See a search for Borges + Line in this journal.
Sunday, January 24, 2016
Wednesday, March 2, 2011
Labyrinth of the Line
“Yo sé de un laberinto griego que es una línea única, recta.”
—Borges, “La Muerte y la Brújula”
“I know of one Greek labyrinth which is a single straight line.”
—Borges, “Death and the Compass”
Another single-line labyrinth—
Robert A. Wilson on the projective line with 24 points
and its image in the Miracle Octad Generator (MOG)—
Related material —
The remarks of Scott Carnahan at Math Overflow on October 25th, 2010
and the remarks at Log24 on that same date.
A search in the latter for miracle octad is updated below.
This search (here in a customized version) provides some context for the
Benedictine University discussion described here on February 25th and for
the number 759 mentioned rather cryptically in last night’s “Ariadne’s Clue.”
Update of March 3— For some historical background from 1931, see The Mathieu Relativity Problem.
Wednesday, February 24, 2021
Annals of Dim Antiquity
“Twenty-four glyphs, each one representing not a letter, not a word,
but a concept, arranged into four groups, written in Boris’s own hand,
an artifact that seemed to have resurrected him from the dead. It was
as if he were sitting across from Bourne now, in the dim antiquity of
the museum library.
This was what Bourne was staring at now, written on the unfolded
bit of onionskin.”
— The Bourne Enigma , published on June 21, 2016
Passing, on June 21, 2016, into a higher dimension —
For those who prefer Borges to Bourne —
Sunday, January 21, 2018
At Which Point
"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.
Wednesday, November 1, 2017
Cameron on All Saints’ Day
"Nowdays, Halloween involves plastic figures of ghosts and bats
bought from the supermarket; this is driven by commerce and
in some people’s view is an American import. But it is clear that
this time of year was traditionally regarded as one where the barrier
between this world and the other was low, and supernatural
manifestations were to be expected."
Remarks related to another "barrier" and vértigo horizontal —
See also a search for Horizon + "Western Australia" in this journal.
From that search: A sort of horizon, a "line at infinity," that is perhaps
more meaningful to most Cameron readers than the above remarks
by Borges —
Thursday, May 8, 2014
Wrinkles in Time
Rivka Galchen, in a piece mentioned here in June 2010—
On Borges: Imagining the Unwritten Book
"Think of it this way: there is a vast unwritten book that the heart reacts to, that it races and skips in response to, that it believes in. But it’s the heart’s belief in that vast unwritten book that brought the book into existence; what appears to be exclusively a response (the heart responding to the book) is, in fact, also a conjuring (the heart inventing the book to which it so desperately wishes to respond)."
Related fictions
Galchen's "The Region of Unlikeness" (New Yorker , March 24, 2008)
Ted Chiang's "Story of Your Life." A film adaptation is to star Amy Adams.
… and non-fiction
"There is such a thing as a 4-set." — January 31, 2012
Saturday, November 24, 2012
Reappearing All Over Again
For the title, see the phrase "reappearing number" in this journal.
Some related mathematics—
the Greek labyrinth of Borges, as well as…
Note that "0" here stands for "23," while ∞ corresponds to today's date.
Sunday, November 18, 2012
Kernel
Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012—
"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'
The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"
The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."
These same words in a different tongue— "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)
"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."
— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization , Pantheon
Books, 1946, page 142
Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.
Tuesday, April 10, 2012
Death on Good Friday
Edward Reed Whittemore Jr. was born |
In memoriam:
PART I —
PART II —
Monday, February 20, 2012
Coxeter and the Relativity Problem
In the Beginning…
"As is well known, the Aleph is the first letter of the Hebrew alphabet."
– Borges, "The Aleph" (1945)
From some 1949 remarks of Weyl—
"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."
— Hermann Weyl, "Relativity Theory as a Stimulus in Mathematical Research," Proceedings of the American Philosophical Society , Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949 (Dec. 30, 1949), pp. 535-541
Weyl in 1946—:
"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."
— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16
Coxeter in 1950 described the elements of the Galois field GF(9) as powers of a primitive root and as ordered pairs of the field of residue-classes modulo 3—
"… the successive powers of the primitive root λ or 10 are
λ = 10, λ2 = 21, λ3 = 22, λ4 = 02,
λ5 = 20, λ6 = 12, λ7 = 11, λ8 = 01.
These are the proper coordinate symbols….
(See Fig. 10, where the points are represented in the Euclidean plane as if the coordinate residue 2 were the ordinary number -1. This representation naturally obscures the collinearity of such points as λ4, λ5, λ7.)"
Coxeter's Figure 10 yields...
The Aleph
The details:
Coxeter's phrase "in the Euclidean plane" obscures the noncontinuous nature of the transformations that are automorphisms of the above linear 2-space over GF(3).
Monday, January 23, 2012
Labyrinth
"Yo sé de un laberinto griego que es una línea única, recta."
—Borges, "La Muerte y la Brújula"
"I know of one Greek labyrinth which is a single straight line."
—Borges, "Death and the Compass"
Sunday, June 19, 2011
Monday, May 9, 2011
Queen’s Gambit*
From March 9 four years ago—
* See this journal and the novel.
Update of 10 AM May 9—
Midrash for Gnostics —
A post linked to under "this journal" (above) has a brief discussion of theology and Wallace Stevens—
"Professor Eucalyptus in 'Ordinary Evening' XIV, for example, 'seeks/ God in the object itself '…."
I have more confidence that God is to be found in the Ping Pong balls of the New York Lottery.
This suggests a check of yesterday's NY numbers. They were… Midday 780, Evening 302.
A search for 780 in this journal yields a post quoting The Scotsman 's reporter Rhiannon Edward.
Related material:
Rhiannon's Scotsman story of May 6—
Rapist gets 20 years after justice system finally believes his victims
See also this journal on May 7 —
For yesterday's NY evening 302, see the "780" post involving Rhiannon—
Glenn Ford as a playboy from Argentina —
— and "302" interpreted as "3/02," which yields…
"Yo sé de un laberinto griego que es una línea única, recta."
—Borges, "La Muerte y la Brújula"
"I know of one Greek labyrinth which is a single straight line."
—Borges, "Death and the Compass"
For some background music, click here.
Sunday, March 6, 2011
Sermon
The Year of Magical Realism
"The non-linear story is narrated via different time frames,
a technique derived from the Argentine writer Jorge Luis Borges
(as in The Garden of Forking Paths )."
—Wikipedia on One Hundred Years of Solitude
One year ago today, in "Deconstructing Alice"—
"When you come to a fork in the road, take it." –Yogi Berra
Friday, January 7, 2011
Ayn Sof
(A continuation of this morning's Coxeter and the Aleph)
"You've got to pick up every stitch… Must be the season of the witch."
— Donovan song at the end of Nicole Kidman's "To Die For"
Mathematics and Narrative, Illustrated | |
Narrative |
"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth, in order to show
that the lower world is the map and mirror of the higher; for Cantor's
Mengenlehre , it is the symbol of transfinite numbers,
of which any part is as great as the whole."
— Borges, "The Aleph"
From WorldLingo.com —
|
"Infinite Jest… now stands as the principal contender
for what serious literature can aspire to
in the late twentieth and early twenty-first centuries."
— All Things Shining, a work of pop philosophy published January 4th
"You're gonna need a bigger boat." — Roy Scheider in "Jaws"
"We're gonna need more holy water." — "Season of the Witch," a film opening tonight
See also, with respect to David Foster Wallace, infinity, nihilism,
and the above reading of "Ayn Sof" as "nothingness,"
the quotations compiled as "Is Nothing Sacred?"
Wednesday, January 31, 2007
Wednesday January 31, 2007
“At times, bullshit can only be
countered with superior bullshit.”
— Norman Mailer
“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962
— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)
Goguen does not give a source for this alleged “thoughts of God” statement.
A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.
Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.
Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.
Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.
Gudder may have been misquoting some other author’s blather about Kepler. Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature—
“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?
Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of Nature.
Sophia. Then these thoughts of Nature are also thoughts of God.
Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”
Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.
Friday, December 15, 2006
Friday December 15, 2006
Putting the
X
in Xmas
“In one of Jorge Luis Borges’s best-known short stories, ‘Pierre Menard, Author of the Quixote,’ a 20th-century French writer sets out to compose a verbatim copy of Cervantes’s 17th-century masterpiece simply because he thinks he can, originality perhaps not being all it’s cracked up to be. He manages two chapters word for word, a spontaneous duplicate that Borges’s narrator finds to be ‘infinitely richer’ than the original because it contains all manner of new meanings and inflections, wrenched as it is from its proper time and context….”
[An artist’s version of a newspaper is]…. “a drawing of a copy of a version of what happened, holding a mirror up to nature with a refraction or two in between. In a way that mixes Borges with a dollop of Jean Baudrillard and a heavy helping of Walter Benjamin, the work also upends ideas….” |
The Work:
Pennsylvania Lottery
December 2006
Daily Number (Day):
Borges, Menard’s Quixote, and The Harvard Crimson |
Mon., Dec. 11: 133 |
Baudrillard (via a white Matrix) |
Sun., Dec. 10: 569 |
Benjamin and a black view of life in “The Garden of Allah” |
Sat., Dec. 9: 602 |
Click on numbers
for commentary.
referenced directly in the
commentary. For Baudrillard,
see Richard Hanley on
Baudrillard and The Matrix:
“There is nothing new under the sun. With the death of the real, or rather with its (re)surrection, hyperreality both emerges and is already always reproducing itself.” –Jean Baudrillard
Sunday, December 10, 2006
Sunday December 10, 2006
"Like all men of the Library,
I have traveled in my youth."
— Jorge Luis Borges,
The Library of Babel
"Papá me mandó un artículo
de J. G. Ballard en el que
se refiere a cómo el lugar
de la muerte es central en
nuestra cultura contemporánea."
— Sonya Walger,
interview dated September 14
(Feast of the Triumph of the Cross),
Anno Domini 2006
Sonya Walger,
said to have been
born on D-Day,
the sixth of June,
in 1974
Walger's father is, like Borges,
from Argentina.
She "studied English Literature
at Christ Church College, Oxford,
where she received
a First Class degree…. "
"… un artículo de J. G. Ballard…."–
A Handful of Dust, by J. G. Ballard
(The Guardian, March 20, 2006):
"… The Atlantic wall was only part of a huge system of German fortifications that included the Siegfried line, submarine pens and huge flak towers that threatened the surrounding land like lines of Teutonic knights. Almost all had survived the war and seemed to be waiting for the next one, left behind by a race of warrior scientists obsessed with geometry and death.
Death was what the Atlantic wall and Siegfried line were all about….
… modernism of the heroic period, from 1920 to 1939, is dead, and it died first in the blockhouses of Utah beach and the Siegfried line…
Modernism's attempt to build a better world with the aid of science and technology now seems almost heroic. Bertolt Brecht, no fan of modernism, remarked that the mud, blood and carnage of the first world war trenches left its survivors longing for a future that resembled a white-tiled bathroom. Architects were in the vanguard of the new movement, led by Le Corbusier and the Bauhaus design school. The old models were thrown out. Function defined form, expressed in a pure geometry that the eye could easily grasp in its entirety."
"This is the garden of Apollo,
the field of Reason…."
— John Outram, architect
(Click on picture for details.)
Related material:
Thursday, August 17, 2006
Thursday August 17, 2006
Special Topics
From a review by Liesl Schillinger in the Aug. 13 New York Times of a new novel by Marisha Pessl:
“… Special Topics in Calamity Physics tells the story of a wise newcomer who joins a circle of students who orbit a charismatic teacher with a tragic secret. The newcomer, a motherless waif named Blue van Meer, spent most of her life driving between college towns with her genius poli-sci professor father, Gareth…. Gareth is fond of making oracular statements, which his daughter laps up as if they were Churchill’s: ‘Everyone is responsible for the page-turning tempo of his or her Life Story,’ he tells her. And, he cautions, ‘never try to change the narrative structure of someone else’s story.’
…. Heeding Gareth van Meer’s dictum that the most page-turning read known to man is the collegiate curriculum, with its ‘celestial, sweet set of instructions, culminating in the scary wonder of the Final Exam,’ Pessl structures Blue’s mystery like a kind of Great Books class…. A professor is all-powerful, Gareth liked to tell his daughter, he puts ‘a veritable frame around life,’ and ‘organizes the unorganizable. Nimbly partitions it into modern and postmodern, renaissance, baroque, primitivism, imperialism and so on. Splice that up with Research Papers, Vacation, Midterms. All that order– simply divine.’ Blue’s syllabus also includes a murder or two. Her book’s last pages are a final exam. You will be relieved to learn it is mostly multiple choice, and there is no time limit.”
Multiple choice:
The examination below, taken from a page by a scholar at a Jesuit university, is on the Borges story “The Garden of Forking Paths”– a classic of multiple choice.
No time limit:
See the first question.
Examination on
“The Garden of Forking Paths“
“What is the meaning of the idea expressed by Yu Tsun that ‘everything happens to a man precisely, precisely now. Centuries of centuries and only in the present do things happen’? What is the significance of the emphasis on the present moment, the here and now? Is this related to the carpe diem (‘seize the day’) idea? How? How is the present effectively connected to the past and the future? How is the present associated simultaneously to choices, actions, and consequences? How is the present moment relevant to the idea of the ‘forking paths’? What is the symbolic meaning of forking paths when understood as a crossroads? What is a person confronted with when standing at a crossroads? What are the implications of a choice of road? May this be connected to the myth of Oedipus and its concerns with human choices and supposed predestination? What is suggested by the idea that ‘in all fictional works, each time a man is confronted with several alternatives, he chooses one and eliminates the others; in the fiction of Ts’ui Pen, he chooses– simultaneously– all of them. He creates, in this way, diverse futures, diverse times which themselves also proliferate and fork’? What does it mean to make all choices at once? What view of life do such beliefs embody?”
Multiverse
Peter Woit on the physics
story in this week’s TIME
Physics and Narrative
Related material on mathematics:
Saturday, May 22, 2004
Saturday May 22, 2004
Star Wars
In memory of Melvin J. Lasky, editor, 1958-1990, of the CIA-funded journal Encounter:
“Once called as lively, and as bitchy, as a literary cocktail party, Encounter published articles of unrivalled authority on politics, history and literature.”
Lasky died on Wednesday, May 19, 2004. From a journal entry of my own on that date:
This newly-digitized diagram is from a
paper journal note of October 21, 1999.
Note that the diagram’s overall form is that of an eight-point star. Here is an excerpt from a Fritz Leiber story dealing with such a star, the symbol of a fictional organization:
Time traveling, which is not quite the good clean boyish fun it’s cracked up to be, started for me when this woman with the sigil on her forehead looked in on me from the open doorway of the hotel bedroom where I’d hidden myself and the bottles and asked me, “Look, Buster, do you want to live?” Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question. The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar. An X superimposed on a plus sign. It looked permanent. … “Here is how it stacks up: You’ve bought your way with something other than money into an organization of which I am an agent….” “It’s a very big organization,” she went on, as if warning me. “Call it an empire or a power if you like. So far as you are concerned, it has always existed and always will exist. It has agents everywhere, literally. Space and time are no barriers to it. Its purpose, so far as you will ever be able to know it, is to change, for its own aggrandizement, not only the present and the future, but also the past. It is a ruthlessly competitive organization and is merciless to its employees.” “I. G. Farben?” I asked grabbing nervously and clumsily at humor. She didn’t rebuke my flippancy, but said, “And it isn’t the Communist Party or the Ku Klux Klan, or the Avenging Angels or the Black Hand, either, though its enemies give it a nastier name.” “Which is?” I asked. “The Spiders,” she said. That word gave me the shudders, coming so suddenly. I expected the sigil to step off her forehead and scuttle down her face and leap at me—something like that. She watched me. “You might call it the Double Cross,” she suggested, “if that seems better.” — Fritz Leiber, |
From last year’s entry,
Indiana Jones and the Hidden Coffer,
of 6/14:
From Borges’s “The Aleph“:
From The Hunchback of Notre Dame:
Lena Olin and Harrison Ford |
Finally, from an excellent site
on the Knights Templar,
a quotation from Umberto Eco:
When all the archetypes burst out shamelessly, we plumb the depths of Homeric profundity. Two cliches make us laugh but a hundred cliches move us because we sense dimly that the cliches are talking among themselves, celebrating a reunion . . . Just as the extreme of pain meets sensual pleasure, and the extreme of perversion borders on mystical energy, so too the extreme of banality allows us to catch a glimpse of the Sublime. — “Casablanca: Cult Movies and Intertextual Collage” (1984) from Travels in Hyperreality |