Log24

For some mathematical background, see Deep + Hardy.

Related entertainment —

Related non-entertainment —

"Wer gab uns den Schwamm, um den ganzen Horizont wegzuwischen?"

— Nietzsche, "Der Tolle Mensch" 
 

A memorable phrase —

"the transcendental horizon of the ‘I’."

For some backstory, see a Google search for

Marion + transcendental + horizon.

For a perhaps more intelligible horizon, see

Line at Infinity  in this journal.

“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:

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

The title is from a post of July 27.

From earlier posts (Feb. 20, 2009) —

Midrash for LA —

The New York Times  eulogizes a man who died Friday —

“Rabbi Steinsaltz was a prolific and wide-ranging writer
and a sharp observer of humanity who wrote more than
60 books on philosophy, mysticism, theology, even zoology.
His study of kabbalah, ‘The Thirteen Petalled Rose,’ is
considered a classic and has been translated into eight languages.”

Another classic of Jewish thought:

Thoughts of the young Carl Reiner as rendered above in 1967 —

“Somewhere, someplace… there must be a lost horizon…
A Shangri-La where a man can find peace, happiness,
and lots of naked ladies.”

Voilà.

In remembrance of Else Blangsted and Nancy Stark Smith,
who each reportedly died on May 1, 2020 —

Posts tagged Mayday 2020.

The previous post suggests a search for Buber in this journal
that yields a passage from New Year's Eve 2017 —

" As for 'that you in which the lines of relation, though parallel,
intersect,' and 'intimations of eternity,' see Log24 posts on
the concept 'line at infinity' as well as 'Lost Horizon.' "

Related illustrations — 

From Pi Day 2017 —

"Don't want to end up a cartoon in a cartoon graveyard."

From April 20, 2019 —

From "A History of Violence" —

"In 'Sophistry,' a new play by Jonathan Marc Sherman
at the Playwrights Horizons Studio, a popular tenured
professor stands accused of sexual harassment
by a male student."

— Frank Rich in The New York Times , theater review
on October 12, 1993

"At which point another play, inchoate but arresting,
edges into view." — Rich, ibid.

"Johansson began acting during childhood,
after her mother started taking her to auditions.
She made her professional acting debut
at the age of eight in the off-Broadway production
of 'Sophistry' with Ethan Hawke, at New York's
Playwrights Horizons."

— IMDb Mini Biography by: Pedro Borges 

" 'Suddenly, I was 19 again and I started to remember
all the men I'd known who had taken advantage of
the fact that I was a young woman who didn't yet have
the tools to say no, or to understand the value of
my own self-worth,' the Avengers star described. 
'I had many relationships both personal and professional
where the power dynamic was so off that I had to create
a narrative in which I was the cool girl who could hang in
and hang out, and that sometimes meant compromising
what felt right for me . . . . ' "

— Scarlett Johansson yesterday at the 2018 Women's March
in Los Angeles, as reported in E! News .

Image in a Log24 post
of March 12, 2009.

Continued from Zen and Language Games
(a post of May 2, 2003, written on March 1, 2002)

From The Harvard Crimson  on St. Andrew's Day 2017 —

See also a larger, clearer view of the titles in the above file photo.

Dialogue suggested by the above Harvard Crimson  line
"I am a book today . . . . I know it all." —

A problem child* of sorts in the 2017 film "Gifted" —

Mary- "Maybe this school isn't as great as you think it is."

Mary is returned to the place of her examination.

Professor- "Mary, you knew that the problem was incorrect, 
            why didn't you say anything?"

Mary- "Frank says I'm not supposed to correct older people. 
       Nobody likes a smart-ass."

* "Problem Child" was a working title related to a novel
    Heinlein wrote in 1941, Beyond This Horizon —

In memory of a resident of the Upper West Side
who reportedly died on Twelfth Night 2018 —

“… the horizon is not the limit of meaning,
but that which extends meaning
from what is directly given
to the whole context in which it is given,
including a sense of a world.”

— David Vessey, Department of Philosophy,
Grand Valley State University,
Gadamer and the Fusion of Horizons,
International Journal of Philosophical Studies, 
17/4 (2009), 531-42.

Recent posts involving the English pronoun IT referred to
classic tales of horror by Madeleine L'Engle and Stephen King.

Those posts suggest some further remarks by Martin Buber: 

THE WORLD IS TWOFOLD for man
     in accordance with his twofold attitude.
The attitude of man is twofold
     in accordance with the two basic words he can speak.
The basic words are not single words but word pairs.
One basic word is the word pair I-You.
The other basic word is the word pair I-It;
     but this basic word is not changed when
     He or She takes the place of It.
Thus the I of man is also twofold.
For the I of the basic word I-You is different from
     that in the basic word I-It.

— Buber, Martin. I and Thou, Trans. Kaufmann
     (p. 53). Kindle Edition. 

Four German pronouns from the above passage
by Martin Buber lead to six pronoun pairs:

ich-du, ich-es, ich-sie, du-es, du-sie, es-sie.

This is in accordance with some 1974 remarks by
Marie-Louise von Franz —

The following passage by Buber may confuse readers of
L'Engle and King with its use, in translation, of "it" instead of
the original German "sie" ("she," corresponding to "die Welt") —

Here, for comparison, are the original German and the translation.

As for "that you in which the lines of relation, though parallel,
intersect," and "intimations of eternity," see Log24 posts on
the concept "line at infinity" as well as "Lost Horizon."

Recommended —

Links to the poems:  "Storm Beach" and "For You." 

* See "The Space of Horizons" and A Search for Crombie.

Frogs:

"Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time."

— Freeman Dyson (See July 22, 2011)

A Rhetorical Question:

Robert Osserman in 2004—

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

Who bestowed the magic kiss on the mathematical frog?"

A Rhetorical Answer:

Above: Amy Adams in "Sunshine Cleaning"

Related material:

• "Decomposition" in this journal 
• "What is Truth (continued)," May 1, 2012
• The Boolean satisfiability problem (SAT)
• Remarks on SAT by Stanislav Busygin
• A related remark on complexity by Busygin
• Hashtag #sexyface and the Empty Chair

"Some mathematicians are birds, others are frogs.
Birds fly high in the air and survey broad vistas of
mathematics out to the far horizon. They delight in
concepts that unify our thinking and bring together
diverse problems from different parts of the
landscape. Frogs live in the mud below and see
only the flowers that grow nearby. They delight in
the details of particular objects, and they solve
problems one at a time. I happen to be a frog, but
many of my best friends are birds. The main theme
of my talk tonight is this. Mathematics needs both
birds and frogs. Mathematics is rich and beautiful
because birds give it broad visions and frogs give it
intricate details. Mathematics is both great art and
important science, because it combines generality
of concepts with depth of structures. It is stupid to
claim that birds are better than frogs because they
see farther, or that frogs are better than birds
because they see deeper. The world of mathematics
is both broad and deep, and we need birds and
frogs working together to explore it.

This talk is called the Einstein lecture…."

— Freeman Dyson, Notices of the American
Mathematical Society , February 2009

The Didion reading was suggested by the "6212" in yesterday evening's New York Lottery.

Benoît Mandelbrot died on Oct. 14.
 

— New York Lottery on Thursday, Oct. 14, 2010

Related material on 109: See 1/09, 2009.
Related material on 060: See Hexagram 60 of the I Ching  and…

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.

For Christopher Fry
and the White Goddess:

The Edge of Eternity

Christian humanist playwright Christopher Fry, author of The Lady’s Not for Burning, died at 97 on June 30, 2005.

From Log24 on June 30:

Robert Graves, author of
The White Goddess:
A Historical Grammar of Poetic Myth—

How may the King hold back?
Royally then he barters life for love.

Or of the undying snake from chaos hatched,
Whose coils contain the ocean,
Into whose chops with naked sword he springs,
Then in black water, tangled by the reeds,
Battles three days and nights…

From Cold Mountain:

“He sat awhile on a rock, and then got up and walked all morning through the dim woods. The track was ill used, so coiled and knotted he could not say what its general tendency was. It aimed nowhere certain but up. The brush and bracken grew thick in the footway, and the ground seemed to be healing over, so that in some near future the way would not even remain as scar. For several miles it mostly wound its way through a forest of immense hemlocks, and the fog lay among them so thick that their green boughs were hidden. Only the black trunks were visible, rising into the low sky like old menhirs stood up by a forgotten race to memorialize the darkest events of their history….

They climbed to a bend and from there they walked on great slabs of rock. It seemed to Inman that they were at the lip of a cliff, for the smell of the thin air spoke of considerable height, though the fog closed off all visual check of loftiness….

Then he looked back down and felt a rush of vertigo as the lower world was suddenly revealed between his boot toes. He was indeed at the lip of a cliff, and he took one step back…. The country around was high, broken. Inman looked about and was startled to see a great knobby mountain forming up out of the fog to the west, looming into the sky.  The sun broke through a slot in the clouds, and a great band of Jacob’s ladder suddenly hung in the air like a gauze curtain between Inman and the blue mountain….

Inman looked at the big grandfather mountain and then he looked beyond it to the lesser mountains as they faded off into the southwest horizon, bathed in faint smoky haze. Waves of mountains. For all the evidence the eye told, they were endless. The grey overlapping humps of the farthest peaks distinguished themselves only as slightly darker values of the pale grey air. The shapes and their ghostly appearance spoke to Inman in a way he could not clearly interpret. They graded off like the tapering of pain from the neck wound as it healed.”

See also the entries of July 3.

The crone figure in this section of Cold Mountain is not entirely unrelated to the girl accused of being a witch in Fry’s play and to Graves’s White Goddess.

From Fry’s obituary in The Guardian:

“Though less of a public theorist than Eliot, Fry still believed passionately in the validity of poetic drama. As he wrote in the magazine Adam: ‘In prose, we convey the eccentricity of things, in poetry their concentricity, the sense of relationship between them: a belief that all things express the same identity and are all contained in one discipline of revelation.'”

From Fry’s obituary in today’s New York Times:

“His plays radiated an optimistic faith in God and humanity, evoking, in his words, ‘a world in which we are poised on the edge of eternity, a world which has deeps and shadows of mystery, and God is anything but a sleeping partner.’ He said he wrote his plays in poetry because that was ‘the language in which man expresses his own amazement’ at the complexity both of himself and of a reality which, beneath the surface, was ‘wildly, perilously, inexplicably fantastic.'”

Intersections

1. Blue Ridge meets Black Mountain,

2. Vertical meets horizontal in music,

3. The timeless meets time in religion.

Details:

1. Blue Ridge, Black Mountain

“Montreat College is located in the beautiful Blue Ridge Mountains of Western North Carolina…. The Black Mountain Campus is… three miles from the main campus in the historic town of Black Mountain.”

Black Mountain College was “established on the Blue Ridge Assembly grounds outside the town of Black Mountain in North Carolina in the fall of 1933.”

USA Today, May 15, 2005, on Billy Graham:

“MONTREAT, N.C. — … It’s here at his… homestead, where the Blue Ridge meets the Black Mountain range east of Asheville, that Graham gave a rare personal interview.”

See also the following from June 24:

“No bridge reaches God, except one…
God’s Bridge: The Cross.”

— Billy Graham Evangelistic Association,
according to messiahpage.com

For some remarks more in the spirit of Black Mountain than of the Blue Ridge, see today’s earlier entry on pianist Grete Sultan and composer Tui St. George Tucker.

2. Vertical, Horizontal in Music

Richard Neuhaus on George Steiner’s
Grammars of Creation:

 “… the facts of the world are not and will never be ‘the end of the matter.’ Music joins grammar in pointing to the possibility, the reality, of more. He thinks Schopenhauer was on to something when he said music will continue after the world ends.

‘The capacity of music to operate simultaneously along horizontal and vertical axes, to proceed simultaneously in opposite directions (as in inverse canons), may well constitute the nearest that men and women can come to absolute freedom.  Music does “keep time” for itself and for us.'”

3. Timeless, Time

A Trinity Sunday sermon quotes T. S. Eliot:

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint.”

See also The Diamond Project.

ART WARS:
Mother of Beauty

In memory of architect Pierre Koenig…

Mother of Beauty: A Note on Modernism.

“… Case Study House #22 … was high drama — one in which the entire city becomes part of the architect’s composition. Approached along a winding street set high in the Hollywood Hills, the house first appears as a blank concrete screen. From here, the visitor steps out onto a concrete deck that overlooks a swimming pool. Just beyond it, the house’s living room — enclosed in a glass-and steel-frame — cantilevers out from the edge of the hill toward the horizon.

The house was immortalized in a now famous image taken by the architectural photographer Julius Shulman. In it, two women, clad in immaculate white cocktail dresses, are perched on the edge of their seats in the glass-enclosed living room, their pose suggesting a kind of sanitized suburban bliss. A night view of the city spreads out beneath them, an endless grid of twinkling lights that perfectly captures the infinite hopes of the postwar American dream….

    “My blue dream…”  
— F. Scott Fitzgerald

Perhaps no house, in fact, better sums up the mix of outward confidence and psychic unease that defined Cold War America….”

— Los Angeles Times, Nicolai Ouroussoff

Toy

“If little else, the brain is an educational toy.  While it may be a frustrating plaything — one whose finer points recede just when you think you are mastering them — it is nonetheless perpetually fascinating, frequently surprising, occasionally rewarding, and it comes already assembled; you don’t have to put it together on Christmas morning.

The problem with possessing such an engaging toy is that other people want to play with it, too.  Sometimes they’d rather play with yours than theirs.  Or they object if you play with yours in a different manner from the way they play with theirs.  The result is, a few games out of a toy department of possibilities are universally and endlessly repeated.  If you don’t play some people’s game, they say that you have ‘lost your marbles,’ not recognizing that,

while Chinese checkers is indeed a fine pastime, a person may also play dominoes, chess, strip poker, tiddlywinks, drop-the-soap or Russian roulette with his brain.

One brain game that is widely, if poorly, played is a gimmick called ‘rational thought.’ “

— Tom Robbins, Even Cowgirls Get the Blues

Sol LeWitt
June 12, 1969:

“I took the number twenty-four and there’s twenty-four ways of expressing the numbers one, two, three, four.  And I assigned one kind of line to one, one to two, one to three, and one to four.  One was a vertical line, two was a horizontal line, three was diagonal left to right, and four was diagonal right to left.  These are the basic kind of directions that lines can take…. the absolute ways that lines can be drawn.   And I drew these things as parallel lines very close to one another in boxes.  And then there was a system of changing them so that within twenty-four pages there were different arrangements of actually sixteen squares, four sets of four.  Everything was based on four.  So this was kind of a… more of a… less of a rational… I mean, it gets into the whole idea of methodology.”

Yes, it does.
See Art Wars, Poetry’s Bones, and Time Fold.

Memories, Dreams, Reflections

Saul Steinberg in The New York Review of Books issue dated August 15, 2002, page 32:

“The idea of reflections came to me in reading an observation by Pascal, cited in a book by W. H. Auden, who wrote an unusual kind of autobiography by collecting all the quotations he had annotated in the course of his life, which is a good way of displaying oneself, as a reflection of these quotations.  Among them this observation by Pascal, which could have been made only by a mathematician….”

Pascal’s observation is that humans, animals, and plants have bilateral symmetry, but in nature at large there is only symmetry about a horizontal axis… reflections in water, nature’s mirror.

This seems related to the puzzling question of why a mirror reverses left and right, but not up and down.

The Steinberg quote is from the book Reflections and Shadows, reviewed here.

Bibliographic data on Auden’s commonplace book:

AUTHOR      Auden, W. H. (Wystan Hugh),              1907-1973. TITLE       A Certain World; a Commonplace Book   
            [selected by] W. H. Auden.
PUBLISHER   New York, Viking Press [1970]
SUBJECT     Commonplace-books.

A couple of websites on commonplace books:

Quotation Collections and

Weblets as Commonplace Books.

A classic:

The Practical Cogitator – The Thinker’s Anthology, 
by Charles P. Curtis, Jr., and Ferris Greenslet,
Houghton Mifflin Company Boston, Massachusetts
c 1962 Third Edition – Revised and Enlarged