From the Associated Press today —
"It's a magic wonderland," said Miriam Leibowitz,
a Jerusalem resident, as she reached a snow-filled
city park with her family. "In the middle of Jerusalem
we felt like we're in Switzerland."
From the Associated Press today —
"It's a magic wonderland," said Miriam Leibowitz,
a Jerusalem resident, as she reached a snow-filled
city park with her family. "In the middle of Jerusalem
we felt like we're in Switzerland."
Einstein and Thomas Mann, Princeton, 1938
A sequel to Princeton Requiem,
Gesamtkunstwerk , and Serial Box —
Fearful Symmetry, Princeton Style:
* See as well other instances of Kulturkampf in this journal.
Recent posts tagged Sagan Dodecahedron
mention an association between that Platonic
solid and the 5×5 grid. That grid, when extended
by the six points on a "line at infinity," yields
the 31 points of the finite projective plane of
order five.
For details of how the dodecahedron serves as
a model of this projective plane (PG(2,5)), see
Polster's A Geometrical Picture Book , p. 120:
For associations of the grid with magic rather than
with Plato, see a search for 5×5 in this journal.
The "Phony Pony" images below by Josefine Lyche
may or may not have been created in response to the link
on "magic" in the previous post to Katy Perry's "Dark Horse" video.
Oslo artist Josefine Lyche has a new Instagram post,
this time on pyramids (the monumental kind).
My response —
Wikipedia's definition of a tetrahedron as a
"triangle-based pyramid" …
… and remarks from a Log24 post of August 14, 2013 :
Norway dance (as interpreted by an American)
I prefer a different, Norwegian, interpretation of "the dance of four."
Related material: |
See also some of Burkard Polster's triangle-based pyramids
and a 1983 triangle-based pyramid in a paper that Polster cites —
(Click image below to enlarge.)
Some other illustrations that are particularly relevant
for Lyche, an enthusiast of magic :
From On Art and Magic (May 5, 2011) —
|
(Updated at about 7 PM ET on Dec. 3.)
Alexander Grothendieck, Récoltes et Semailles , 18.5.9.5. e, p. 1181 :
Pour mettre la joie à son comble, j’ajoute que le dénommé Saavedra
semble avoir disparu de la circulation sans plus laisser aucune trace….
Du coup, l’histoire prend des allures de sombre intrigue policière.
Man of La Mancha :
"Who knows where madness lies?"
An author quoted here at 10 PM ET Monday, Nov. 24, 2014 :
And then there is author Dan McGirt :
It sounded fun, so I signed up — and soon learned writing a story set in someone else’s fictional world presents certain … challenges. It was an enjoyable experience, yet very different than being able to write and run with whatever crazy idea pops into my head. Trying to capture the feel of a game that is more based on action and blowing stuff up than on deep character moments (not that I would know much about that … ) was also a challenge. I experimented with things like using comic book sound effects, lean descriptions (do I really need to describe a fireball spell in detail?) and other tricks to keep things moving. I also got to add to Magicka lore. Often the answer to my questions about some bit of in-world history or “fact” was “Make something up.” So I did! (Often getting a response of … “Odin’s onions, no! You can’t do that!”) So I was thrilled and excited to contribute in a small way to the development of Midgård. The result is Magicka: The Ninth Element , in which four young Wizards are sent on a quest to pursue the mysterious Purple Wizard who has stolen a powerful artifact from the Order of Magick. Which powerful artifact? No one is quite sure (for reasons explained in the story). What does it do? Again, unclear. But it can’t be good. Thus our heroes Davlo, Grimnir, Fafnir and Tuonetar set out on their quest — and promptly go off the map. (I’m not even kidding. The Midgård map in the front of the book will of little use to you. But it’s pretty!) Will they survive the dangers of the Unmapped Lands? Will they catch the Purple Wizard in time? Will they save the world? Read the book to find out! |
For the late novelist P. D. James, author of, among other things,
The Children of Men .
Michael Caine in the film of that book —
Detail —
Raven's Progressive Matrices example —
A quote for tellers of tales —
“There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”
— Website of Magicka: The Ninth Element Novel
“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”
— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121
Cf. Raiders of the Lost Theorem, Oct. 13, 2014.
See also tonight’s previous post and
“Feng Shui” in this journal.
See a University of Wisconsin obituary for Schneider,
a leading expert on linear algebra who reportedly died
at 87 on Tuesday, October 28, 2014.
Some background on linear algebra and “magic” squares:
tonight’s 3 AM (ET) post and a search in this
journal for Knight, Death, and the Devil.
Click image to enlarge.
Introducing a group of 322,560 affine transformations of Dürer’s ‘Magic’ Square
The four vector-space substructures of digits in 1st, 2nd, 3rd, 4th place,
together with the diamond theorem, indicate that Dürer’s square “minus one”
can be transformed by permutations of rows, columns, and quadrants to a
square with (decimal) digits in the usual numerical order, increasing from
top left to bottom right. Such permutations form a group of order 322,560.
(Continued from Vector Addition in a Finite Field, Twelfth Night, 2013.)
Two news items on art as a tool:
Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:
Finally, leftist art theorist Rosalind Krauss in this journal
on AntiChristmas, 2010:
Which is the tool here, the grid or Krauss?
The title is from a Log24 post, "Diabolically Complex Riddle," of Sept. 27, 2014.
(See also a search for "Diabolic" in this journal, which yields an application to
"magic" squares.)
(Continued from Nov. 16, 2013.)
The 48 actions of GL(2,3) on a 3×3 array include the 8-element
quaternion group as a subgroup. This was illustrated in a Log24 post,
Hamilton’s Whirligig, of Jan. 5, 2006, and in a webpage whose
earliest version in the Internet Archive is from June 14, 2006.
One of these quaternion actions is pictured, without any reference
to quaternions, in a 2013 book by a Netherlands author whose
background in pure mathematics is apparently minimal:
In context (click to enlarge):
Update of later the same day —
Lee Sallows, Sept. 2011 foreword to Geometric Magic Squares —
“I first hit on the idea of a geometric magic square* in October 2001,**
and I sensed at once that I had penetrated some previously hidden portal
and was now standing on the threshold of a great adventure. It was going
to be like exploring Aladdin’s Cave. That there were treasures in the cave,
I was convinced, but how they were to be found was far from clear. The
concept of a geometric magic square is so simple that a child will grasp it
in a single glance. Ask a mathematician to create an actual specimen and
you may have a long wait before getting a response; such are the formidable
difficulties confronting the would-be constructor.”
* Defined by Sallows later in the book:
“Geometric or, less formally, geomagic is the term I use for
a magic square in which higher dimensional geometrical shapes
(or tiles or pieces ) may appear in the cells instead of numbers.”
** See some geometric matrices by Cullinane in a March 2001 webpage.
Earlier actual specimens — see Diamond Theory excerpts published in
February 1977 and a brief description of the original 1976 monograph:
“51 pp. on the symmetries & algebra of
matrices with geometric-figure entries.”
— Steven H. Cullinane, 1977 ad in
Notices of the American Mathematical Society
The recreational topic of “magic” squares is of little relevance
to my own interests— group actions on such matrices and the
matrices’ role as models of finite geometries.
“Nine is a very powerful Nordic number.”
— Katherine Neville, The Magic Circle
See also Arcade Fire in this journal.
“Rarely is a TV show as brilliant and as terrible as Selfie .”
— Kevin Fallon on a new ABC TV show that starts tonight at 8 PM ET
A recent selfie from Josefine Lyche’s Instagram page:
For some remarks related to Lyche’s pentagram, see
Lyche + Mathmagic* and also yesterday’s Michaelmas Mystery.
In today’s previous post, the late Harvey Cohn posed a question that
he said might have been asked by Pythagoras:
“It is an elementary observation that an integral right triangle
has an even area. Suppose the hypotenuse is prime.
Q. How do we determine from the prime value of the hypotenuse
when the area is divisible by 4, 8, 16, or any higher power of 2?
A. We use class fields constructed by means of transcendental
functions, of course!”
— From the preface to Introduction to the Construction of Class Fields ,
by Harvey Cohn (Cambridge University Press, 1985)
Illustration:
For a related song, see Prime Suspect (Dec. 13, 2007).
Footnote of 12:14 AM Oct. 1, 2014 —
* That search yields a link to…
This Lyche webpage’s pentagram indicates an interest in Disney rather than
in Satanism. Other Lyche webpages have been less reassuring.
Related material — Posts tagged Elegantly Packaged.
Some related material in this journal: “Peter J. Cameron” + Magic.
(Continued from St. Augustine's Day, 2012)
"Plan 9 deals with the resurrection of the dead."
Epigraph to "No Great Magic," a story by Fritz Leiber:
To bring the dead to life
Is no great magic.
Few are wholly dead:
Blow on a dead man’s embers
And a live flame will start.
—Graves
"Shakespeare, Dante, Milton, Homer: those writers trafficked in
witches and fairies and ghosts and monsters. Why shouldn’t I?"
— Novelist Lev Grossman in The New York Times this afternoon
Grossman's father was the poet Allen Grossman.
See that Grossman in this journal, as well as a search for Holy Water.
See a post, The Omega Matrix, from the date of her death.
Related material:
"When Death tells a story, you really have to listen."
— Cover of The Book Thief
A scene from the film of the above book —
“Looking carefully at Golay’s code is like staring into the sun.”
Some context — "Mathematics, Magic, and Mystery" —
See posts tagged April Awareness 2014.
In memoriam :
“Margot Adler, an iconic NPR correspondent and Wiccan priestess,
died on Monday July 28 from endometrial cancer at the age of 68.”
— Huffington Post 07/28/2014 5:39 pm EDT
See also Log24 posts tagged NPR Magic.
“It’s going to be accomplished in steps,
this establishment of the Talented
in the scheme of things.”
— Anne McCaffrey, Radcliffe ’47, To Ride Pegasus
From a review of the new film “Magic in the Moonlight”—
“Sophie seems to have some actual talent….
When Sophie meets Aunt Vanessa, she uncovers the spinster’s
long-ago love affair with a member of parliament. It’s eerie.”
Material that is related, if only in story space:
“Lord knows when the cold wind blows
it’ll turn your head around.”
— James Taylor, “Fire and Rain”
Ricky Jay’s head turns around in “The Amazing Maleeni,”
episode 8 of season 7 of “The X-Files.”
“It was the middle of summer, but
the cold wind blew in full force.”
— David Kushner, Jonny Magic and the Card Shark Kids
(Quoted here in House of Cards, June 11, 2014,
a post on magic, cards, and Multnomah County.)
Related material:
Recent posts on artist Otto Piene and the Whiskey Bar song,
as well as the following Multnomah County story from yesterday’s
online NY Times :
From Wikipedia:
Wilf might prefer to be remembered not,
as in Thursday’s post, on the latter day above,
but rather on the former.
Happy birthday, Stellan Skarsgård.
Skarsgård in Exorcist: The Beginning .
“What was this Frankenstein he was creating?”
— David Kushner, Jonny Magic and the Card Shark Kids
Happy birthday, Gene Wilder.
See the Field
“There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”
— Website of Magicka: The Ninth Element Novel
William Worthy in Beijing —
This journal on the date of Worthy’s death,
May 4, 2014, had a link to…
See last night’s pentagram photo and a post from May 13, 2012.
That post links to a little-known video of a 1972 film.
A speech from the film was used by Oslo artist Josefine Lyche as a
voice-over in her 2011 golden-ratio video (with pentagrams) that she
exhibited along with a large, wall-filling copy of some of my own work.
The speech (see video below) is clearly nonsense.
The patterns* Lyche copied are not.
“Who are you, anyway?”
— Question at 00:41 of 15:00, Rainbow Bridge (Part 5 of 9)
at YouTube, addressed to Baron Bingen as “Mr. Rabbit”
* Patterns exhibited again later, apparently without the Lyche pentagram video.
It turns out, by the way, that Lyche created that video by superimposing
audio from the above “Rainbow Bridge” film onto a section of Disney’s 1959
“Donald in Mathmagic Land” (see 7:17 to 8:57 of the 27:33 Disney video).
For those disappointed by the cancellation
of this evening’s Black Mass at Harvard,
here is a somewhat less exciting substitute.
See also Peter J. Cameron + Magic.
From a New York Times obituary by Bruce Weber tonight—
Charles Marowitz, Director and Playwright, Dies at 82
“There are two kinds of bafflement in the theater: the kind that fascinates as it perplexes, and the kind that just perplexes,” he wrote in The Times in 1969 in an essay about Mr. Shepard’s play “La Turista,” which had recently opened in London. “If a play doesn’t make quick sense, but enters into some kind of dialogue with our subconscious, we tend to admit it to that lounge where we entertain interesting-albeit-unfamiliar strangers.
“If it only baffles, there are several courses open to us: we can assume it is ‘above our heads’ or directed ‘to some other kind of person,’ or regretfully conclude that it confuses us because it is itself confused. However, the fear of being proved wrong is so great today that almost every new work which isn’t patently drivel gets the benefit of the doubt.”
Another play by Sam Shepard mentioned in the obituary suggests a review of…
Scarlett Johansson stars in a new film, "Lucy," due to be
released on August 8, directed by Luc Besson, auteur of
The Fifth Element (1997). In other pop culture…
"There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But…."
— Website of Magicka: The Ninth Element Novel
See also, in this journal, Holy Field as well as Power of the Center.
Or: Three Shades of Gray
(Continued from previous Gray Space posts.)
Click the above image for some related mathematics.
Those who prefer “magic” approaches to mathematics*
may consult the works of Robert J. Stewart and his
mentor William G. Gray.
Robert J. Stewart (left) and a pentagram photo posted yesterday evening
by Oslo artist Josefine Lyche. See also Lyche in this journal.
* See the April 2014 banners displayed at the websites
of the American Mathematical Society and of the
Mathematical Association of America, as well as
a mathematician’s remarks linked to here last evening.
See also, in this journal, Arcade Fire and Witch Ball.
This post was suggested by remarks today of mathematician
Peter J. Cameron, who seems to enjoy playing the role of
Lord Summerisle (from The Wicker Man , a 1973 horror classic).
For John Milton at the Cervecería XX —
Related material: Peter J. Cameron on Bertrand Russell
in A Midnight Exorcism.
(Continued from June 9, 2009)
“The craziness is receding but no clarity is taking its place.”
— Joan Didion, The Year of Magical Thinking
A possible source of clarity:
Katy Perry in her new "Dark Horse" video—
"So you wanna play with magic.
Boy you should know what you're fallin' for.
Baby do you dare to do this?"
Bill Murray in Ghostbusters —
Continued from a post of January 28 —
In Memory of Pete Seeger.
The spiritual tribute link in that post suggests a review
of the following page from a pop-philosophy novel —
"Turn, turn, turn." — Pete Seeger. See also this morning's news.
The summoning of the spirit of Bertrand Russell
yesterday by Peter J. Cameron at his weblog
suggests a review of this weblog’s posts of
Christmas Eve, December 24-25, 2013.
(Recall that Robert D. Carmichael, who, in a book
linked to at midnight last Christmas Eve discusses
some “magic” mathematical structures,
reportedly was trained as a Presbyterian minister.
See also The Presbyterian Exorcist.)
Einstein and Thomas Mann, Princeton, 1938
See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.
January 13 was also the dies natalis of St. James Joyce.
Some related reflections —
"Praeterit figura huius mundi " — I Corinthians 7:31 —
Conclusion of of "The Dead," by James Joyce— The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live. Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling. A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead. |
Review —
From a Jan. 20, 2011, Emory University press release —
"Finite formula found for partition numbers" —
"We found a function, that we call P, that is like
a magical oracle," Ono says. "I can take any number,
plug it into P, and instantly calculate the partitions
of that number. P does not return gruesome numbers
with infinitely many decimal places. It's the finite,
algebraic formula that we have all been looking for."
Some may prefer Chinese oracles.
… Continues. See today's MAA news story about magic,
mystery, and the upcoming Joint Mathematics Meetings.
The New York Times this evening has a story
on "A Piece of Work," an avant-garde production
at Brooklyn Academy of Music (BAM) that is to open
Wednesday.
A background check on Annie Dorsen, the production's
author-director, yields the following remarks on a video
promoting a show titled "Magical"—
"This video is sent us by the company for promotion
of their show in Bergen the 15. and 16. of April 2011.
Excerpt from the program:
Do magic and feminism go together? Anne Juren, the
French choreographer living in Vienna, and Annie
Dorsen, the New York based director, attempt to prove
that it can: it’s alchemical, it’s political and it works."
Related material: This journal eight years ago today, and
the Log24 posts from the dates, April 15-16, 2011, of the
"Magical" production in Bergen, Norway.
Happy birthday, Julie Taymor.
Yes. See …
The 48 actions of GL(2,3) on a 3×3 coordinate-array A,
when matrices of that group right-multiply the elements of A,
with A =
(1,1) (1,0) (1,2) (0,1) (0,0) (0,2) (2,1) (2,0) (2,2) |
Actions of GL(2,p) on a pxp coordinate-array have the
same sorts of symmetries, where p is any odd prime.
Note that A, regarded in the Sallows manner as a magic square,
has the constant sum (0,0) in rows, columns, both diagonals, and
all four broken diagonals (with arithmetic modulo 3).
For a more sophisticated approach to the structure of the
ninefold square, see Coxeter + Aleph.
“DEVIL – MUSIC
20 pages of incidental music written at school
for G. K. Chesterton’s play MAGIC
by D. Coxeter.”
See also…
Related material — Chesterton + Magic in this journal.
This post was suggested by…
1. Movie reviews links on the NY Times online front page—
2. "When Death tells a story…" in this journal
3. A search for "Recognition" in this journal
(suggested by Terence Cave's Recognitions ,
mentioned in a post of October 31.)
4. The play "Magic," by G. K. Chesterton
5. The following posts —
The post itself consists simply of the title,
together with the above items that suggested
the title.
Scene I:
"Pinter's particular usage of reverse chronology
in structuring the plot is innovative…."
— Wikipedia on the play "Betrayal," a version of which
opens tonight
Scene II:
Reverse Chronology in Wikipedia —
"As a hypothetical example, if the fairy tale Jack and the Beanstalk
was told using reverse chronology, the opening scene would depict
Jack chopping the beanstalk down and killing the giant. The next
scene would feature Jack being discovered by the giant and climbing
down the beanstalk in fear of his life. Later, we would see Jack running
into the man with the infamous magic beans, then, at the end of the film,
being sent off by his mother to sell the cow."
Scene III:
Dialogue for Scene III —
"Sell the damn cow, Jack."
Epilogue: Jack + Jill.
A sequel to last night's "For Baron Samedi" —
Sigils
The music in the trailer for the new film "American Hustle"
is a 1969 tune by Led Zeppelin. This, together with the
magick sigils posted at Facebook yesterday by artist
Josefine Lyche, suggests a review of Zeppelin sigils
from a 1971 album. These are, as shown above on a
record label, the personal symbols of the four musicians
in the band. Two of the symbols may, of course, be
interpreted as representing the Holy Trinity.
Click on the image for a video.
See also Josefine Lyche's "Grids, you say?"
I prefer Lyche's versions of the diagonal
3×3 grid. Her versions have no lettering.
(This post was suggested by a photo of magical sigils
that Lyche posted a few hours ago at Facebook.
The above seems to be another such sigil that may
or may not be intended to function like those posted
today by Lyche.)
Part I: Paranoia
" 'The Truman Show' did not single-handedly cause
Truman delusions, any more than 'The Manchurian
Candidate' caused Cold War paranoia. In the fifteen
years since 'The Truman Show' was released, its
premise has increasingly come to seem nonbizarre."
— Andrew Marantz in The New Yorker ,
issue dated Sept. 16, 2013, page 35
Part II: Amen
Part III: The Magic 8-Ball
Part IV: Sinking the Magic 8-Ball
Part V: The Color of Money
Legendary Magician John Calvert Dies at 102
The Hollywood Reporter , 8:36 PM PDT 9/27/2013
by Mike Barnes —
" 'Out in Hollywood many years ago, Danny Kaye was
in my show and came out and impersonated Hitler,'
Calvert said in a 1998 interview. 'Then the Marines
would come out and grab him and put him in the buzz saw
and we’d cut his head off, put his head in a sausage grinder,
and out came German wieners!' "
See MAX in the posts of September 9th.
"Calvert died Friday [Sept. 27] in Lancaster, Calif., according to
The International Brotherhood of Magicians."
See also The Carlin Code (May 12, 2006).
The title is taken from Isak Dinesen— See the previous post,
which posed the question, "Stylist or fraud?"
Stylist and fraud—
The stylist: Gerard Manley Hopkins, Society of Jesus
The fraud (i.e., the fiction):
Click on the cover art for further details.
The cover artist, by the way, died on the date*
mentioned prominently in the previous post.
* September 7, 2009.
See also that date in this journal, with its post
"Magic Boxes." Happy birthday, J. K. Rowling.
Profile picture of "Jo Lyxe" (Josefine Lyche) at Vimeo—
Compare to an image of Vril muse Maria Orsitsch.
From the catalog of a current art exhibition
(25 May – 31 August, 2013) in Norway,
I DE LANGE NÆTTER —
Josefine Lyche
Keywords (to help place my artwork in the (See also the original catalog page.) |
Clearly most of this (the non-highlighted parts) was taken
from my webpage Diamond Theory. I suppose I should be
flattered, but I am not thrilled to be associated with the
(apparently fictional) Vril Society.
For some background, see (for instance)
Conspiracy Theories and Secret Societies for Dummies .
"Da hats ein Eck" —
"you've/she's (etc.) got problems there"
St. Galluskirche:
St. Gallus's Day, 2012:
Click image for a St. Gallus's Day post.
A related problem:
Discuss the structure of the 4x4x4 "magic" cube
sent by Pierre de Fermat to Father Marin Mersenne
on April 1, 1640, in light of the above post.
Promotional description of a new book:
“Like Gödel, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking.”
“Like Gödel, Escher, Bach before it….”
Or like Metamagical Themas .
Rubik core:
Non- Rubik cores:
Of the odd nxnxn cube: | Of the even nxnxn cube: |
Related material: The Eightfold Cube and…
“A core component in the construction
is a 3-dimensional vector space V over F2 .”
— Page 29 of “A twist in the M24 moonshine story,”
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
Let's do the twist. The image at left See this journal |
A phrase from yesterday's noon post:
Sinking the Magic 8-Ball .
A scene from the above film is related to this phrase.
Another image from the film poster:
A review of the film:
"The final 'twist' seems to negate the entire story,
like a bad shaggy-dog joke."
Such a joke:
“Words and numbers are of equal value,
for, in the cloak of knowledge,
one is warp and the other woof.”
— The princesses Rhyme and Reason
in The Phantom Tollbooth
"A core component in the construction
is a 3-dimensional vector space V over F2 ."
— Page 29 of "A twist in the M24 moonshine story,"
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
The number of points in such a space is, of course, 8.
This morning's previous post pictured the cover
of a book titled "The Mystery of the Quantum World."
That title, together with Peter Woit's post on Hawking
yesterday, suggests a review of the phrase "M -theory."
See remarks on that topic in the October 1998
Notices of the American Mathematical Society :
"The richer theory, which has as limiting cases
the five string theories studied in the last generation,
has come to be called M -theory, where M stands for
magic, mystery, or matrix, according to taste."
— "Magic, Mystery, and Matrix," by Edward Witten
See also, in this journal, a post mentioning Hawking's
vulgarized M -theory book The Grand Design , as well
as a post of January 9, 2012, titled "M Theory."
Of Witten's three alternative meanings for M , I prefer "matrix."
For the cruelest month
Click for a much larger version of the photo below.
These four Kountry Korn quartets are from the Fox Valleyaires
Men's Barbershop Chorus of Appleton, Wisconsin.
See also the fine arts here on Saturday, April 6, 2013—
The New York Times Magazine cover story
a decade ago, on Sunday, April 6, 2003:
"The artists demanded space
in tune with their aesthetic."
— "The Dia Generation,"
by Michael Kimmelman
Related material:
See Wikipedia for the difference between binary numbers
and binary coordinates from the finite Galois field GF(2).
For some background, see the relativity problem.
See also the chapter on vector spaces in Korn & Korn
(originally published by McGraw-Hill)—
.
On this journal:
"he seems to repeat stuff compulsively punctuated with citing others and berating them for note taken nor credit given of his precedence .. but like i said, he more than makes up for that, dredging up and dusting off his all time faves like a super expensive store keeper who moves a piece only once a decade"
— "poetpiet" on Feb. 23, 2013
This suggests moving a piece linked to here
(in an update; scroll down) a decade ago.
Photo source: http://evanfazio.com/public-relations-lessons-from-the-chess-board/
The New York Times Magazine cover story
a decade ago, on Sunday, April 6, 2003:
"The artists demanded space
in tune with their aesthetic."
— "The Dia Generation,"
by Michael Kimmelman
Related material: Occupy Space in this journal.
The previous post described briefly a 2002
book on magic and religion, Golems of Gotham .
For a Sunday New York Times review, click here.
"Hans Castorp is a searcher after the Holy Grail.
You would never have thought it when you read
his story—if I did myself, it was both more and
less than thinking. Perhaps you will read the
book again from this point of view. And perhaps
you will find out what the Grail is: the knowledge
and the wisdom, the consecration, the highest
reward, for which not only the foolish hero but
the book itself is seeking. You will find it in the
chapter called 'Snow'…."
— Thomas Mann, "The Making of
The Magic Mountain "
In related entertainment news…
Click image for some backstory.
Mann's tale is set in Davos, Switzerland.
See also Mayer at Davos.
Yesterday's post Treasure Hunt, on a Brazilian weblog,
suggests a review of Brazil in this journal. The post
most relevant to yesterday's remarks is from
August 15, 2003, with a link, now broken, to the work
of Brazilian artist Nicole Sigaud* that also uses the
four half-square tiles used in 1704 by Sebastien Truchet
and somewhat later by myself in Diamond Theory
(see a 1977 version).
A more recent link that works:
http://vismath9.tripod.com/sigaud/e-index.html ANACOM PROJECT
APPLICATIONS
© 1997 – 2002 Nicole Sigaud |
* Sigaud shares the interests of her fellow Brazilian
whose weblog was the subject of yesterday's
Treasure Hunt.—
"For many years I have dedicated myself to the study
of medieval magic, demonology, Kabbalah, Astrology,
Alchemy, Tarot and divination in general."
— Nicole Sigaud (translated by Google) in a self-profile:
http://www.recantodasletras.com.br/autor.php?id=78359.
I do not share the interest of these authors in such matters,
except as they are reflected in the works of authors like
Charles Williams and Umberto Eco.
In memory of Charles Rosen:
Related material:
The Magic Square in Doctor Faustus (October 10th, 2012)
Elementary Finite Geometry (August 1st, 2012)
The Space of Horizons (August 7th, 2012)
Chromatic Plenitude (Rosen on Schoenberg)
Do you know where the mushrooms are?
Above: Image from Log24 on Dec. 4th, 2012, at 4:23 PM ET.
See also… on that date at that time …
The American College of Neuropsychopharmacology… (click to enlarge)—
For the Dec. 3rd-4th graduate conference
at the University of Cambridge on
"Occultism, Magic, and the History of Art"—
Four novels by Charles Williams—
See also the life, and Dec. 1st death, of a former Chief Justice of South Africa.
For the scholars gathered at a graduate conference
today and tomorrow at Cambridge University* on
"Occultism, Magic, and the History of Art"—
Part I: Krapp
Click image for a 2006 New York Times story —
Part II: Hash
A magic— indeed, diabolic— square:
For the construction, see a book
by W. W. Rouse Ball, founding president
of a Cambridge University magic society.
For some related religious remarks,
see Raiders of the Lost Matrix.
"Any sufficiently advanced technology is indistinguishable from magic."
"The HP/Autonomy Debacle," by John C. Dvorak at pcmag.com on Tuesday, Nov. 20, 2012—
"The whole Autonomy thing was weird since the company seemed to be performing magic. On co-founder Michael Richard Lynch's Wikipedia page, the company is described as 'a leader in the area of computer understanding of unstructured information, an area which is becoming known as meaning-based computing .'
I do not know how gullible HP's board of directors is, but when I see the sudden emergence of something called 'meaning-based computing,' the alarms sound and the bullcrap meter begins to tag the red line."
A story by Terence K. Huwe in Online magazine, Sept.-Oct. 2011, defines meaning-based computing (MBC), discusses Autonomy , and llnks to…
John Markoff in The New York Times , March 4, 2011—
"Engineers and linguists at Cataphora, an information-sifting company based in Silicon Valley, have their software mine documents for the activities and interactions of people— who did what when, and who talks to whom. The software seeks to visualize chains of events. It identifies discussions that might have taken place across e-mail, instant messages and telephone calls.
Then the computer pounces, so to speak, capturing 'digital anomalies' that white-collar criminals often create in trying to hide their activities.
For example, it finds 'call me' moments— those incidents when an employee decides to hide a particular action by having a private conversation. This usually involves switching media, perhaps from an e-mail conversation to instant messaging, telephone or even a face-to-face encounter."
For example…
This morning's New York Times obituaries—
These suggest a look at Solving Nabokov's Lolita Riddle ,
by Joanne Morgan (Sydney: Cosynch Press, 2005).
That book discusses Lolita as a character like Lewis Carroll's Alice.
(The Red Queen and Alice of course correspond to figures in
the first two thumbnails above.)
From the obituary associated with the third thumbnail above:
"Front-page headlines combined concision and dark humor."
The title of this post, Bend Sinister , is not unlike such a headline.
It is the title of a novel by Nabokov (often compared with Orwell's 1984 )
that is discussed in the Lolita Riddle book.
Related material— The bend sinister found in Log24 searches
for Hexagram 14 and for the phrase Hands-On—
Last Wednesday's 11 PM post mentioned the
adjacency-isomorphism relating the 4-dimensional
hypercube over the 2-element Galois field GF(2) to
the 4×4 array made up of 16 square cells, with
opposite edges of the 4×4 array identified.
A web page illustrates this property with diagrams that
enjoy the Karnaugh property— adjacent vertices, or cells,
differ in exactly one coordinate. A brief paper by two German
authors relates the Karnaugh property to the construction
of a magic square like that of Dürer (see last Wednesday).
In a similar way (search the Web for Karnaugh + cube ),
vertex adjacency in the 6-dimensional hypercube over GF(2)
is isomorphic to cell adjacency in the 4x4x4 cube, with
opposite faces of the 4x4x4 cube identified.
The above cube may be used to illustrate some properties
of the 64-point Galois 6-space that are more advanced
than those studied by enthusiasts of "magic" squares
and cubes.
See
Those who prefer narrative to mathematics may
consult posts in this journal containing the word "Cuber."
Occurrences of the phrase "magic square" in Lowe-Porter's translation of the Thomas Mann novel Doctor Faustus—
"On the wall above the piano was an arithmetical diagram fastened with drawing-pins, something he had found in a second-hand shop: a so-called magic square, such as appears also in Dürer's Melancolia , along with the hour-glass, the circle, the scale, the polyhedron, and other symbols. Here as there, the figure was divided into sixteen Arabic-numbered fields, in such a way that number one was in the right-hand lower corner, sixteen in the upper left; and the magic, or the oddity, simply consisted in the fact that the sum of these numerals, however you added them, straight down, crosswise, or diagonally, always came to thirty-four. What the principle was upon which this magic uniformity rested I never made out, but by virtue of the prominent place Adrian had given it over the piano, it always attracted the eye, and I believe I never visited his room without giving a quick glance, slanting up or straight down and testing once more the invariable, incredible result."
….
"Adrian kept without changing during the whole four and a half years he spent in Leipzig his two-room quarters in Peterstrasse near the Collegium Beatae Virginis, where he had again pinned the magic square above his cottage piano."
….
" 'The decisive factor is that every note, without exception, has significance and function according to its place in the basic series or its derivatives. That would guarantee what I call the indifference to harmony and melody.'
'A magic square,' I said. 'But do you hope to have people hear all that?' "
….
" 'Extraordinarily Dürerish. You love it. First "how will I shiver after the sun"; and then the houre-glasse of the Melancolia . Is the magic square coming too?' "
….
"Here I will remind the reader of a conversation I had with Adrian on a long-ago day, the day of his sister's wedding at Buchel, as we walked round the Cow Trough. He developed for me— under pressure of a headache— his idea of the 'strict style,' derived from the way in which, as in the lied 'O lieb Madel, wie schlecht bist du ' melody and harmony are determined by the permutation of a fundamental five-note motif, the symbolic letters h, e, a, e, e-flat. He showed me the 'magic square' of a style of technique which yet developed the extreme of variety out of identical material and in which there is no longer anything unthematic, anything that could not prove itself to be a variation of an ever constant element. This style, this technique, he said, admitted no note, not one, which did not fulfil its thematic function in the whole structure— there was no longer any free note."
Review of related material—
Last night's midnight post (disambiguation), the followup 1 AM post (ambiguation), today's noon post (ambiguity), and Dürer in this journal.
The tesseracts of the noon post are related to the Dürer magic square by a well-known adjacency property.
"… the once stable 'father's depression' has been transmuted into a shifting reality that shimmered in a multiplicity of facets."
— Haim Omer, Tel-Aviv University, on Milanese ambiguation therapy,
p. 321 in "Three Styles of Constructive Therapy,"
Constructive Therapies, Vol. 2 , pp. 319-333,
ed. by Michael F. Hoyt (Guilford Press paperback, 1998)
(Continued from Tuesday, Oct. 2)
From today's online New York Times—
"The Schoenberg proved the highlight of the evening,
sandwiched between polished but otherwise routine
performances of Bach’s Keyboard Concerto No. 1
in D minor and Mozart’s Symphony No. 36 ('Linz'),
which ended the evening."
From a Wikipedia article— The Jew of Linz is a controversial 1998 book by Australian writer Kimberley Cornish. It alleges that the Austrian philosopher Ludwig Wittgenstein had a profound effect on Adolf Hitler when they were both pupils at the Realschule (lower secondary school) in Linz, Austria, in the early 1900s. One section of the article—
No-ownership theory of mind |
See also Dreamcatcher in this journal.
Yesterday's online Los Angeles Times
on a film that inspired recent protests in Cairo—
The film… was shown on June 23
to an audience of less than 10
at a theater on Hollywood Boulevard,
a source familiar with the screening said….
The screening was at The Vine Theater,
which rents itself out for private screenings,
said one person involved in the theater.
An image from this journal on that same day, June 23—
Source: Rudolf Koch, The Book of Signs
For some background on the symbol, see Damnation Morning.
See also Don Henley's Hollywood hymn "Garden of Allah."
Update of 8 PM Sept. 13, 2012—
Other sources give the film's screening date not as June 23,
2012, but rather as June 30, 2012. (BBC News, LAWEEKLY blogs)
The following post from this journal on that date may or
may not have some religious relevance.
Saturday, June 30, 2012
Filed under: Uncategorized — m759 @ 7:20 PM "… to snare the spirits of mankind in nets of magic" — The aim of the artist, according to Thomas Wolfe Related entertainment— High-minded— Many Dimensions . Not so high-minded— The Cosmic Cube . |
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:
"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?"
Above: Amy Adams in "Sunshine Cleaning"
Related material:
Wikipedia on a magical ring—
Background— The Ring and the Stone, a story linked to here Wednesday.
"By then he was familiar with the work of the Vienna Actionists….
He once said that he had his first taste of the movement
when he heard the screams of his mother’s dental patients
from her office next door to the family’s apartment."
— Obituary of a Viennese artist who reportedly died Wednesday
(Mathematics and Narrative, continued)
Narrative—
The Ring and The Stone from yesterday’s post, and…
“In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon….”
— Wikipedia article, Seal of Solomon
Mathematics—
A fact related to the mathematical
“Solomon’s seal” described above by Bell:
The reference to Edge is as follows—
[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group,
Canadian J. Maths. 11 (1959) ….
(This reference relates Hirschfeld’s remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective space PG (5, 2)).
"… to snare the spirits of mankind in nets of magic"
— The aim of the artist, according to Thomas Wolfe
Related entertainment—
High-minded— Many Dimensions .
Not so high-minded— The Cosmic Cube .
It Must Be Abstract
It Must Change
It Must Give Pleasure
— Parts of a poem by Wallace Stevens
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
– Thomas Wolfe, Of Time and the River
Of Time and the River and the Frogs —
* This post's title refers to the above uploading date— Jan. 26, 2008.
The New York Times today—
"Reality and our perception of it are incommensurate…."
The above New York Times Wire item from 3:35 PM ET today
mentions two topics touched on in today's earlier Log24 post
Bowling in Diagon Alley— magic (implied by the title) and
incommensurability. The connection in that post
between the two topics is the diagonal of a square.
The wire item shows one detail from a Times illustration
of the linked article— a blindfolded woman.
Another detail from the same illustration—
Hands-on Wand Work
See also remarks on Magic in this journal and on Harry Potter.
I dislike both topics.
In memory of Paul Sussman, author of archaeological
mystery novels about Egypt—
"… the sacred symbols of the cosmic elements — Thrice-Great Hermes: Excerpts and Fragments , |
Sussman's last novel, not yet published, was
Sussman, 45, reportedly died suddenly on May 31, 2012.
A perhaps relevant thought—
"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical
ultraomnipotence."
– e. e. cummings, 1944
“… Which makes it a gilt-edged priority that one of us
gets into that Krell lab and takes that brain boost.”
— American adaptation of Shakespeare's Tempest , 1956
From "The Onto-theological Origin of Play:
Heraclitus and Plato," by Yücel Dursun, in
Lingua ac Communitas Vol 17 (October 2007)—
"Heraclitus’s Aion and His Transformations
The saying is as follows:
αἰὼν παῖς ἐστι παίζων, πεττεύων·
παιδὸς ἡ βασιληίη
(Aion is a child playing draughts;
the kingship is the child’s)
(Krell 1972: 64).*
* KRELL, David Farrell.
“Towards an Ontology of Play:
Eugen Fink’s Notion of Spiel,”
Research in Phenomemology ,
2, 1972: 63-93.
This is the translation of the fragment in Greek by Krell.
There are many versions of the translation of the fragment….."
See also Child's Play and Froebel's Magic Box.
Update of May 5— For some background
from the date May 4 seven years ago, see
The Fano Plane Revisualized.
For some background on the word "aion,"
see that word in this journal.
"… he continued to make brief appearances
on the show, including the one this past
New Year's Eve.* "
— Bruce Weber, New York Times
"The only stars Clark coveted
for his show in those early years
but could not get were
the Beatles and Ricky Nelson…."
— Geoff Boucher, Los Angeles Times
"I don't know why you say goodbye"
"There was … magic in the air"
"At the still point…" — T. S. Eliot
In memory of David L. Waltz, artificial-intelligence pioneer,
who died Thursday, March 22, 2012—
The following from the First of May, 2010—
Some context–
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."
– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71
"Imbedding the God character in a holy book's very detailed narrative
and building an entire culture around this narrative
seems by itself to confer a kind of existence on Him."
— John Allen Paulos in the philosophy column "The Stone,"
New York Times online, Oct. 24, 2010
A related post from Log24 later that year—
Sunday, November 28, 2010
|
"Next come the crown of thorns and Jesus' agonized crawl across the stage,
bearing the weight of his own crucifix. And at last, after making
yet another entrance, Mr. Nolan strikes the pose immortalized
in centuries of art, clad in a demure loincloth, arms held out to his sides,
one leg artfully bent in front of the other, head hanging down
in tortured exhaustion. Gently spotlighted, he rises from the stage
as if by magic, while a giant cross, pulsing with hot gold lights,
descends from above to meet him. Mr. Lloyd Webber's churning guitar rock
hits a climactic note, and the audience erupts in excited applause."
— Charles Isherwood, review of "Jesus Christ Superstar" in today's New York Times
Other remarks on embedding —
Part I
Review of a new book on linguistics, embedding, and a South American tribe—
"Imagine a linguist from Mars lands on Earth to survey the planet's languages…."
— Chronicle of Higher Education , March 20, 2012
Part II
The Embedding , by Ian Watson (Review of a 1973 novel from Shakespeare's birthday, 2006)
For Women's History Month—
The Beam of Pink Light
From a post linked to on Lyxe's upload date, Feb. 6, 2012—
“… 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.
See also the NY Lottery for St. Luke's Day, 2011, publication date
of the new edition of Philip K. Dick's VALIS quoted above.
Today's previous post, on the Feb. 2012 Scientific American
article "Is Space Digital?", suggested a review of a notion
that the theoretical physicist John Archibald Wheeler called
pregeometry .
From a paper on that topic—
"… the idea that geometry should constitute
'the magic building material of the universe'
had to collapse on behalf of what Wheeler
has called pregeometry (see Misner et al. 1973,
pp. 1203-1212; Wheeler 1980), a somewhat
indefinite term which expresses “a combination
of hope and need, of philosophy and physics
and mathematics and logic” (Misner et al. 1973,
p. 1203)."
— Jacques Demaret, Michael Heller, and
Dominique Lambert, "Local and Global Properties
of the World," preprint of paper published in
Foundations of Science 2 (1): 137-176
Misner, C. W., Thorne, K. S. and Wheeler, J. A.
1973, Gravitation , W.H. Freeman and Company:
San Francisco.
Wheeler, J.A. 1980, "Pregeometry: Motivations
and Prospects," in: Quantum Theory and Gravitation ,
ed. A.R. Marlow, Academic Press: New York, pp. 1-11.
Some related material from pure mathematics—
Click image for further details.
Maureen Dowd's NY Times column today is on exorcism.
Related material— This morning's update at the end of
yesterday morning's Valentine's Day post Notable Transitions.
See also another post for St. Valentine — The Ninth Configuration.
The twin topics of autism and of narrowing definitions
suggested the following remarks.
The mystical number "318" in the pilot episode
of Kiefer Sutherland's new series about autism, "Touch,"
is so small that it can easily apply (as the pilot
illustrated) to many different things: a date, a
time, a bus number, an address, etc.
The last 3/18 Log24 post— Defining Configurations—
led, after a false start and some further research,
to the writing of the webpage Configurations and Squares.
An image from that page—
Interpreting this, in an autistic manner, as the number
287501346 lets us search for more specific items
than those labeled simply 318.
The search yields, among other things, an offer of
Night Magic Cologne (unsold)—
For further mystery and magic, see, from the date
the Night Magic offer closed— May 8, 2010— "A Better Story."
See also the next day's followup, "The Ninth Gate."
“Examples galore of this feeling must have arisen in the minds of the people who extended the Magic Cube concept to other polyhedra, other dimensions, other ways of slicing. And once you have made or acquired a new ‘cube’… you will want to know how to export a known algorithm , broken up into its fundamental operators , from a familiar cube. What is the essence of each operator? One senses a deep invariant lying somehow ‘down underneath’ it all, something that one can’t quite verbalize but that one recognizes so clearly and unmistakably in each new example, even though that example might violate some feature one had thought necessary up to that very moment. In fact, sometimes that violation is what makes you sure you’re seeing the same thing , because it reveals slippabilities you hadn’t sensed up till that time….
… example: There is clearly only one sensible 4 × 4 × 4 Magic Cube. It is the answer; it simply has the right spirit .”
— Douglas R. Hofstadter, 1985, Metamagical Themas: Questing for the Essence of Mind and Pattern (Kindle edition, locations 11557-11572)
See also Many Dimensions in this journal and Solomon’s Cube.
(Continued from Epiphany and from yesterday.)
Detail from the current American Mathematical Society homepage—
Further detail, with a comparison to Dürer’s magic square—
The three interpenetrating planes in the foreground of Donmoyer‘s picture
provide a clue to the structure of the the magic square array behind them.
Group the 16 elements of Donmoyer’s array into four 4-sets corresponding to the
four rows of Dürer’s square, and apply the 4-color decomposition theorem.
Note the symmetry of the set of 3 line diagrams that result.
Now consider the 4-sets 1-4, 5-8, 9-12, and 13-16, and note that these
occupy the same positions in the Donmoyer square that 4-sets of
like elements occupy in the diamond-puzzle figure below—
Thus the Donmoyer array also enjoys the structural symmetry,
invariant under 322,560 transformations, of the diamond-puzzle figure.
Just as the decomposition theorem’s interpenetrating lines explain the structure
of a 4×4 square , the foreground’s interpenetrating planes explain the structure
of a 2x2x2 cube .
For an application to theology, recall that interpenetration is a technical term
in that field, and see the following post from last year—
Saturday, June 25, 2011
— m759 @ 12:00 PM “… the formula ‘Three Hypostases in one Ousia ‘ Ousia
|
Stephen Rachman on "The Purloined Letter"
"Poe’s tale established the modern paradigm (which, as it happens, Dashiell Hammett and John Huston followed) of the hermetically sealed fiction of cross and double-cross in which spirited antagonists pursue a prized artifact of dubious or uncertain value."
For one such artifact, the diamond rhombus formed by two equilateral triangles, see Osserman in this journal.
Some background on the artifact is given by John T. Irwin's essay "Mysteries We Reread…" reprinted in Detecting Texts: The Metaphysical Detective Story from Poe to Postmodernism .
Related material—
Mathematics vulgarizer Robert Osserman died on St. Andrew's Day, 2011.
A Rhetorical Question
"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"
Christopher Hitchens on J. K. Rowling—
“We must not let in daylight upon magic,” as Walter Bagehot remarked in another connection, and the wish to have everything clarified is eventually self-defeating in its own terms. In her correct determination to bring down the curtain decisively, Rowling has gone further than she should, and given us not so much a happy ending as an ending which suggests that evil has actually been defeated (you should forgive the expression) for good.
Greater authors— Arthur Conan Doyle most notably— have been in the same dilemma when seeking closure. And, like Conan Doyle, Rowling has won imperishable renown for giving us an identifiable hero and a fine caricature of a villain, and for making a fictional bit of King’s Cross station as luminous as a certain address on nearby Baker Street. It is given to few authors to create a world apart, and to populate it as well as illustrate it in the mind.
"A fictional bit of King's Cross Station"—
Throughout the series, Harry has traveled to King's Cross Station, either to depart for Hogwarts or return to London on the Hogwarts Express. The station has always symbolized the crossroad between the Muggle world and the Wizarding realm and Harry's constant shuffling between, and his conflict with, the two extremes. As Harry now finds himself at a transition point between life and death, it is purely to be expected that he would see it within his own mind as a simulacrum of that station. And though Dumbledore assures Harry that he (Harry) is not actually dead, it seems Harry can choose that option if he so wishes. Harry has literally and figuratively been stripped bare, and must decide either to board a train that will transport him to the "other side", or return to the living world…. — Wikibooks.org
From "Elegy to the Void," by Cathleen Schine, New York Review of Books , issue dated Nov. 24, 2011—
“We tell ourselves stories in order to live,” Didion famously wrote in The White Album . Blue Nights is about what happens when there are no more stories we can tell ourselves, no narrative to guide us and make sense out of the chaos, no order, no meaning, no conclusion to the tale. The book has, instead, an incantatory quality: it is a beautiful, soaring, polyphonic eulogy, a beseeching prayer that is sung even as one knows the answer to one’s plea, and that answer is: No.
Blue Nights is a sequel of sorts to The Year of Magical Thinking , Didion's story of the year following the death on December 30th, 2003, of her husband, fellow writer John Gregory Dunne.
Related material:
For some context, see
For a different link to that aria, see a journal entry dated December 28, 2003.
(Click link, scroll down.)
The Catholic Encyclopedia on Mind—
"If we are told that the explanation of a page of a newspaper is to be found in the contact of the paper with a plate of set types, we are still compelled to ask how the particular arrangement of the types came about, and we are certain that the sufficient explanation ultimately rests in the action of mind or intelligent being."
Or not so certain—
"These capacities for conscious deliberation, rational thinking and self-control are not magical abilities. They need not belong to immaterial souls outside the realm of scientific understanding (indeed, since we don’t know how souls are supposed to work, souls would not help to explain these capacities). Rather, these are the sorts of cognitive capacities that psychologists and neuroscientists are well positioned to study."
— "The Stone" column in yesterday's online New York Times
See also the Catholic Encyclopedia on Soul.
It turns out that Fabrizio Palombi, author and editor of books on the late combinatorialist-philosopher Gian-Carlo Rota, is also an expert on the French charlatan Lacan. (For recent remarks related to Rota, see yesterday's Primordiality and the link "6.7 (June 7)" in today's The Crowe Sphere.)
"We all have our little mythologies."
— "Lacan’s Mathematics," by Amadou Guissé, Alexandre Leupin, and Steven D. Wallace (a preprint from the website of Steven D. Wallace, assistant professor of mathematics at Macon State College, Macon, GA.) A more extensive quote from "Lacan's Mathematics"—
Epistemological Cuts* or Births?
An epistemological cut can be described as the production of homonyms. For example, the word orb in Ptolemaic cosmology and the same word in the Kepler’s system, albeit similar, designate two entities that have nothing in common: the first one, in the Ancients’ cosmology, is a crystal sphere to which stars are attached; orb, for Kepler, is an ellipsis whose sole material existence is the algorithm describing its path. A cut becomes major when all word of different eras change meaning. A case in point is the cut between polytheism and monotheism (Judaism): the word god or god takes an entirely different meaning, and this change affects all areas of a vision of the world. From the non created world of the Ancients, inhabited by eternal Gods, we pass on to a world created by a unique God, who is outside of his creation. This cut affects all areas of thinking. However, mythology, albeit separated from the new vision by the cut, survives as an enduring residue. Our sexual thinking, for example, is essential mythological, as proven by the endurance of the Oedipus complex or our cult of this ancient deity called Eros. Love is inherently tied to what Freud called the omnipotence of thought or magical thinking.
Of course, the quintessential major epistemological cut for us is the break effectuated by modern science in the 17th century. All the names are affected by it: however, who can claim he or she has been entirely purged of pre-scientific reasoning? Despite us living in a scientific universe, we all have our little mythologies, residues of an era before the major epistemological cut.
Any modeling of major epistemological cuts, or paradigm changes as Thomas Kuhn would have it, has therefore to account at the same time for a complete break with past names (that is, new visions of the world) as well as the survival of old names and mythologies.
* For some background on this Marxist jargon, see Epistemological Break (La Coupure Épistémologique ) at the website Concept and Form: The Cahiers pour l’Analyse and Contemporary French Thought.
For more about Rome, see two pages from Stevens suggested
by the New York Lottery numbers from today, St. Peter's Day.
The pages mention "Rome after dark" and a "disused ambit
of the soul." Those who prefer a "more severe, more
harassing master" may consult the date 8/6/79 suggested by
the New York Lottery this afternoon and, from that date,
Freeman Dyson's memoir in The New Yorker .
This evening's four-digit number, 0006, may, if one likes,
be regarded as an "artist's signature" of sorts.
The New Yorker on Dyson—
"He recalls that at age 8 he read 'The Magic City,'
by Edith Nesbit. It is the story of a crazy universe.
He now sees that this universe bears a strong
resemblance to the one we live in."
Yesterday's post Ad Meld featured Harry Potter (succeeding in business),
a 4×6 array from a video of the song "Abracadabra," and a link to a post
with some background on the 4×6 Miracle Octad Generator of R.T. Curtis.
A search tonight for related material on the Web yielded…
Weblog post by Steve Richards titled "The Search for Invariants:
The Diamond Theory of Truth, the Miracle Octad Generator
and Metalibrarianship." The artwork is by Steven H. Cullinane.
Richards has omitted Cullinane's name and retitled the artwork.
The author of the post is an artist who seems to be interested in the occult.
His post continues with photos of pages, some from my own work (as above), some not.
My own work does not deal with the occult, but some enthusiasts of "sacred geometry" may imagine otherwise.
The artist's post concludes with the following (note also the beginning of the preceding post)—
"The Struggle of the Magicians" is a 1914 ballet by Gurdjieff. Perhaps it would interest Harry.
Magic Time!
For fans of Douglas Adams and St. Augustine
Update of 2:20 AM June 13:
For the midday "042" as a reference to Adams, see Wikipedia. The "828" may be interpreted as a reference to St. Augustine's feast day, 8/28… or, for the more secularly minded, a reference to the time 8:28 PM (to go with the evening "0845" as a reference to 8:45 PM). For further details, see Times of the Times . The midday "7286" is more difficult. See midnight's Broadway Cinderella.
From this journal on July 23, 2007—
It is not enough to cover the rock with leaves. We must be cured of it by a cure of the ground Or a cure of ourselves, that is equal to a cure Of the ground, a cure beyond forgetfulness. And if we ate the incipient colorings – Wallace Stevens, “The Rock” |
This quotation from Stevens (Harvard class of 1901) was posted here on when Daniel Radcliffe (i.e., Harry Potter) turned 18 in July 2007.
Other material from that post suggests it is time for a review of magic at Harvard.
On September 9, 2007, President Faust of Harvard
“encouraged the incoming class to explore Harvard’s many opportunities.
‘Think of it as a treasure room of hidden objects Harry discovers at Hogwarts,’ Faust said.”
That class is now about to graduate.
It is not clear what “hidden objects” it will take from four years in the Harvard treasure room.
Perhaps the following from a book published in 1985 will help…
The March 8, 2011, Harvard Crimson illustrates a central topic of Metamagical Themas , the Rubik’s Cube—
Hofstadter in 1985 offered a similar picture—
Hofstadter asks in his Metamagical introduction, “How can both Rubik’s Cube and nuclear Armageddon be discussed at equal length in one book by one author?”
For a different approach to such a discussion, see Paradigms Lost, a post made here a few hours before the March 11, 2011, Japanese earthquake, tsunami, and nuclear disaster—
Whether Paradigms Lost is beyond forgetfulness is open to question.
Perhaps a later post, in the lighthearted spirit of Faust, will help. See April 20th’s “Ready When You Are, C.B.“
Background— Why Me? and the Fritz Leiber story "Damnation Morning."
The story, about the afterlife of a dead drunk, contains an intriguing dark lady.
Related material — Search for the Spider Woman.
See also Julie Taymor in an interview published last Dec. 12 —
“I’ve got two Broadway shows, a feature film, and Mozart,’’ she said.
“It’s a very interesting place to be and to be able to move back and forth,
but at a certain point you have to be able to step outside and see,’’
and here she dropped her voice to a tranquil whisper, “it’s just theater.
It’s all theater. It’s all theater. The whole thing is theater.’’
— and search for Taymor + Spider in this journal.
Happy Shakespeare's Birthday.
Literary remarks for Maundy Thursday—
— C. P. Snow, foreword to G. H. Hardy's A Mathematician's Apology
Related material—
Emory University press release of January 20th, 2011:
"In 1937, Hans Rademacher found an exact formula for calculating partition values. While the method was a big improvement over Euler's exact formula, it required adding together infinitely many numbers that have infinitely many decimal places. 'These numbers are gruesome,' Ono says….
… The final eureka moment occurred near another Georgia landmark: Spaghetti Junction. Ono and Jan Bruinier were stuck in traffic near the notorious Atlanta interchange. While chatting in the car, they hit upon a way to overcome the infinite complexity of Rademacher's method. They went on to prove a formula that requires only finitely many simple numbers.
'We found a function, that we call P, that is like a magical oracle,' Ono says. 'I can take any number, plug it into P, and instantly calculate the partitions of that number….'"
See also this journal on April 15 and a Google Groups [sage-devel] thread, Ono-Bruinier partition formula. That thread started on April 15 and was last updated this morning.
Picture by Robert Vickrey.
Vickrey died Sunday.
See Sunday School.
From Thomas Pynchon's 1997 Introduction to Stone Junction—
"He takes the Diamond, and then the Diamond takes him. For it turns out to be a gateway to elsewhere, and Daniel's life's tale an account of the incarnation of a god, not the usual sort that ends up bringing aid and comfort to earthly powers, but that favorite of writers, the incorruptible wiseguy known to anthropologists as the Trickster, to working alchemists as Hermes, to card-players everywhere as the Joker. We don't learn this till the end of the story, by which point, knowing Daniel as we've come to, we are free to take it literally as a real transfiguration, or as a metaphor of spiritual enlightenment, or as a description of Daniel's unusually exalted state of mind as he prepares to cross, forever, the stone junction between Above and Below— by this point, all of these possibilities have become equally true, for we have been along on one of those indispensable literary journeys, taken nearly as far as Daniel— though it is for him to slip along across the last borderline, into what Wittgenstein once supposed cannot be spoken of, and upon which, as Eliphaz Levi advised us— after 'To know, to will, to dare' as the last and greatest of the rules of Magic— we must keep silent."
"The devil likes metamorphoses." —The Club Dumas
The April Scientific American on the partition function p (n )—
"… in January, Ono and another collaborator [Bruinier] described the first formula that directly calculates p (n ) for any n, a feat that had eluded number theorists for centuries."
Exercise: Is this remarkable claim true or false?
For commentary here, see Jan. 27, "Indiana Jones and the Magical Oracle."
For further comments (the most recent from March 11), see mathoverflow.net, "Exact formulas for the partition function?"
Last night's Saturday Night Live —
Related material— See Cleavage.
Background— Yesterday evening's Star Quality as well as earlier posts on Horseness and Mysteries of Faith.
From “This Week’s Hype II,” a post at Peter Woit’s physics weblog this afternoon, a comment—
TedUnger says:
March 17, 2011 at 5:34 pm
“… there’s been nothing from these CERN scientists
except some lousy boring data on physics!
They better at least give us some time travel or else!
You know that is what Joe Public is thinking.”
The commenter’s identity is not clear. Even less clear is the identity of his subject, Joe Public.
For some remarks on time travel from literature rather than science, see “Damnation Morning” in this journal.
Erin O’Connor’s St. Patrick’s Day post this morning says,
“[Roddy] Doyle’s take on the Irish struggle for independence,
A Star Called Henry , has a lovely touch of magical realism.”
Note that the remarks by Henry Baker in this morning’s post here were dated Thursday, 11 September 1913.
Related material—
Yet they were of a different kind
The names that stilled your childish play,
They have gone about the world like wind,
But little time had they to pray
For whom the hangman’s rope was spun,
And what, God help us, could they save:
Romantic Ireland’s dead and gone,
It’s with O’Leary in the grave.
William Butler Yeats, “September 1913“
From Rough Magic , starring Russell Crowe and Bridget Fonda (1995)—
Bridget brought her rabbits,
There was magic in the air…
— Adapted from "Garden Party"—
Can't please everyone, so you
Got to please yourself.
From The Chronicles of Narnia, Voyage of the Dawn Treader—
"… Sometimes, perhaps, I am a little impatient, waiting for the day
when they can be governed by wisdom instead of this rough magic."
"All in good time, Coriakin," said Aslan.
"Yes, all in very good time, Sir," was the answer.
From Another Manic Monday (Feb. 21)—
We are now at the Year of the Rabbit —
(Click images for sources.)
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
In memory of Jane Russell —
H.S.M. Coxeter's classic
Introduction to Geometry (2nd ed.):
Note the resemblance of the central part to
a magical counterpart— the Ojo de Dios
of Mexico's Sierra Madre.
Related material— page 55 of Polly and the Aunt ,
by Mary E. Blatchford.
"Why don't you come with me, little girl,
On a magic carpet ride?"
– Steppenwolf lyrics
"I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another."
– Vladimir Nabokov in Speak, Memory
See also Nabokov at Harvard in today's Crimson
and the Russian boxes of Henry James.
Quotation from an obituary on page A24 of the New York edition of today's New York TImes—
“Even Gods Must Die.”
Related material from Log24 on the day this classical singer of India died
and on the following day—
Monday, January 24, 2011A Reappearing Number, continued"In the work of Ramanujan, the number 24 appears repeatedly. This is an example of what mathematicians call magic numbers, which continually appear, where we least expect them, for reasons that no one understands." – Michio Kaku, Hyperspace, Oxford U. Press, 1994, p. 173 See also "A Reappearing Number," this journal, July 4, 2010. Tuesday, January 25, 2011Related material— a video of the song— See also this journal's Twelfth Night posts. (Note particularly the 4/01 link.) |
Indiana Jones and the Magical Oracle
Mathematician Ken Ono in the December 2010 American Mathematical Society Notices—
The "dying genius" here is Ramanujan, not Galois. The story now continues at the AMS website—
(Excerpt from Jan. 27 screenshot;
the partitions story has been the top
news item at the site all week.)
From a Jan. 20, 2011, Emory University press release —
"Finite formula found for partition numbers" —
"We found a function, that we call P, that is like a magical oracle," Ono says. "I can take any number, plug it into P, and instantly calculate the partitions of that number. P does not return gruesome numbers with infinitely many decimal places. It's the finite, algebraic formula that we have all been looking for."
For an introduction to the magical oracle, see a preprint, "Bruinier-Ono," at the American Institute of Mathematics website.
Ono also discussed the oracle in a video (see minute 25) recorded Jan. 21 and placed online today.
See as well "Exact formulas for the partition function?" at mathoverflow.net.
A Nov. 29, 2010, remark by Thomas Bloom on that page leads to a 2006 preprint by Ono and Kathrin Bringmann, "An Arithmetic Formula for the Partition Function*," that seems not unrelated to Ono's new "magical oracle" formula—
The Bruinier-Ono paper does not mention the earlier Bringmann-Ono work.
(Both the 2011 Bruinier-Ono paper and the 2006 Bringmann-Ono paper mention their debt to a 2002 work by Zagier— Don Zagier, "Traces of singular moduli," in Motives, Polylogarithms and Hodge theory, Part II (Irvine, CA, 1998), International Press Lecture Series 3 (International Press, Somerville, MA, 2002), pages 211-244.)
Some background for those who prefer mathematics to narrative—
The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series ,
by Ken Ono, American Mathematical Society CBMS Series, 2004.
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