A version more explicitly connected to finite geometry —
For the six synthematic totals , see The Joy of Six.
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," |
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 lexicographic Golay code
contains, embedded within it,
the Miracle Octad Generator.
By Steven H. Cullinane, July 13, 2020
Background —
The Miracle Octad Generator (MOG)
of R. T. Curtis (Conway-Sloane version) —
A basis for the Golay code, excerpted from a version of
the code generated in lexicographic order, in
“Constructing the Extended Binary Golay Code“
Ben Adlam
Harvard University
August 9, 2011:
000000000000000011111111
000000000000111100001111
000000000011001100110011
000000000101010101010101
000000001001011001101001
000000110000001101010110
000001010000010101100011
000010010000011000111010
000100010001000101111000
001000010001001000011101
010000010001010001001110
100000010001011100100100
Below, each vector above has been reordered within
a 4×6 array, by Steven H. Cullinane, to form twelve
independent Miracle Octad Generator vectors
(as in the Conway-Sloane SPLAG version above, in
which Curtis’s earlier heavy bricks are reflected in
their vertical axes) —
01 02 03 04 05 . . . 20 21 22 23 24 --> 01 05 09 13 17 21 02 06 10 14 18 22 03 07 11 15 19 23 04 08 12 16 20 24 0000 0000 0000 0000 1111 1111 --> 0000 11 0000 11 0000 11 0000 11 as in the MOG. 0000 0000 0000 1111 0000 1111 --> 0001 01 0001 01 0001 01 0001 01 as in the MOG. 0000 0000 0011 0011 0011 0011 --> 0000 00 0000 00 0011 11 0011 11 as in the MOG. 0000 0000 0101 0101 0101 0101 --> 0000 00 0011 11 0000 00 0011 11 as in the MOG. 0000 0000 1001 0110 0110 1001 --> 0010 01 0001 10 0001 10 0010 01 as in the MOG. 0000 0011 0000 0011 0101 0110 --> 0000 00 0000 11 0101 01 0101 10 as in the MOG. 0000 0101 0000 0101 0110 0011 --> 0000 00 0101 10 0000 11 0101 01 as in the MOG. 0000 1001 0000 0110 0011 1010 --> 0100 01 0001 00 0001 11 0100 10 as in the MOG. 0001 0001 0001 0001 0111 1000 --> 0000 01 0000 10 0000 10 1111 10 as in the MOG. 0010 0001 0001 0010 0001 1101 --> 0000 01 0000 01 1001 00 0110 11 as in the MOG. 0100 0001 0001 0100 0100 1110 --> 0000 01 1001 11 0000 01 0110 00 as in the MOG. 1000 0001 0001 0111 0010 0100 --> 10 00 00 00 01 01 00 01 10 01 11 00 as in the MOG (heavy brick at center).
Update at 7:41 PM ET the same day —
A check of SPLAG shows that the above result is not new:
And at 7:59 PM ET the same day —
Conway seems to be saying that at some unspecified point in the past,
M.J.T. Guy, examining the lexicographic Golay code, found (as I just did)
that weight-8 lexicographic Golay codewords, when arranged naturally
in 4×6 arrays, yield certain intriguing visual patterns. If the MOG existed
at the time of his discovery, he would have identified these patterns as
those of the MOG. (Lexicographic codes have apparently been
known since 1960, the MOG since the mid-1970s.)
* Addendum at 4 AM ET the next day —
See also Logline (Walpurgisnacht 2013).
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:
|
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 memory of Claude Shannon, who would have turned 100 today.
See "The Matthias Defense" and citations of that page in this journal.
“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
And an especially Faustian
Walpurgis Night to
Harvard University, home of
Robert Langdon, fictional professor
of Religious Symbology —
“That corpse you planted
last year in your garden,
Has it begun to sprout?
Will it bloom this year?
Or has the sudden frost
disturbed its bed?”
— T. S. Eliot, “The Waste Land”
A man returns a crucifix
to a Huichol village chapel.
Photo by Rachel Cobb
for National Geographic
Lucy in the Sky
with Diamonds
and Sacred Heart
PARIS — Albert Hofmann, the mystical Swiss chemist who gave the world LSD, the most powerful psychotropic substance known, died Tuesday at his hilltop home near Basel, Switzerland. He was 102.
Related material:
and
a film by Julie Taymor,
Across the Universe:
Detail of the
Strawberry Fields Forever
Sacred Heart:
A song:Julie Taymor
“Shinin’ like a diamond,
she had tombstones
in her eyes.”— Album “The Dark,”
by Guy ClarkFor related tombstones,
see May 16-19, 2006,
and April 19, 2008.Further background:
Art Wars for
Red October.
Q: If the opposite of Christmas (December 25) is Anti-Christmas (June 25), and the opposite of Halloween (October 31) is May Day (May 1), then what is the opposite of April 30?
A: October 30… Devil’s Night!
Related material:
…da ist der Tanz;
Doch weder Stillstand noch Bewegung.
Und nenne es nicht Beständigkeit,
Wo Vergangenheit und Zukunft sich sammeln.
|
|
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.
|
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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