jersey received
its charter.”

Today in History
by The Associated Press

“The charter… authorized
the erection of a college….”

Princeton University

Tuesday, March 14, 2006

Tuesday March 14, 2006

Filed under: General — Tags: — m759 @ 12:00 pm
Fearful Symmetry
and Minkowski Space-Time

(For the tigers of Princeton,
a selection suggested by
the work of Richard Parker
 on Lorentzian lattices)

The image “http://www.log24.com/log/pix06/060314-Lorentzian.jpg” cannot be displayed, because it contains errors.

Sunday, August 7, 2005

Sunday August 7, 2005

Filed under: General — Tags: — m759 @ 7:20 am
Presbyterian Justice

News from today’s New York Times:

The Rev. Dr. Theodore Alexander Gill Sr., a Presbyterian theologian, a philosophy teacher, and an influential provost emeritus of John Jay College of Criminal Justice in Manhattan, died at 85 on June 10 in Princeton.  In retirement from John Jay, The Rev. Dr. Gill was theologian in residence at Nassau Presbyterian Church in Princeton.

In memory of The Rev. Dr. Gill:

Religious Symbolism at Princeton
    (on Nassau Presbyterian Church),
Pro-Semitism
    (on number theory at Princeton),
For the Mad Musicians of Princeton,
     (on Schroeder and Bernstein),
Movie Date and its preceding entries
   (on Princeton’s St. John von Neumann),
Why Me?
   (for Princeton theologian Elaine Pagels),
Notes on Literary and Philosophical Puzzles
   (Princeton’s John Nash as Ya Ya Fontana), and
Go Tigers!
   (for the Princeton Evangelical Fellowship).

For a more conventional memorial, see

The image “http://www.log24.com/log/pix05B/050807-SFTS-Logo.gif” cannot be displayed, because it contains errors.

the obituary from

San Francisco Theological Seminary.

Saturday, January 22, 2005

Saturday January 22, 2005

Filed under: General — Tags: — m759 @ 9:00 am

Go Tigers!

Recommended reading for the
Princeton Evangelical Fellowship (PEF):

Walter Kirn, Lost in the Meritocracy,
Atlantic Monthly Jan.-Feb. 2005

The PEF in action:

The image “http://www.log24.com/log/pix05/050122-PEF.jpg” cannot be displayed, because it contains errors.

"Only by the form, the pattern,
Can words or music reach
The stillness."

— T. S. Eliot 

Wednesday, January 19, 2005

Wednesday January 19, 2005

Filed under: General — Tags: , , — m759 @ 3:00 pm

But seriously…

A follow-up to the previous "tiger" entry (which was about an old but good dirty joke).

I just subscribed to The New York Review of Books online for another year, prompted by my desire to read Roger Shattuck on Rimbaud, a tiger of another sort:

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.  (See Sunday's Death and the Spirit, Part II.)

Tuesday, January 18, 2005

Tuesday January 18, 2005

Filed under: General — Tags: , , — m759 @ 1:44 pm
Death and
the Spirit, Part III

In memory of comedian
Gene Baylos, who died
on Jan. 10, 2005:

From the dark jungle
as a tiger bright,
Form from the viewless Spirit
leaps to light.

— Rumi, "Reality and Appearance"

The image “http://www.log24.com/log/pix05/050118-Tiger2.gif” cannot be displayed, because it contains errors.

 

Related material:

Sunday, January 16, 2005

Sunday January 16, 2005

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

Death and the
Spirit, Part II

Readings

Are you a lucky little lady
in The City of Light
Or just another lost angel…

City of Night

— Jim Morrison, L.A. Woman

Fourmillante cité,
cité pleine de rêves,
Où le spectre en plein jour
raccroche le passant

— Baudelaire,
Les Fleurs du Mal,
and T. S. Eliot,
Notes to The Waste Land

"When you got the mojo, brother —
when you're on the inside —
the world is fantastic."

— Pablo Tabor in Robert Stone's
A Flag for Sunrise,
Knopf, 1981, p. 428

Now it was Avril's turn to understand and he was frightened out of his wits.

"The Science of Luck," he said cautiously. "You watch, do you?  That takes a lot of self-discipline."

"Of course it does, but it's worth it.  I watch everything, all the time.  I'm one of the lucky ones.  I've got the gift.  I knew it when I was a kid, but I didn't grasp it."  The murmur had intensified.  "This last time, when I was alone so long, I got it right.  I watch for every opportunity and I never do the soft thing.  That's why I succeed."

Avril was silent for a long time.  "It is the fashion," he said at last.  "You've been reading the Frenchmen, I suppose?  Or no, no, perhaps you haven't.  How absurd of me."

"Don't blether."  The voice, stripped of all its disguises, was harsh and naive.  "You always blethered.  You never said anything straight.  What do you know about the Science of Luck?  Go on, tell me.  You're the only one who's understood at all.  Have you ever heard of it before?"

"Not under that name."

"I don't suppose you have.  That's my name for it.  What's its real name?"

"The Pursuit of Death."

— Margery Allingham,
Chapter Seventeen,
"On the Staircase," from
The Tiger in the Smoke

Anagrams

In memory of Danny Sugerman,
late manager of The Doors:

The image “http://www.log24.com/log/pix05/050116-Sugerman.jpg” cannot be displayed, because it contains errors.
Danny Sugerman
Photo by
Frank Alan Bella, 2002

"Mr Mojo Risin" = "Jim Morrison."
"Audible Era" = "Baudelaire."
"Bad Rumi" = "Rimbaud."

From the dark jungle
as a tiger bright,
Form from the viewless Spirit
leaps to light.

— Rumi,  "Reality and Appearance,"
translated by R. A. Nicholson

(See also Death and the Spirit
from Twelfth Night, 2005, the date
of Danny Sugerman's death.)

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