Also from Walpurgisnacht 2024 — Vuelo de Brujas.
Also from Walpurgisnacht 2024 — Vuelo de Brujas.
In related news . . .
Wednesday, April 30, 2014
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Note that if the "compact Riemann surface" is a torus formed by
joining opposite edges of a 4×4 square array, and the phrase
"vector bundle" is replaced by "projective line," and so forth,
the above ChatGPT hallucination is not completely unrelated to
the following illustration from the webpage "galois.space" —
See as well the Cullinane diamond theorem.
In 2007, April 30 — Walpurgisnacht — was also the
release date of the "Back to Black" single . . .
A related music venue —
A version more explicitly connected to finite geometry —
For the six synthematic totals , see The Joy of Six.
Father Flynn in this morning’s post “Hollywood Interpretation
of Quantum Mechanics” suggests a flashback to Tron: Legacy —
A search for the above blogger “hilbertthm90”
yields some of his remarks from April 30, 2008
in his weblog “A Mind for Madness.” See as well
this journal on Walpurgisnacht 2008.
In memory of Anatole Katok, who reportedly died on Walpurgisnacht,
two readings from a source cited by Dan Brown in his recent novel
Origin —
Brown is reportedly a graduate of Phillips Exeter Academy and
of Amherst College.
Those associated with institutions that are more respectable
may prefer Katok on entropy.
"Kroto is believed to have died on Saturday, April 30.
Responding to the news on Twitter, Prof Brian Cox
tweeted: 'RIP Harry Kroto – brilliant scientist and a
strong, passionate advocate for science as a vital
part of our culture.' — The Guardian
See also Walpurgisnacht 2016 in this journal.
Update of 10:45 PM — Some related pure mathematics :
A more impressive Lucifer —
The late theoretical physicist John Archibald Wheeler,
author of the phrase "it from bit."
Related material —
"The Thing and I" (April 17, 2016) and an essay by
Julian Barbour, "Bit from It."
Part I — Unity and Multiplicity
(Continued from The Talented and Galois Cube)
Part II — "A feeling, an angel, the moon, and Italy"—
A film by Julie Taymor, Across the Universe — Detail of the Strawberry Fields Forever Sacred Heart — Julie Taymor "Shinin' like a diamond, — Album "The Dark," |
Continues . See other posts now tagged
The Emmanuel Bride.
Wednesday, May 1, 2024
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This year's April –
For my own views on this theme as it applies
For some other views, see this year's
One of the authors at that site,
"'The discovery of non-Euclidean geometries
contradicted the "absolute truth" view
of the Platonists.'"
— Sarah J. Greenwald,
Associate Professor, Department of Mathematics Appalachian State University, Boone, NC
Damned nonsense. See Math16.com.
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This post was suggested by a mention of Boone
in an Atlantic article yesterday, "OopsGPT."
See as well Emmanuel here on Walpurgisnacht 2024
in "The Invitation" (2022) —
Wednesday, May 1, 2024
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From the end credits for "The Invitation" —
In 2007, April 30 — Walpurgisnacht — was the
release date of the "Back to Black" single . . .
A related music venue —
A related map —
This post was suggested by . . .
A Bon Jovi "Stripped" video released May 1, 2007 —
Synchronology check —
This journal in the early morning of the above release date —
"Nine is a very |
From Schicksalstag 2012:
EAST LANSING, Mich., Nov. 9, 2012 /PRNewswire-USNewswire/ —
“The Eli and Edythe Broad Art Museum at Michigan State University,
a new Zaha Hadid-designed contemporary art museum, will open on
Saturday, Nov. 10 . . . .
In Search of Time (on view through February 10, 2013).
In celebrating the opening of this iconic building at
Michigan State University, In Search of Time seeks to explore
the longing artists have held for hundreds of years to express
their relationship to time and memory.”
See also, from Log24, posts now tagged Nov. 10, 2012 , and
posts earlier tagged Battlefield Geometry .
Related material to commemorate Walpurgisnacht 2021 (last night) —
https://www.latimes.com/story/2021-04-30/
photos-eli-broad-philanthropist-art-collector-builder-created-
part-of-the-los-angeles-landscape
Related reading — Notes for Watchmen.
Published today —
Related quotation —
Cover art published today —
Some mathematics related to the The Fixed Stars cover art,
from a post of May 1, 2020 —
The Escape from Plato’s Cave to . . .
See also Numberland and Walpurgisnacht Geometry.
The above novel uses extensively the term “inscape.”
The term’s originator, a 19th-century Jesuit poet,
is credited . . . sort of. For other uses of the term,
search for Inscape in this journal. From that search —
A quote from a 1962 novel —
“There’s something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz.”
Addendum for the Church of Synchronology —
The Joe Hill novel above was published (in hardcover)
on Walpurgisnacht —April 30, 2013. See also this journal
on that date.
See also a theater review of a Walpurgisnacht 2008
Brooklyn Academy of Music production —
The New York Times on the Walpurgisnacht production —
"Specifically grim but never merely glum, the production fully taps
the self-conscious theatricality of the play ('I’m warming up for
my last soliloquy,' Hamm announces toward the end) without
letting us forget that its strange figures are appallingly real,
enacting a grotesque pantomime of humanity’s hungry need to
distract itself by wresting order, meaning and a sliver of satisfaction —
just one more sugarplum, please, or maybe a Vicodin — from
the formless, aimless, timeless nothingness of life."
— Charles Isherwood
Hexagram 29,
The Abyss (Water)
This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —
In that post, the designer quotes the Wilhelm/Baynes I Ching to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —
"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."
See also this journal on Walpurgisnacht (April 30), 2010 —
Hexagram 29:
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Hexagram 30: |
A thought from another German-speaking philosopher —
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.
"In August 1884, he wrote to Resa von Schirnhofer:
'Here one can live well, in this strong, bright atmosphere,
here where nature is amazingly mild and solemn
and mysterious all at once— in fact, there is no place
that I like better than Sils-Maria.'"
For more about Resa, see another weblog's post
of April 30, 2013.
A remark on Nietzsche from the epigraph of that weblog:
"His life's work was devoted to finding one's 'style'
within the chaos of existence. The trick, obviously,
is not to lose your mind in the process."
A remark from this weblog on the above date —
Walpurgisnacht 2013 —
(Where Entertainment Is God , continued)
Yesterday's evening numbers in the New York Lottery
were 007 and 3856. You are free to supply your own
interpretation of the former. The latter may, if you like,
be interpreted as post 3856, The Illuminati Stone .
Some context:
(Click for a larger, clearer image.)
Arts and Letters Daily today links to a July 17
Washington Post review of two books on the
occult and the enlightenment. The review, by
Michael Dirda, ends on a cheerful note:
"Happy synchronicity."
In related news, a Walpurgisnacht obituary also
ends cheerfully:
"He was still trying to get out a joke
with his final breath."
That obituary describes a life that reportedly ended
on April 21, 2013. Synchronicity involving that date—
The posts of April 21, 2013 (and related material in
this morning's previous post).
(Continued from Walpurgisnacht 2012)
Wikipedia article on functional decomposition—
"Outside of purely mathematical considerations,
perhaps the greatest value of functional decomposition
is the insight it provides into the structure of the world."
Certainly this is true for the sort of decomposition
known as harmonic analysis .
It is not, however, true of my own decomposition theorem,
which deals only with structures made up of at most four
different sorts of elementary parts.
But my own approach has at least some poetic value.
See the four elements of the Greeks in (for instance)
Eliot's Four Quartets and in Auden's For the Time Being .
(An episode of Mathematics and Narrative )
A report on the August 9th opening of Sondheim's Into the Woods—
Amy Adams… explained why she decided to take on the role of the Baker’s Wife.
“It’s the ‘Be careful what you wish’ part,” she said. “Since having a child, I’m really aware that we’re all under a social responsibility to understand the consequences of our actions.” —Amanda Gordon at businessweek.com
Related material—
Amy Adams in Sunshine Cleaning "quickly learns the rules and ropes of her unlikely new market. (For instance, there are products out there specially formulated for cleaning up a 'decomp.')" —David Savage at Cinema Retro
Compare and contrast…
1. The following item from Walpurgisnacht 2012—
2. The six partitions of a tesseract's 16 vertices
into four parallel faces in Diamond Theory in 1937—
Poster from Walpurgisnacht 2012
Raven’s Progressive Matrices problem:
Click the problem for a related story.
For some related geometry, see Elements Diamond.
See also a post (Dream Time, May 3, 2010)
about geometry and an earlier Walpurgisnacht.
Last October, Harvard celebrated its 375th anniversary
with Pandemonium. For remarks of a different sort,
see Andrew Cusack on Walpurgisnacht.
"There is a pleasantly discursive treatment of
Pontius Pilate's unanswered question 'What is truth?'"
— H. S. M. Coxeter, 1987
Returning to the Walpurgisnacht posts
Decomposition (continued) and
Decomposition– Part III —
Some further background…
SAT
(Not a Scholastic Aptitude Test)
"In computer science, satisfiability (often written
in all capitals or abbreviated SAT) is the problem
of determining if the variables of a given Boolean
formula can be assigned in such a way as to
make the formula evaluate to TRUE."
— Wikipedia article Boolean satisfiability problem
For the relationship of logic decomposition to SAT,
see (for instance) these topics in the introduction to—
Advanced Techniques in Logic Synthesis,
Optimizations and Applications* —
Click image for a synopsis.
* Edited by Sunil P. Khatri and Kanupriya Gulati
A search tonight for material related to the four-color
decomposition theorem yielded the Wikipedia article
Functional decomposition.
The article, of more philosophical than mathematical
interest, is largely due to one David Fass at Rutgers.
(See the article's revision history for mid-August 2007.)
Fass's interest in function decomposition may or may not
be related to the above-mentioned theorem, which
originated in the investigation of functions into the
four-element Galois field from a 4×4 square domain.
Some related material involving Fass and 4×4 squares—
A 2003 paper he wrote with Jacob Feldman—
"Design is how it works." — Steve Jobs
An assignment for Jobs in the afterlife—
Discuss the Fass-Feldman approach to "categorization under
complexity" in the context of the Wikipedia article's
philosophical remarks on "reductionist tradition."
The Fass-Feldman paper was assigned in an MIT course
for a class on Walpurgisnacht 2003.
This morning's post has the following from Borges—
"Yo sé de un laberinto griego que es una línea única, recta."
—Borges, "La Muerte y la Brújula"
This suggests a search for "bruja brújula" (witch compass).
The search yields a Facebook page that leads, in turn, to Lhasa de Sela—
A search for material in this journal from the date of her death, 1/1/10, yields
The Celestine Dream, with its text on Doctor Parnassus and its image from Shutter Island —
Click to enlarge this item from Christmas 2009.
All this is by way of commentary on the April-30-to-May-1 Walpurgisnacht-to-May-Day scenes in Disney's Fantasia … which I watched last night.
I had not known anything about Lhasa de Sela until this morning, but in the combined context of Fantasia and of Russia's Victory Day observances today, her song "Los Peces" seems worth noting.
* For the title, see Celestine Bohlen on the Bolshoi Ballet.
“Mere anarchy is loosed upon the world”
From a document linked to here on April 30, Walpurgisnacht–
“…the Golden Age, or Dream Time, is remote only from the rational mind. It is not accessible to euclidean reason….”
“The utopia of the Grand Inquisitor ‘is the product of “the euclidean mind” (a phrase Dostoyevsky often used)….'”
“The purer, the more euclidean the reason that builds a utopia, the greater is its self-destructive capacity. I submit that our lack of faith in the benevolence of reason as the controlling power is well founded. We must test and trust our reason, but to have faith in it is to elevate it to godhead.”
“Utopia has been euclidean, it has been European, and it has been masculine. I am trying to suggest, in an evasive, distrustful, untrustworthy fashion, and as obscurely as I can, that our final loss of faith in that radiant sandcastle may enable our eyes to adjust to a dimmer light and in it perceive another kind of utopia.”
“You will recall that the quality of static perfection is an essential element of the non-inhabitability of the euclidean utopia….”
“The euclidean utopia is mapped; it is geometrically organized, with the parts labeled….”
— Ursula K. Le Guin, “A Non-Euclidean View of California as a Cold Place to Be”
San Francisco Chronicle today—
“A May Day rally in Santa Cruz erupted into chaos Saturday night….”
“Had Goodman Brown fallen asleep in the forest,
and only dreamed a wild dream of a witch-meeting?”
From today's NY Times—
Obituaries for mystery authors
Ralph McInerny and Dick Francis
From the date (Jan. 29) of McInerny's death–
"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"
– Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson
From the date (Feb. 14) of Francis's death–
The EIghtfold Cube
The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.
This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.
For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
and the death of Coxeter–
Putting Descartes Before Dehors
For a more Protestant meditation,
see The Cross of Descartes—
"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke
For further details, click on
the image below–
Notre Dame Philosophical Reviews
Cover of Underworld,
by Don DeLillo, First Edition,
Advance Reader's Copy, 1997
"Time and chance
happeneth to them all."
— Ecclesiastes 9:11
Related material:
1. The previous entry, on
Copenhagen physicist
Aage Bohr, and
2. Notes from this journal
from Bohr's birthday,
June 19th, through
Midsummer Night, 2007…
including notes on
Faust in Copenhagen
3. Walpurgisnacht 2008 and
Walpurgisnacht 2009
…da ist der Tanz;
Doch weder Stillstand noch Bewegung.
Und nenne es nicht Beständigkeit,
Wo Vergangenheit und Zukunft sich sammeln.
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to put one's back into something |
bei etwas Einsatz zeigen |
to up the ante |
den Einsatz erhöhen |
to debrief | den Einsatz nachher besprechen |
to be on duty |
im Einsatz sein |
mil.to be in action | im Einsatz sein |
to play for high stakes |
mit hohem Einsatz spielen |
"Nine is a very
powerful Nordic number."
— Katherine Neville,
The Magic Circle
Two Literary Classics
(and a visit from a saint)
On this date in 1962, Edward Albee's classic play, "Who's Afraid of Virginia Woolf?" opened on Broadway.
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As I was preparing this entry, based on the October 13 date of the Albee play's opening, after I looked for a picture of Marshall's book I thought I'd better check dates related to Marshall, too. This is what I was surprised to find: Marshall (b. Oct. 10, 1942) died in 1992 on today's date, October 13. This may be verified at
The James Edward Marshall memorial page,
A James Edward Marshall biography, and
Author Anniversaries for October 13.
The titles of the three acts of Albee's play suffice to indicate its dark spiritual undercurrents:
"Fun and Games" (Act One),
"Walpurgisnacht" (Act Two) and
"The Exorcism" (Act Three).
A theological writer pondered Albee in 1963:
"If, as Tillich has said of Picasso's Guernica, a 'Protestant' picture means not covering up anything but looking at 'the human situation in its depths of estrangement and despair,' then we could call Edward Albee's Who's Afraid of Virginia Woolf? a 'Protestant' play. On any other definition it might be difficult to justify its religious significance except as sheer nihilism."
— Hugh T. Kerr, Theological Table-Talk, July 1963
It is a great relief to have another George and Martha (who first appeared in 1972) to turn to on this dark anniversary, and a doubly great relief to know that Albee's darkness is balanced by the light of Saint James Edward Marshall, whose feast day is today.
For more on the carousel theme of the Marshall book's cover, click the link for "Spinning Wheel" in the entry below.
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