Readings for
Devil’s Night
1. Today’s New York Times review of Peter Brook’s production of “The Grand Inquisitor” 2. Mathematics and Theology 3. Christmas, 2005 4. Cube Space, 1984-2003 |
Readings for
Devil’s Night
1. Today’s New York Times review of Peter Brook’s production of “The Grand Inquisitor” 2. Mathematics and Theology 3. Christmas, 2005 4. Cube Space, 1984-2003 |
Katherine Neville, author of perhaps the greatest bad novel of the twentieth century, The Eight, has now graced a new century with her sequel, titled The Fire. An excerpt:
“Our family lodge had been built at about this same period in the prior century, by neighboring tribes, for my great-great-grandmother, a pioneering mountain lass. Constructed of hand-hewn rock and massive tree trunks chinked together, it was a huge log cabin that was shaped like an octagon– patterned after a hogan or sweat lodge– with many-paned windows facing in each cardinal direction, like a vast, architectural compass rose.
……..
From here on the mountaintop, fourteen thousand feet atop the Colorado Plateau, I could see the vast, billowing sea of three-mile-high mountain peaks, licked by the rosy morning light. On a clear day like this, I could see all the way to Mount Hesperus– which the Diné call Dibé Nitsaa: Black Mountain. One of the four sacred mountains created by First Man and First Woman.Together with Sisnaajinii, white mountain (Mt. Blanca) in the east; Tsoodzil, blue mountain (Mt. Taylor) in the south, and Dook’o’osliid, yellow mountain (San Francisco Peaks) in the west, these four marked out the four corners of Dinétah– ‘Home of the Diné,’ as the Navajo call themselves.
And they pointed as well to the high plateau I was standing on: Four Corners, the only place in the U.S. where four states– Colorado, Utah, New Mexico, and Arizona– come together at right angles to form a cross.”
The Eight
Lest the reader of the previous entry mistakenly take Katherine Neville’s book The Eight more seriously than Fritz Leiber’s greatly superior writings on eightness, here are two classic interpretations of Leiber’s “spider” or “double cross” symbol:
|
The eight-rayed star may be taken
as representing what is known
in philosophy as a “universal.”
See also
5:07:33 AM ET
33 Retreat
THE IMAGE
Mountain under heaven:
the image of RETREAT.
Thus the superior man
keeps the inferior man
at a distance,
not angrily
but with reserve.
The New York Times Book Review online today has a review by Sam Tanenhaus of a new John Updike book.
The title of the review (not the book) is "Mr. Wizard."
"John Updike is the great genial sorcerer of American letters. His output alone (60 books, almost 40 of them novels or story collections) has been supernatural. More wizardly still is the ingenuity of his prose. He has now written tens of thousands of sentences, many of them tiny miracles of transubstantiation whereby some hitherto overlooked datum of the human or natural world– from the anatomical to the zoological, the socio-economic to the spiritual– emerges, as if for the first time, in the completeness of its actual being."
Rolling Stone interview with Sting, February 7, 1991:
"'I was brought up in a very strong Catholic community,' Sting says. 'My parents were Catholic, and in the Fifties and Sixties, Catholicism was very strong. You know, they say, "Once a Catholic, always a Catholic." In a way I'm grateful for that background. There's a very rich imagery in Catholicism: blood, guilt, death, all that stuff.' He laughs."
RS 597, Feb. 7, 1991
Last night's 12:00 AM
Log24 entry:
Midnight BingoFrom this date six years ago:
From this morning's newspaper,
a religious meditation I had not
seen last night:
Related material:
Juneteenth through
Midsummer Night, 2007and
“The Cube Space” is a name given to the eightfold cube in a vulgarized mathematics text, Discrete Mathematics: Elementary and Beyond, by Laszlo Lovasz et al., published by Springer in 2003. The identification in a natural way of the eight points of the linear 3-space over the 2-element field GF(2) with the eight vertices of a cube is an elementary and rather obvious construction, doubtless found in a number of discussions of discrete mathematics. But the less-obvious generation of the affine group AGL(3,2) of order 1344 by permutations of parallel edges in such a cube may (or may not) have originated with me. For descriptions of this process I wrote in 1984, see Diamonds and Whirls and Binary Coordinate Systems. For a vulgarized description of this process by Lovasz, without any acknowledgement of his sources, see an excerpt from his book.
Along Came
a Spider
A phrase from 1959
"Look, Buster, |
… Todo lo sé
por el lucero puro
que brilla en la diadema
de la Muerte.
The link to
"Buffalo Soldier"
in this entry
is in memory of
Vittorio Foa, who
died Monday
at his home
outside Rome.
On May 4, 2005, I wrote a note about how to visualize the 7-point Fano plane within a cube.
Last month, John Baez showed slides that touched on the same topic. This note is to clear up possible confusion between our two approaches.
From Baez’s Rankin Lectures at the University of Glasgow:
The statement is, however, true of the eightfold cube, whose eight subcubes correspond to points of the linear 3-space over the two-element field, if “planes through the origin” is interpreted as planes within that linear 3-space, as in Galois geometry, rather than within the Euclidean cube that Baez’s slides seem to picture.
This Galois-geometry interpretation is, as an article of his from 2001 shows, actually what Baez was driving at. His remarks, however, both in 2001 and 2008, on the plane-cube relationship are both somewhat trivial– since “planes through the origin” is a standard definition of lines in projective geometry– and also unrelated– apart from the possibility of confusion– to my own efforts in this area. For further details, see The Eightfold Cube.
Thoughts suggested by Saturday's entry–
"… with primitives the beginnings of art, science, and religion coalesce in the undifferentiated chaos of the magical mentality…."
— Carl G. Jung, "On the Relation of Analytical Psychology to Poetry," Collected Works, Vol. 15, The Spirit in Man, Art, and Literature, Princeton University Press, 1966, excerpted in Twentieth Century Theories of Art, edited by James M. Thompson.
For a video of such undifferentiated chaos, see the Four Tops' "Loco in Acapulco."
"Yes, you'll be goin' loco
down in Acapulco,
the magic down there
is so strong."
This song is from the 1988 film "Buster."
(For a related religious use of that name– "Look, Buster, do you want to live?"– see Fritz Leiber's "Damnation Morning," quoted here on Sept. 28.)
Art, science, and religion are not apparent within the undifferentiated chaos of the Four Tops' Acapulco video, which appears to incorporate time travel in its cross-cutting of scenes that seem to be from the Mexican revolution with contemporary pool-party scenes. Art, science, and religion do, however, appear within my own memories of Acapulco. While staying at a small thatched-roof hostel on a beach at Acapulco in the early 1960's, I read a paperback edition of Three Philosophical Poets, a book by George Santayana on Lucretius, Dante, and Goethe. Here we may regard art as represented by Goethe, science by Lucretius, and religion by Dante. For a more recent and personal combination of these topics, see Juneteenth through Midsummer Night, 2007, which also has references to the "primitives" and "magical mentality" discussed by Jung.
"The major structures of the psyche for Jung include the ego, which is comprised of the persona and the shadow. The persona is the 'mask' which the person presents [to] the world, while the shadow holds the parts of the self which the person feels ashamed and guilty about."
— Brent Dean Robbins, Jung page at Mythos & Logos
As for shame and guilt, see Malcolm Lowry's classic Under the Volcano, a novel dealing not with Acapulco but with a part of Mexico where in my youth I spent much more time– Cuernavaca.
Lest Lowry's reflections prove too depressing, I recommend as background music the jazz piano of the late Dave McKenna… in particular, "Me and My Shadow."
McKenna died on Saturday, the date of the entry that included "Loco in Acapulco." Saturday was also the Feast of Saint Luke.
This morning’s New York Times
has an obituary for the father
of the paper’s executive editor,
Bill Keller:
For more on George Keller and on
the more colorful Levi Stubbs,
who also died on Friday,
see the Times‘s AP obituaries.
Keller’s son Bill has emphasized
what he calls the “allure” of the
Times‘s lifestyles coverage.
An example of such coverage–
a 2006 story on visual art in Mexico
that included a reference to…
For descriptions of such life,
I prefer the literary art of
Robert Stone– in particular,
Stone’s novel
A Flag for Sunrise.
Credit must be given to
the Times for an excellent
1981 review of that novel.
(This was well before
the younger Keller
joined the Times in 1984.)
My own views on life are
less like those of either Keller
than like those of Stone and
perhaps of Levi Stubbs, the
other father figure who
died on Friday.
Related material:
“Yes, you’ll be goin’ loco
down in Acapulco,
the magic down there
is so strong.”
— Levi Stubbs
“Every musician wants to do something of lasting quality, something which will hold up for a long time, and I guess we did it with ‘Stairway.'”
— Jimmy Page on “Stairway to Heaven“
“… it’s going to be accomplished in steps,
Alec Guinness and Ernie Kovacs
play checkers in
“Our Man in Havana” (1959)
Et cetera,
Et cetera,
Et cetera
“…Once in a lullaby….”
— Judy Garland
Edie Adams sings on the
final episode of
“The Lucy-Desi Comedy Hour”
in April 1960
Hint:
The above symbol
does not stand for
"Walter Winchell."
Related material:
Log24 entries for the
Halloween season
of 2005 —
"This is the turning point Funny But by the end Bitter and serious and deadly"
— Jill O'Hara singing |
See also
The Quality of Diamond.
Links for the birthday of the late mathematician Bernhard H. Neumann:
Variety (Universal Algebra) at Wikipedia
Preface to Varieties of Groups (1967), by Hanna Neumann
Some related notes on algebra suggested by finite geometry:
Dynamic and algebraic compatibility of groups (1985 Dec. 11)
Groups related by a nontrivial identity (1985 Nov. 17)
Transformations over a bridge (1983 Aug. 16)
Group identity algebras (1983 Aug. 4)
I have no idea if any work has been done in this area since my own efforts in 1983-1985.
Related material:
Dec. 16, 2003—
Kaleidoscope turning… |
— Today’s New York Times
review of the Very Rev.
Francis Bowes Sayre Jr.
Related material:
Log24 entries from
the anniversary this
year of Sayre’s birth
and from the date
of his death:
A link from the former
suggests the following
graphic meditation–
(Click on figure for details.)
A link from the latter
suggests another
graphic meditation–
(Click on figure for details.)
Although less specifically
American than the late
Reverend, who was
born in the White House,
hence perhaps irrelevant
to his political views,
these figures are not
without relevance to
his religion, which is
more about metanoia
than about paranoia.
“Haider was pronounced dead
in a hospital shortly after his
Volkswagen Phaeton veered
off the road….”
“In the version of the myth told by Ovid in the Metamorphoses, Phaeton bragged to his friends that his father was the sun-god. One of his friends, who was rumored to be a son of Zeus, refused to believe him and said his mother was lying. So Phaeton went to his father Helios, who swore by the river Styx to give Phaeton anything he should ask for in order to prove his divine paternity. Phaeton wanted to drive his chariot (the sun) for a day. Though Helios tried to talk him out of it, Phaeton was adamant. When the day came, Phaeton panicked and lost control of the mean horses that drew the chariot. First it veered too high, so that the earth grew chill. Then it dipped too close, and the vegetation dried and burned. He accidentally turned most of Africa into desert, burning the skin of the Ethiopians black. Eventually, Zeus was forced to intervene by striking the runaway chariot with a lightning bolt to stop it, and Phaeton plunged into the river Eridanos. His sisters the Heliades grieved so much that they were turned into poplar trees that weep golden amber.
This story has given rise to two latter-day meanings of ‘phaeton’: one who drives a chariot or coach, especially at a reckless or dangerous speed, and one that would or may set the world on fire.” —Wikipedia
Maureen Dowd’s New York Times column, “Sound, but No Fury,” on the September 26 debate at Oxford, Mississippi–
“Who would have dreamed that when socialism finally came to the U.S.A. it would be brought not by Bolsheviks in blue jeans but Wall Street bankers….?”
Perhaps Ernest Lehman, author of screenplays for “The Prize” and “From the Terrace.” (See recent Log24 entries.)
Paul Krugman’s column in today’s online Times, “Moment of Truth“–
“The consequences of Lehman’s fall were apparent within days, yet key policy players have largely wasted the past four weeks. Now they’ve reached a moment of truth: They’d better do something soon– in fact, they’d better announce a coordinated rescue plan this weekend– or the world economy may well experience its worst slump since the Great Depression.
Let’s talk about where we are right now.”
The Sound and the Fury
(Log24, June 8, 2003)
and Lehman’s
“Sweet Smell of Success.”
(A modest proposal from
the date of Paul Newman’s death)
Paul Newman and Elke Sommer
in “The Prize” (1963,
screenplay by Ernest Lehman)
Happy Yom Kippur.
Midsummer Night
in the Garden
of Good and Evil
“Right through hell
there is a path…“
(Voice-over by
Richard Burton,
“Volcano,” 1976)
Serious Numbers
A Yom Kippur
Meditation
"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
Trudeau's 1987 book uses the phrase "diamond theory" to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls "diamonds") that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle's angles is 180 degrees. As the excerpt below shows, Trudeau prefers what he calls the "story theory" of truth–
"There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.'"
(By the way, the phrase "diamond theory" was used earlier, in 1976, as the title of a monograph on geometry of which Coxeter was aware.)
What does this have to do with numbers?
Pilate's skeptical tone suggests he may have shared a certain confusion about geometric truth with thinkers like Trudeau and the slave boy in Plato's Meno. Truth in a different part of mathematics– elementary arithmetic– is perhaps more easily understood, although even there, the existence of what might be called "non-Euclidean number theory"– i.e., arithmetic over finite fields, in which 1+1 can equal zero– might prove baffling to thinkers like Trudeau.
Trudeau's book exhibits, though it does not discuss, a less confusing use of numbers– to mark the location of pages. For some philosophical background on this version of numerical truth that may be of interest to devotees of the Semitic religions on this evening's High Holiday, see Zen and Language Games.
For uses of numbers that are more confusing, see– for instance– the new website The Daily Beast and the old website Story Theory and the Number of the Beast.
The previous two entries mention,
and illustrate, the color grey.
Another illustration, on the cover
of one of my favorite books:
"A colour is eternal.
It haunts time like a spirit."
— Alfred North Whitehead
From John Lahr's
winter 2002 review
of "Our Town"–
"We all know that something is eternal," the Stage Manager says. "And it ain't houses and it ain't names, and it ain't earth, and it ain't even stars– everybody knows in their bones that something is eternal, and that something has to do with human beings."
The Stage Manager was played by Paul Newman. The review was subtitled "Getting the Spirit Onstage."
Yesterday's entry contained the following unattributed quotation:
"One must join forces with friends of like mind."
As the link to Leap Day indicated, the source of the quotation is the I Ching.
Yesterday's entry also quoted the late Terence McKenna, a confused writer on psychosis and the I Ching. Lest the reader conclude that I consider McKenna or similar authors (for instance, Timothy Leary in Cuernavaca) as "friends of like mind," I would point rather to more sober students of the I Ching (cf. my June 2002 notes on philosophy, religion, and science) and to the late Scottish theologian John Macquarrie:
Macquarrie's connection in this journal to the I Ching is, like that book itself, purely coincidental. For details, click on the figure below.
The persistent reader will
find a further link that
leads to an entry titled
"Notes on the I Ching."
"A colour is eternal. It haunts time like a spirit. It comes and it goes. But where it comes it is the same colour. It neither survives nor does it live. It appears when it is wanted."
Last night's entry presented a
short story summarized by
four lottery numbers.
Today's mid-day lotteries
and associated material:
Pennsylvania, 201– i.e., 2/01:
Kindergarten Theology —
"In a game of chess, the knight's move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a 'knight's move' in intelligence."
"One must join forces with friends of like mind"
Related material:
"Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey 'haunts time like a ghost.'"
"'Knight's move thinking' is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia."
I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.
For more on the sleep of Apollo,
see the front page of today's
New York Times Book Review.
Garrison Keillor's piece there,
"Dying of the Light," is
about the fear of death felt
by an agnostic British twit.
For relevant remarks by
a British non-twit, see
William Dunbar–
“The Ambition of the Short Story,” the essay by Steven Millhauser quoted here on Tuesday, September 30, is now online.
“The secret to life, and
to love, is getting started,
keeping going, and then
getting started again.”
Nobel Laureate
Seamus Heaney
at Sanders Theatre,
Harvard College,
September 30, 2008
On Elke Sommer:
“…Young Elke… studied
in the prestigious
Gymnasium School
in Erlangen….”
Erlangen Prize Lecture:
Variations on a Theme of
Plato, Goethe, and Klein
(Background:
Christmas Knot, Sept. 26,
and Hard Core, July 17-18.)
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