(Continued. For the title, see Lucero in this journal.)
See Newton in several works of literary art:
The date, Nov. 23, 2010, of the Westminster Abbey remarks
in the second Newton link above suggests a quite different church
from that date.
"Let X equal the month of full bookstores."
— Proof by David Auburn
|
"Harvard Book Store is thrilled to welcome Stephen King for a special event to celebrate the release of Doctor Sleep , the long-anticipated sequel to 1977’s The Shining . Mr. King will read from and discuss the new book, followed by a Q&A with the audience at Memorial Church in Harvard Yard on September 27." |
See as well Corpse + Eliot and some remarks
on the mathematics of Kummer
from this September and from last September.
Eisenman I: DuBois, PA (Of German descent)
Eisenman II: Yale (Apparently related to Eisenman I)
Eisenman III: Newark, NJ (Jewish)
"Confusion is nothing new." — Song lyric
Continued from September 3rd, 2013.
On that date, there were two posts in this journal:
"The Stone" today suggests…"* and
"An End in Itself."
The former dealt with some philosophy and
mathematics related to graphic design.
The latter dealt with death and finality.
The New York Times today has an obituary
that, revisiting Sept. 3rd, unites the topics of
death and design.
|
Alvin Eisenman,
By DANIEL E. SLOTNIK Alvin Eisenman, a graphic designer who in 1951 became the first director of Yale’s graduate program for graphic design, the first offered by a major American university, died on Sept. 3 at his home, which he also designed, on Martha’s Vineyard. He was 92. More>> |
For greater depth, see the American Institute of Graphic Arts.
* This post's title and "The Stone" above refer to the New York Times
philosophy column "The Stone"— In particular, to its Sept. 2nd post
"Women in Philosophy? Do the Math."
"The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine."
— Joseph Conrad in Heart of Darkness
Kernel — See Nocciolo.
Glow — See Moonshine and Moonshine II.
See also Cold Open (Jan. 29, 2011) and
Where Entertainment is God (Aug. 25, 2013).
Margalit Fox in The New York Times this evening—
Judith Daniels, the founding editor in chief of Savvy ,
the first glossy magazine aimed at executive women,
died on Sunday at her home in Union, Me. She was 74….
“Savvy will not tell you how to be a good secretary,”
one of its early promotional fliers read. “Savvy will tell you
how to hire a good secretary— and how to fire.”
From the date of Daniels' death: The Crossword Omen.
See, too, Vogue in this journal and Ontology.
From a post of January 26, 2013—
Sally in the 2013 film Oblivion : "Are you an effective team?"
(A sequel to today's noon post, Hymn)
Portrait, in the 2013 film Oblivion , of a 2005 graduate
of London's Royal Academy of Dramatic Art —
London derrière.
For the late Julie Harris —
By slow and carefully modulated steps Bradford's narrative
has brought his community of separatists to the place he
calls Cape Harbor… where, face-to-face with the bleak
and wintry reduction that is his image for American space,
he finds himself stopped, able to do nothing but come to
an astonished pause. The final step, that of imaginative
crossing into the land that lies before them, remains
beyond the power of narrative to take. Narrative falters, and
finding his journey advanced to an "odd Fork in Being's Road"
and himself nothing so much as an "empty spirit / In vacant
space" (to adopt apt phrases from Dickinson and Stevens…),
Bradford requires the sublime if he is to continue moving
forward: separation becomes exaltation as it becomes
manifest that only an influx of "the Spirit of God and His
grace" can have permitted the community to survive its
passage to the limit depicted.
— David Laurence, "William Bradford's American Sublime,"
PMLA , Vol. 102, No. 1, 1987, pp. 55-65
The following excerpt from a January 20, 2013, preprint shows that
a Galois-geometry version of the large Desargues 154203 configuration,
although based on the nineteenth-century work of Galois* and of Fano,**
may at times have twenty-first-century applications.
Atkinson's paper does not use the square model of PG(3,2), which later
in 2013 provided a natural view of the large Desargues 154203 configuration.
See my own Classical Geometry in Light of Galois Geometry. Atkinson's
"subset of 20 lines" corresponds to 20 of the 80 Rosenhain tetrads
mentioned in that later article and pictured within 4×4 squares in Hudson's
1905 classic Kummer's Quartic Surface.
* E. Galois, definition of finite fields in "Sur la Théorie des Nombres,"
Bulletin des Sciences Mathématiques de M. Férussac,
Vol. 13, 1830, pp. 428-435.
** G. Fano, definition of PG(3,2) in "Sui Postulati Fondamentali…,"
Giornale di Matematiche, Vol. 30, 1892, pp. 106-132.
See the title in this journal.
Related material:
Philosophers on the Beach—
George Santayana in Acapulco, Colin McGinn in Miami.
Maya Alexandri on September 7, 2009—
|
… Blixen herself may have cut closer to the truth In it, a character explains,
What exactly [the imposter to the Prince] has told
Later, the imposter utters the following enigma: "Life and Death Stylist or fraud, that's the question. |
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 .
Wikipedia:
The Chinese name of the gate, Tiānānmén 天安門 …
is made up of the Chinese characters for "heaven,"
"peace" and "gate" respectively, which is why the
name is conventionally translated as "The Gate of
Heavenly Peace". However, this translation is
somewhat misleading, since the Chinese name is
derived from the much longer phrase "receiving the
mandate from heaven, and stabilizing the dynasty."
Another anniversary today:
See also some related philosophy and mathematics.
Harvard Gazette , March 4th, 2013:
"Winfrey will speak on May 30 during Commencement day’s
Afternoon Exercises, which serve as the annual meeting of
the Harvard Alumni Association. The exercises will take place
in the Tercentenary Theatre of Harvard Yard,
between Memorial Church and Widener Library."
On the 1977 Octavia Butler novel Mind of My Mind :
"The first chapter in a history that Butler has already taken up
at a much later stage in Patternmaster (1976).
Mind of My Mind begins with Doro, a ruthless mutant
as old as the pyramids who has spent the last 4,000 years
trying to breed a race in his own image. The culminating
experiment is his daughter Mary. But, to Doro's astonishment,
Mary's first instinct on attaining her full powers is to begin
building a mental community— a Pattern— out of the
wretched thousands of Doro's half-telepathic failures
and partial successes. Despite some ragged moments,
Butler is clearly on to a promising vein— something like
Zenna Henderson's 'People' stories without their
saccharine silliness. There's a lot of intrinsic energy in the
Pattern idea, and one wants to see where this erratic, gifted
storyteller will pick it up next."
— Kirkus Reviews , Vol. XLV, No. 8 (1977), p. 453.
See this journal on Butler's dies natalis , the feast of St. Matthias, 2006.
Those who prefer Eastern approaches to religion may consult
Robert Thurman and his daughter Uma.
"Oprah, Uma. Uma, Oprah." — David Letterman
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)—
.
For some images related to this rather biblical topic,
see Hillman + Dream in this journal.
“She was dazzled by light and shade, by the confusing
duplication of reflections and of frames. All coming from
too many directions for the mind to take account of.
The various images bounced against each other
until she felt a desperate vertigo….”
Summary image:
“… Margaret Murry, wrapped in an old patchwork quilt, sat on the foot of her bed….”
"It should be emphasized that block models are physical models, the elements of which can be physically manipulated. Their manipulation differs in obvious and fundamental ways from the manipulation of symbols in formal axiomatic systems and in mathematics. For example the transformations described above, in which two linear arrays are joined together to form one array, or a rectangle of blocks is re-assembled into a linear array, are physical transformations not symbolic transformations. …"
— Storrs McCall, Department of Philosophy, McGill University, "The Consistency of Arithmetic"
"It should be emphasized…."
OK:
Storrs McCall at a 2008 philosophy conference .
His blocks talk was at 2:50 PM July 21, 2008.
See also this journal at noon that same day:
Froebel's Third Gift and the Eightfold Cube
Quoted in the March 13 post Blackboard Jungle:
"Every morning you take your machete into the jungle
and explore and make observations, and every day
you fall more in love with the richness and splendor
of the place."
— Paul Lockhart, A Mathematician's Lament
More from Lockhart's jungle—
|
Mathematical objects, even if initially inspired by some aspect of reality (e.g., piles of rocks, the disc of the moon), are still nothing more than figments of our imagination. Not only that, but they are created by us and are endowed by us with certain characteristics; that is, they are what we ask them to be…. … in Mathematical Reality, because it is an imaginary place, I actually can have pretty much whatever I want…. The point is that there is no reality to any of this, so there are no rules or restrictions other than the ones we care to impose…. Make up anything you want, so long as it isn’t boring. Of course this is a matter of taste, and tastes change and evolve. Welcome to art history! — Lockhart, Paul (2009-04-01). A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form (pp. 100-104). Bellevue Literary Press. Kindle Edition. |
Related material in this journal: Bellevue and Wechsler.
See also Gombrich in this journal and in the following:
Related material (Click for some background.) —
Sistine Chapel Smoke
Tromso Kunsthall Mirrors
Background for the smoke image:
A remark by Michelangelo in a 2007 post, High Concept.
Background for the mirrors image:
Note the publication date— Mar. 10, 2013.
"In 2005 Arthur Jaffe succeeded Sir Michael Atiyah as
Chair of the Board of the Dublin Institute for Advanced Study,
School of Theoretical Physics."
Related material:
Biddies in this journal and…
Detail:
An early version of quaternions.
Related material: "universe of discourse"—
"The serpent's eyes shine as he wraps around the vine" — Don Henley
Excerpt from an essay cached nine years ago:
"The current dominant conceptual framework
which pictures the self as an inner entity
is slowly breaking up. And I am convinced that
some, if not all, of the approaches to the self
sketched here will form the basis for a new
conceptual framework…."
Context for the essay:
A journal issue titled "The Opening of Narrative Space" (pdf, 475 KB)
For one sort of narrative space, see Giordano Bruno in this journal.
See also Nine Years.
The title was suggested by an ad for a film that opens
at 10 PM EST today: "Hansel & Gretel: Witch Hunters."
Related material: Grimm Day 2012, as well as
Amy Adams in Raiders of the Lost Tesseract
and in a Film School Rejects page today.
See also some Norwegian art in
Trish Mayo's Photostream today and in
Omega Point (Log24, Oct. 15, 2012)—
Monday, October 15, 2012
|
"I, the Rock, I, the River, I, the Tree
I am yours—your passages have been paid."
"The way, when we climb a mountain,
Vermont throws itself together"
— Wallace Stevens, "July Mountain"
For another view of reality in New Haven, see the
brief biography of Vermont poet Frances Frost
at the Yale University Library. From that biography:
"She was survived by her son, the poet Paul Blackburn,
and by her daughter, Sister Marguerite of the Order
of St. Joseph."
See also a figure from The New York Times published
online on Epiphany, 2013:
Old Stone-Cutter
His gravestones are his everlasting children.
He loves to get his cramped left hand around
the solid faithful feeling of his chisel
and dig the names of those below the ground
or the family names of provident ones above
who cross their fingers and defy the fates
and acknowledge death their enemy and master
by ordering headstones with their birthing dates.
He carves his holy head, a solemn cherub
with granite wings and childish eyes cast down.
Those who prefer a willowed urn, disliking
angels, can go and die in another town.
(From The North American Review , Vol. 248, No. 2,
1939, page 301)
Solemn cherub by Albrecht Dürer in 1514—
|
From Don DeLillo's novel Point Omega — I knew what he was, or what he was supposed to be, a defense intellectual, without the usual credentials, and when I used the term it made him tense his jaw with a proud longing for the early weeks and months, before he began to understand that he was occupying an empty seat. "There were times when no map existed to match the reality we were trying to create." "What reality?" "This is something we do with every eyeblink. Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation. Lying is necessary. The state has to lie. There is no lie in war or in preparation for war that can't be defended. We went beyond this. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional. The reality stands, it walks, it squats. Except when it doesn't." He didn't smoke but his voice had a sandlike texture, maybe just raspy with age, sometimes slipping inward, becoming nearly inaudible. We sat for some time. He was slouched in the middle of the sofa, looking off toward some point in a high corner of the room. He had scotch and water in a coffee mug secured to his midsection. Finally he said, "Haiku." I nodded thoughtfully, idiotically, a slow series of gestures meant to indicate that I understood completely. "Haiku means nothing beyond what it is. A pond in summer, a leaf in the wind. It's human consciousness located in nature. It's the answer to everything in a set number of lines, a prescribed syllable count. I wanted a haiku war," he said. "I wanted a war in three lines. This was not a matter of force levels or logistics. What I wanted was a set of ideas linked to transient things. This is the soul of haiku. Bare everything to plain sight. See what's there. Things in war are transient. See what's there and then be prepared to watch it disappear." |
What's there—
This view of a die's faces 3, 6, and 5, in counter-
clockwise order (see previous post) suggests a way
of labeling the eight corners of a die (or cube):
123, 135, 142, 154, 246, 263, 365, 456.
Here opposite faces of the die sum to 7, and the
three faces meeting at each corner are listed
in counter-clockwise order. (This corresponds
to a labeling of one of MacMahon's* 30 colored cubes.)
A similar vertex-labeling may be used in describing
the automorphisms of the order-8 quaternion group.
For a more literary approach to quaternions, see
Pynchon's novel Against the Day .
* From Peter J. Cameron's weblog:
"The big name associated with this is Major MacMahon,
an associate of Hardy, Littlewood and Ramanujan,
of whom Robert Kanigel said,
His expertise lay in combinatorics, a sort of
glorified dice-throwing, and in it he had made
contributions original enough to be named
a Fellow of the Royal Society.
Glorified dice-throwing, indeed…"
For a modern Adam and Eve—
W. Tecumseh Fitch and Gesche Westphal Fitch,
editors of a new four-volume collection titled
Language Evolution (Feb. 2, 2012, $1,360)—
Related material—
|
"At the point of convergence
by Octavio Paz, translated by |
The "play of mirrors" link above is my own.
Click on W. Tecumseh Fitch for links to some
examples of mirror-play in graphic design—
from, say, my own work in a version of 1977, not from
the Fitches' related work published online last June—
See also Log24 posts from the publication date
of the Fitches' Language Evolution—
Happy birthday to the late Alfred Bester.
"If a man does not keep pace with his companions,
perhaps it is because he hears a different drummer.
Let him step to the music which he hears, however
measured or far away." — Thoreau
"I got a line on you." — Spirit
See also today's previous post and Eve's Menorah.
The concept of "deep structure," once a popular meme,
has long been abandoned by Chomskians.
It still applies, however, to the 1976 mathematics, diamond theory ,
underlying the formal patterns discussed in a Royal Society paper
this year.
A review of deep structure, from the Wikipedia article Cartesian linguistics—
|
[Numbers in parentheses refer to pages in the original 1966 Harper edition of Chomsky's book Cartesian Linguistics .] Deep structure vs. surface structure "Pursuing the fundamental distinction between body and mind, Cartesian linguistics characteristically assumes that language has two aspects" (32). These are namely the sound/character of a linguistic sign and its significance (32). Semantic interpretation or phonetic interpretation may not be identical in Cartesian linguistics (32). Deep structures are often only represented in the mind (a mirror of thought), as opposed to surface structures, which are not. Deep structures vary less between languages than surface structures. For instance, the transformational operations to derive surface forms of Latin and French may obscure common features of their deep structures (39). Chomsky proposes, "In many respects, it seems to me quite accurate, then, to regard the theory of transformational generative grammar, as it is developing in current work, as essentially a modern and more explicit version of the Port-Royal theory" (39). Summary of Port Royal Grammar The Port Royal Grammar is an often cited reference in Cartesian Linguistics and is considered by Chomsky to be a more than suitable example of Cartesian linguistic philosophy. "A sentence has an inner mental aspect (a deep structure that conveys its meaning) and an outer, physical aspect as a sound sequence"***** This theory of deep and surface structures, developed in Port Royal linguistics, meets the formal requirements of language theory. Chomsky describes it in modern terms as "a base system that generates deep structures and a transformational system that maps these into surface structures", essentially a form of transformational grammar akin to modern studies (42). |
The corresponding concepts from diamond theory are…
"Deep structure"— The line diagrams indicating the underlying
structure of varying patterns
"A base system that generates deep structures"—
Group actions on square arrays… for instance, on the 4×4 square
"A transformational system"— The decomposition theorem
that maps deep structure into surface structure (and vice-versa)
… Chomsky vs. Santa
From a New Yorker weblog yesterday—
"Happy Birthday, Noam Chomsky." by Gary Marcus—
"… two titans facing off, with Chomsky, as ever,
defining the contest"
"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."
See Meno Diamond in this journal. For instance, from
the Feast of Saint Nicholas (Dec. 6th) this year—
The Meno Embedding
For related truths about geometry, see the diamond theorem.
For a related contest of language theory vs. geometry,
see pattern theory (Sept. 11, 16, and 17, 2012).
See esp. the Sept. 11 post, on a Royal Society paper from July 2012
claiming that
"With the results presented here, we have taken the first steps
in decoding the uniquely human fascination with visual patterns,
what Gombrich* termed our ‘sense of order.’ "
The sorts of patterns discussed in the 2012 paper —
"First steps"? The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.
* See Gombrich-Douat in this journal.
This post was suggested by the December 4th death
of modernist composer Jonathan Harvey, 73,
and by Harvey's reflections on his 2007 opera
Wagner Dream .
For related reflections, see the Oct. 10 post on
the Dürer magic square in Mann's Doctor Faustus .
See also a December 2nd post on the Nov. 18 death of
chess grandmaster Elena Akhmilovskaya Donaldson.
From the Los Angeles Times yesterday—
"Chess player Elena Akhmilovskaya Donaldson sits
in deep concentration at the U.S. chess championship
in Seattle in 2002. (Greg Gilbert / Seattle Times /
January 5, 2002)"
Linda Shaw, Seattle Times :
"Elena Akhmilovskaya Donaldson, who was once the world's
second-ranked women's chess player and eloped in 1988
with the captain of the U.S. chess team when they were both
playing at a tournament in Greece, has died. She was 55.
Donaldson, who earned the title of international women's
grandmaster, died Nov. 18 in her adopted hometown of Seattle…."
From the Log24 post "Sermon" on the date of Donaldson's death,
Sunday, Nov. 18, 2012—
"You must allow us to play every conceivable combination of chess."
— Marie-Louise von Franz in Number and Time
An October 2011 post titled Realism in Plato's Cave displays
the following image:
Cover illustration: Knight, Death, and the Devil,
by Albrecht Dürer
George Steiner and myself in Closing the Circle, a Log24 post
of Sept. 4, 2009:
“Allegoric associations of death with chess are perennial….”
"Yes, they are."
For related remarks on knight moves and the devil, see
today's previous two posts, Knight's Labyrinth and The Rite.
"It's a grim joke." — Amy Adams in "The Master"
When Irish Eyes Are Smiling…
Click diagram for some background from 3/17.
See, too, some background on Amy Adams and on Leap Day.
For related Harvard humor, see Venn Diagram.
Happy birthday to…
Today's sermon, by Marie-Louise von Franz—
For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.
Another modern physicist, Niels Bohr, died
on this date in 1962…
|
The circle above is marked with a version For the square, see the diamond theorem. "Two things of opposite natures seem to depend — Wallace Stevens, |
Last evening's NY Lottery numbers
985 and 3274, interpreted as the
numbers of Log24 posts, suggest
a look at Joyce's nightmare— history.
* The title refers both to a film and to
a Log24 post, Random Access Memory.
On a mathematician who died on All Souls' Day 2012—
"… he enthusiastically shared with us the many stories
of Indian epics like Mahabharata." — Online tribute
This suggests a pictorial review incorporating some
images from past Log24 posts.
Best Exotic Ananga Ranga
Click images for some background.
From a Washington Post book review of
The Essays of Leonard Michaels
by Jonathan Yardley, Sunday, July 26, 2009—
"Michaels said that his literary influences included Franz Kafka, Lord Byron and Wallace Stevens (this last is frequently quoted in these essays), but reading that paragraph one can't help thinking that as a young man in the 1950s he must have spent a lot of time listening to Mort Sahl, Lenny Bruce and the other great Jewish comedians of the day, as his own comic voice and timing bear more than passing resemblance to theirs. In another essay, 'A Sentimental Memoir,' he recalls being 'saved' as a young man by a professor of English at the University of Michigan named Austin Warren, and then he meanders into an account of falling 'insanely in love' (which seems to have been a strong predilection with him) with a girl in Warren's class:
'The girl had a slender boyish figure and blondish hair. I thought nobody but me considered her striking or had noticed the subtle perfection of her beautiful face. When I told my friend Julian that the most beautiful girl in Michigan was in Warren's class, he named her. He told me that she modeled naked for art students, she had a horrible reputation for licentiousness, everybody knew who she was, and that he was in love with her too. I decided that I was ready to forgive her everything. To forgive a girl was a very popular sentiment of the day. There were plays, novels, and movies about forgiving bad girls. As for the girl I was ready to forgive, I now suppose there were a couple of hundred other men who were forgiving her at the same time, all of us subject to a sort of spiritual narcissism that has long since gone out of the world. Too bad, I think, since it had extraordinary intensity and made a man feel tortured by goodness, which is a very high order of feeling.' "
"The yarns of seamen have a direct simplicity,
the whole meaning of which
lies within the shell of a cracked nut.
But Marlow was not typical
(if his propensity to spin yarns be excepted),
and to him the meaning of an episode
was not inside like a kernel but outside,
enveloping the tale which brought it out
only as a glow brings out a haze,
in the likeness of one of these misty halos
that sometimes are made visible by
the spectral illumination of moonshine."
— Joseph Conrad in Heart of Darkness
(Continued from August 29.)
movies.broadwayworld.com, Friday, Oct, 5, 2012; 1:13 PM
"Bradley Cooper, Jeremy Renner, and Amy Adams will be joined by Christian Bale in David O. Russell’s ensemble drama….
The Untitled David O. Russell Project is based on the true story of a notorious financial con artist (Bale) and his mistress/partner in crime (Adams), who were forced to work with an out of control federal agent (Cooper) to turn the tables on other con artists, mobsters, and politicians."
For Amy—
"Put on your red dress, baby
Ya know we're goin' out tonight
Put on your red dress, baby
Lord, we're goin' out tonight
And-a bring along some boxin' gloves
In case some fool might wanna fight"
(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.
The "1961" Oscars ceremony shown above was for the films of 1961.
The ceremony itself was held on April 9, 1962.
For a different Tiffany, see Tuesday's Another Day.
Where Entertainment is God continues…
|
Excerpts from "Today in History," Today's Birthdays: Thought for Today: "The crisis of yesterday |
And the joke of yesterday?
Related material:
http://en.wikipedia.org/wiki/Al-Qiyama
The "FLT" of the above title is not Fermat's Last Theorem,
but Formal Language Theory (see image below).
In memory of George A. Miller, Harvard cognitive psychologist, who
reportedly died at 92 on July 22, 2012, the first page of a tribute
published shortly before his death—
The complete introduction is available online. It ends by saying—
"In conclusion, the research discussed in this issue
breathes new life into a set of issues that were raised,
but never resolved, by Miller 60 years ago…."
Related material: Symmetry and Hierarchy (a post of 9/11), and
Notes on Groups and Geometry, 1978-1986 .
A followup to Intelligence Test (April 2, 2012).
Philosophical Transactions of the Royal Society
B (2012) 367, 2007–2022
(theme issue of July 19, 2012) —
"… the modern meritocracy dates only to the 1930s,
when Harvard President James Bryant Conant
directed his admissions staff to find a measure of
ability to supplement the old boys’ network. They
settled on the exam we know as the SAT."
— "Tyranny of Merit," by Samuel Goldman,
a book review dated August 21, 2012
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:
(Continued from Up to Date, Aug. 28.)
Voyager 1 Story
By Amy Hubbard in the Los Angeles Times
September 4, 2012, 3:11 p.m. [PDT]
How long does it take to fly to the edge of
the solar system? At least 35 years.
Voyager 1 is there now….
Related material—
Dinga dong ding.
Last night's 10 PM post linked to an April 7, 2012,
post that through a series of further links leads
to Columbia Film Theory .
For other film-related remarks, by a
Columbia alumnus,* see last night's post.
See also the 1.3 MB image from Aug. 16, the night
of Elvis's Wrap Party. An excerpt from that image
stars Amy Adams—
For Amy, from the current New Yorker—
The Master—
* N.O.C.D.
"History instructs. History also has
a very dark sense of humor.
Irish history, especially."
— John Kelly in The Daily Beast this morning
See also Joyce's Nightmare and
Nightmare Alley in this journal.
(Continued from August 13. See also Coxeter Graveyard.)
Here the tombstone says
"GEOMETRY… 600 BC — 1900 AD… R.I.P."
In the geometry of Plato illustrated below,
"the figure of eight [square] feet" is not , at this point
in the dialogue, the diamond in Jowett's picture.
An 1892 figure by Jowett illustrating Plato's Meno—
Jowett's picture is nonetheless of interest for
its resemblance to a figure drawn some decades later
by the Toronto geometer H. S. M. Coxeter.
A similar 1950 figure by Coxeter illustrating a tesseract—
For a less scholarly, but equally confusing, view of the number 8,
see The Eight , a novel by Katherine Neville.
"I am a skeptic to whom the idea that a benign God
created us and watches over us is something between
a fairy story and a bad joke."
— The late art critic Robert Hughes in Things I Didn't Know*
A followup to this afternoon's previous Amy Adams post—
"Here was finality indeed, and cleavage!"
* Vintage paperback, December 2007, page 7
Judy Davis in the Marabar Caves
The above image is from this journal on Sunday, April 13, 2008.
The preceding cover of a book by Northrop Frye was suggested
by material in this journal from February 2003.
See also Yankee Puzzle and Doodle Dandy.
"A Saturday morning cartoon is the colloquial term
for the animated television programming that has
typically been scheduled on Saturday mornings
on the major American television networks from
the 1960s to the present…." —Wikipedia
Martin Gardner in the Notices of the
American Mathematical Society ,
June/July 2005:
“I did a column in Scientific American
on minimal art, and I reproduced one of
Ed Rinehart’s [sic ] black paintings.
Of course, it was just a solid square of
pure black.”
Click on picture for details.
For a cartoon graveyard—
http://www.latimes.com/news/politics/ la-pn-romney-colorado-shooting-is- unspeakable-tragedy-20120720,0,1226295.story Romney: Colorado shooting is 'unspeakable tragedy' By Seema Mehta July 20, 2012, 11:15 a.m. BOW, N.H.—Hours after a shooter killed a dozen people in a Colorado cinema, Mitt Romney scrubbed a scheduled campaign rally Friday and instead offered his somber condolences and prayers to the victims and their families. “Our hearts break with the sadness of this unspeakable tragedy. Ann and I join the president and first lady and all Americans in offering our deepest condolences to those whose lives were shattered in a few moments, a few moments of evil in Colorado,” Romney told a few hundred people gathered at a lumber yard here. “I stand before you today not as a man running for office but as a father and grandfather, a husband, an American. This is a time for each of us to look into our hearts and remember how much we love one another and how much we love and how much we care for our great country. There’s so much love and goodness in the heart of America.” Romney, wearing a navy blue suit and blue tie, spoke for four minutes. The trademark campaign banners with slogans such as “Believe in America” or “Obama’s Upside- Down Economy” were gone, leaving a handful of American flags as the backdrop. Before Romney spoke, Father Christian Tutor, an Anglican Catholic priest, led a prayer. ... |
I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard
— Paul Simon
For a White House daughter…
From this evening's Capitol Fourth—
She goes off with a great big bang
Boys I tell ya it's a beautiful thing
Related material— Big Bang in this journal—
Detective Cruz enters Planck's Constant Café in "The Big Bang."
Last night's post on The Trinity of Max Black and the use of
the term "eightfold" by the Mathematical Sciences Research Institute
at Berkeley suggest a review of an image from Sept. 22, 2011—
The triskele detail above echoes a Buddhist symbol found,
for instance, on the Internet in an ad for meditation supplies—
Related remarks—
http://www.spencerart.ku.edu/about/dialogue/fdpt.shtml—
Mary Dusenbury (Radcliffe '64)—
"… I think a textile, like any work of art, holds a tremendous amount of information— technical, material, historical, social, philosophical— but beyond that, many works of art are very beautiful and they speak to us on many layers— our intellect, our heart, our emotions. I've been going to museums since I was a very small child, thinking about what I saw, and going back to discover new things, to see pieces that spoke very deeply to me, to look at them again, and to find more and more meaning relevant to me in different ways and at different times of my life. …
… I think I would suggest to people that first of all they just look. Linger by pieces they find intriguing and beautiful, and look deeply. Then, if something interests them, we have tried to put a little information around the galleries to give a bit of history, a bit of context, for each piece. But the most important is just to look very deeply."
http://en.wikipedia.org/wiki/Nikaya_Buddhism—
According to Robert Thurman, the term "Nikāya Buddhism" was coined by Professor Masatoshi Nagatomi of Harvard University, as a way to avoid the usage of the term Hinayana.[12] "Nikaya Buddhism" is thus an attempt to find a more neutral way of referring to Buddhists who follow one of the early Buddhist schools, and their practice.
12. The Emptiness That is Compassion:
An Essay on Buddhist Ethics, Robert A. F. Thurman, 1980
[Religious Traditions , Vol. 4 No. 2, Oct.-Nov. 1981, pp. 11-34]
http://dsal.uchicago.edu/cgi-bin/philologic/getobject.pl?c.2:1:6.pali—
Nikāya [Sk. nikāya, ni+kāya]
collection ("body") assemblage, class, group
http://en.wiktionary.org/wiki/नि—
Sanskrit etymology for नि (ni)
नि (ni)
http://www.rigpawiki.org/index.php?title=Kaya—
Kaya (Skt. kāya ; སྐུ་, Tib. ku ; Wyl. sku ) —
the Sanskrit word kaya literally means ‘body’
but can also signify dimension, field or basis.
• structure, existentiality, founding stratum ▷HVG KBEU
Note that The Trinity of Max Black is a picture of a set—
i.e., of an "assemblage, class, group."
Note also the reference above to the word "gestalt."
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
"Ayant été conduit par des recherches particulières
à considérer les solutions incommensurables, je suis
parvenu à quelques résultats que je crois nouveaux."
— Évariste Galois, "Sur la Théorie des Nombres"
Soon to be a major motion picture!
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
"What we need is… a third way
between the longstanding models
of war and peace. Movement in
this direction is already under way."
— Yale Law professor John Fabian Witt,
"The Legal Fog Between War and Peace"
Tolstoy he ain't.
Witt's remarks appeared yesterday
evening (between 8 and 9 PM EDT)
in the online New York Times .
For related "third way" material, see
yesterday's 7 PM EDT post in this journal.
Lee Marvin in the 1983 film Gorky Park
For related material, see yesterday's post on Nietzsche's
Birth of Tragedy and a May 27, 2010, post— Masks .
The link to the Masks post was suggested by four things:
* The title is in memory of business writer Mike Hammer.
In memory of Sir Andrew Huxley, OM, who died on May 30, 2012
C. P. Snow on G. H. Hardy at Trinity College, Cambridge—
He played his games and indulged his eccentricities.
He was living in some of the best intellectual company
in the world— G. E. Moore, Whitehead, Bertrand Russell,
Trevelyan, the high Trinity society which was shortly to
find its artistic complement in Bloomsbury. (Hardy himself
had links with Bloomsbury, both of personal friendship
and of sympathy.)
See also "Max Black" + Trinity in this journal.
(Continued from May 29, 2002)
May 29, 1832—
Évariste Galois, Lettre de Galois à M. Auguste Chevalier—
Après cela, il se trouvera, j'espère, des gens qui trouveront leur profit à déchiffrer tout ce gâchis.
(Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.)
Martin Gardner on the above letter—
"Galois had written several articles on group theory, and was merely annotating and correcting those earlier published papers."
– The Last Recreations , by Martin Gardner, published by Springer in 2007, page 156.
Commentary from Dec. 2011 on Gardner's word "published" —
| SPOILER ALERT
This post links to a column that |
The title is from a column by Stanley Fish
on The Hunger Games books in today's
online New York Times . The column
was posted at 9 PM EDT on May 7th, but I
did not see it until this morning.
Fish says—
"In the end… [spoiler details omitted]…
children… 'don’t know they play
on a graveyard'…."
For some literary background, see last night's post
on the May 7th, 2012, NY Times obituaries as well
as the May 7th, 2006, Log24 post featuring 24 squares
arranged in a rectangular frame.
See also Frame Tales and, more generally,
The King and the Corpse.
"Et cetera, et cetera, et cetera." — Yul Brynner
"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 meditation suggested by the April 20 post Complex Reflection
and by the life and April 20 death of a scientist who worked
at Los Alamos (home of the Monte Carlo method) and at
the Santa Fe Institute (home of complexity theory).
A search for 286 in this journal yields "Yet Another Cartoon Graveyard."
That June 1, 2008, post linked to poem 286 in a 1919 anthology.
Here is that poem, together with poem 823.
Together, these poems may be regarded as a meditation on
Simone Weil and her brother André Weil or,
more abstractly, on Love and Death.
Happy birthday to Al Pacino.
(Not Olympus )
(Continued from Mythopoetic, a post of April 12)
This post was suggested by a 2010 film about fictional Olympians,
by today's New York Times obituaries, and by a bar brawl at the Olympian
New York Athletic Club in "the wee hours of April 13."
Rick Riordan in the image below advertises another large
"Demigod Gathering" on October 12, 2010.
The Riordan image is from a post at ComposersCave.com
made on October 3, 2010.
Applying Jung's principle of synchronicity to this demigod material,
we find the October 3, 2010, Log24 post Search for the Basic Picture
and the October 12, 2010, Log24 post King Solomon's Mind.
Note that the latter October date is that of the traditional
Columbus Day, and that the 2010 film of The Lightning Thief
was directed by Chris Columbus of 1492 Pictures.
The film's release was earlier in 2010, on February 12.
|
Edward Reed Whittemore Jr. was born |
In memoriam:
PART I —
PART II —
A search today (Élie Cartan's birthday) for material related to triality*
yielded references to something that has been called a Bhargava cube .
Two pages from a 2006 paper by Bhargava—
Bhargava's reference [4] above for "the story of the cube" is to…
Higher Composition Laws I:
A New View on Gauss Composition,
and Quadratic Generalizations
Manjul Bhargava
The Annals of Mathematics
Second Series, Vol. 159, No. 1 (Jan., 2004), pp. 217-250
Published by: Annals of Mathematics
Article Stable URL: http://www.jstor.org/stable/3597249
A brief account in the context of embedding problems (click to enlarge)—
For more ways of slicing a cube,
see The Eightfold Cube —
* Note (1) some remarks by Tony Smith
related to the above Dynkin diagram
and (2) another colorful variation on the diagram.
March 28 review in the Times Literary Supplement of
George Steiner's new book The Poetry of Thought—
"If this new book opens with the concession that
language has neither the performative power of music
nor the elegant precision of mathematics,
it is language, for Steiner, that defines the human.
The survey accordingly begins from the ancient Greek
view of man as the 'language-animal.'"
A check of this phrase yields, in a 1969 Steiner essay,
"The Language Animal," a Greek form of the phrase—
In short, the least inadequate definition we can arrive at
of the genus homo , the definition that fully distinguishes
him from all neighbouring life-forms, is this:
man is a zoon phonanta , a language-animal.
— p. 10 in Encounter , August 1969 (essay on pp. 7-23)
After introducing "language-animal" as a translation of "zoon phonanta " in 1969,
Steiner in later writing went on to attribute this phrase to the ancient Greeks.
"The inception of critical thought, of a philosophic anthropology,
is contained in the archaic Greek definition of man as a
'language-animal'…."
— George Steiner, Real Presences , U. of Chicago Press, 1991, p. 89
"… the 'language-animal' we have been since ancient Greece
so designated us…. "
— George Steiner, Grammars of Creation , Yale U. Press, 2002, p. 265
Despite this, there seems to be no evidence for use of this phrase
by the ancient Greeks.
A Google search today for zoon phonanta (ζῷον φωνᾶντα)—
There are also no results from searches for the similar phrases
"ζωον φωναντα," "ζωον φωνᾶντα," and "ζῷον φωναντα."
In memory of director Ulu Grosbard (continued from yesterday)
From http://scripturetext.com/matthew/13-44.htm —
Again the kingdom of heaven is like unto treasure hid in a field
the which when a man hath found he hideth and for joy thereof
goeth and selleth all that he hath and buyeth that field
ΚΑΤΑ ΜΑΤΘΑΙΟΝ 13:44 Greek NT: Byzantine/Majority Text (2000)
παλιν ομοια εστιν η βασιλεια των ουρανων θησαυρω κεκρυμμενω εν τω αγρω
LEXICON —
παλιν adverb
palin pal'-in: (adverbially) anew, i.e. (of place) back, (of time) once more, or (conjunctionally) furthermore or on the other hand — again.
ομοια adjective – nominative singular feminine
homoios hom'-oy-os: similar (in appearance or character) — like, + manner.
εστιν verb – present indicative – third person singular
esti es-tee': he (she or it) is; also (with neuter plural) they are
η definite article – nominative singular feminine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.
βασιλεια noun – nominative singular feminine
basileia bas-il-i'-ah: royalty, i.e. (abstractly) rule, or (concretely) a realm — kingdom, + reign.
των definite article – genitive plural masculine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.
ουρανων noun – genitive plural masculine
ouranos oo-ran-os': the sky; by extension, heaven (as the abode of God); by implication, happiness, power, eternity; specially, the Gospel (Christianity) — air, heaven(-ly), sky.
θησαυρω noun – dative singular masculine
thesauros thay-sow-ros': a deposit, i.e. wealth — treasure.
κεκρυμμενω verb – perfect passive participle – dative singular masculine
krupto kroop'-to: to conceal (properly, by covering) — hide (self), keep secret, secret(-ly).
εν preposition
en en: in, at, (up-)on, by, etc.
τω definite article – dative singular masculine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.
αγρω noun – dative singular masculine
agros ag-ros': a field (as a drive for cattle); genitive case, the country; specially, a farm, i.e. hamlet — country, farm, piece of ground, land.
"In 1957, as an incoming freshman,
I was traded by Harvard to Yale.
Harvard got a guy who could row
and Yale got a Jewish boy with good SATs."
— The late Peter Bergman
Title of a treatise by Dominique Douat—
"Méthode pour faire une infinité de desseins différens avec des carreaux mi-partis de deux couleurs par une ligne diagonale : ou observations du Père Dominique Doüat Religieux Carmes de la Province de Toulouse sur un mémoire inséré dans l'Histoire de l'Académie Royale des Sciences de Paris l'année 1704, présenté par le Révérend Père Sébastien Truchet religieux du même ordre, Académicien honoraire " (Paris, 1722)
"The earliest (and perhaps the rarest) treatise on the theory of design"
— E. H. Gombrich, 1979, in The Sense of Order
A facsimile version (excerpts, 108 pp., Feb. 5, 2010) of this treatise is available from
http://jacques-andre.fr/ed/ in a 23.1 MB pdf.
Sample page—
For a treatise on the finite geometry underlying such designs (based on a monograph I wrote in 1976, before I had heard of Douat or his predecessor Truchet), see Diamond Theory.
The following passage by Tolkien was suggested by a copy of next Sunday's New York Times Book Review that arrived in the mail today. (See Orson Scott Card's remarks on page 26— "Uncle Orson"— and the Review 's concluding essay "Grand Allusion.")
"Lastly, tengwesta [system or code of signs] has also become an impediment. It is in Incarnates clearer and more precise than their direct reception of thought. By it also they can communicate easily with others, when no strength is added to their thought: as, for example, when strangers first meet. And, as we have seen, the use of 'language' soon becomes habitual, so that the practice of ósanwe (interchange of thought) is neglected and becomes more difficult. Thus we see that the Incarnate tend more and more to use or to endeavour to use ósanwe only in great need and urgency, and especially when lambe is unavailing. As when the voice cannot be heard, which comes most often because of distance. For distance in itself offers no impediment whatever to ósanwe . But those who by affinity might well use ósanwe will use lambe when in proximity, by habit or preference. Yet we may mark also how the 'affine' may more quickly understand the lambe that they use between them, and indeed all that they would say is not put into words. With fewer words they come swifter to a better understanding. There can be no doubt that here ósanwe is also often taking place; for the will to converse in lambe is a will to communicate thought, and lays the minds open. It may be, of course, that the two that converse know already part of the matter and the thought of the other upon it, so that only allusions dark to the stranger need be made; but this is not always so. The affine** will reach an understanding more swiftly than strangers upon matters that neither have before discussed, and they will more quickly perceive the import of words that, however numerous, well-chosen, and precise, must remain inadequate."
* "If a poem catches a student's interest at all, he or she should damned well be able to look up an unfamiliar word in the dictionary…."
— Elizabeth Bishop, quoted in the essay "Grand Allusion" mentioned above. For a brief dictionary of most of the unfamiliar words in this post's title and in the above passage, see Vinyar Tengwar 39 (July 1998). This is copyrighted but freely available on the Web.
** The word "affine" has connotations not intended by Tolkien. See that word in this journal. See also page 5 of next Sunday's Times Book Review , which contains a full-page ad for the 50th anniversary edition of A Wrinkle in Time . "There is such a thing as a tesseract."
"The transcripts of the 2006 meetings, released after a standard five-year delay,
clearly show some of the nation’s pre-eminent economic minds did not fully understand
the basic mechanics of the economy that they were charged with supervising."
— Binyamin Appelbaum in the Jan. 12 online New York Times
Academics may recall other examples of comfortably ignorant collegiality.
Today's Google Doodle for the 100th birthday of Charles Addams—
A doodle from this year's Feast of the Epiphany—
A doodle based on today's previous post and on a post for Twelfth Night, 2003—
Stanley Fish in The New York Times yesterday evening—
From the MLA program Fish discussed—
Above: An MLA session, “Defining Form,” led
by Colleen Rosenfeld of Pomona College
An example from Pomona College in 1968—
The same underlying geometries (i.e., “form”) may be modeled with
a square figure and a cubical figure rather than with the triangular
figures of 1968 shown above.
See Finite Geometry of the Square and Cube.
Those who prefer a literary approach to form may enjoy the recent post As Is.
(For some context, see Game of Shadows.)
Yesterday's "diamond globe" post linked to a picture by Prof. Mike Zabrocki
of York University in Toronto. Here is the picture itself—
Some related material from 2004—
Prof Talk: Thursday, April 1st, from 2:30pm to 3:30pm in North Ross 638.
Speaker: Prof. Mike Zabrocki
Title: "Gems of Algebra: The Secret Life of the Symmetric Group"
Prof. Zabrocki's talk was enjoyable and accessible. One of the notable aspects of the talk was that Prof. Zabrocki presented some open problems related to the topics he was speaking about. Unfortunately, there were some technical problems that resulted in some images not appearing in Prof. Zabrocki's PowerPoint presentation, but Prof. Zabrocki easily made up for the problem by some work at the chalk board. Please feel free to take a look at Prof. Zabrocki's PowerPoint presentation, as well as the pictures of the permutahedron for n=4 and the permutahedron for n=5.
Some slides from the talk—
Detail from the slides—
A less academic ornament, from this journal on the date
of the Zabrocki talk—
Click image for context.
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"
From a review of the film "Wild Palms" in The New Yorker by James Wolcott
(issue dated May 17, 1993, pages 104-106)—
"The MacGuffin that will determine the outcome is a piece of
software [sic ] called the Go chip, its name taken from the
strategy board game. (There's a nod in the script to the Japanese
novelist Yasunari Kawabata, author of 'The Master of Go.')
Whoever possesses the Go chip possesses the
'techno-shamanistic key to eternity'…."
"In tomorrow's techno-pop tyranny, reruns are the basis of order."
"As Kreutzer's mistress, Kim Cattrall has excellent posture."
From Saturday Night Live on December 10, 2011, a portrayal of Kim Cattrall—
See also "Sex and the City" fans in The Crimson Passion.
For other keys (perhaps related to the Wild Palms "image sickness"),
see "Claves Regni Caelorum (Escher)" — Images, 1.9 MB.
A check tonight of Norwegian artist Josefine Lyche's recent activities
shows she has added a video to her web page that has for some time
contained a wall piece based on the 2×2 case of the diamond theorem —
The video (top left in screenshot above) is a tasteless New-Age discourse
that sounds frighteningly like the teachings of the late Heaven's Gate cult.
Investigating the source of the video on vimeo.com, I found the account of one "Jo Lyxe,"
who joined vimeo in September 2011. This is apparently a variant of Josefine Lyche's name.
The account has three videos—
Lyche has elsewhere discussed her New-Age interests, so the contents of the videos
were not too surprising… except for one thing. Vimeo.com states that all three videos
were uploaded "2 months ago"— apparently when "Lyxe" first set up an account.*
I do not know, or particularly care, where she got the Blue Star video, but the other
videos interested me considerably when I found them tonight… since they are
drawn from films I discussed in this journal much more recently than "2 months ago."
"High on RAM (OverLoad)" is taken from the 1984 film "Electric Dreams" that I came across
and discussed here yesterday afternoon, well before re-encountering it again tonight.
And "Death 2 Everyone" (whose title** is perhaps a philosophical statement about inevitable mortality
rather than a mad terrorist curse) is taken from the 1983 Natalie Wood film "Brainstorm."
"Brainstorm" was also discussed here recently… on November 18th, in a post suggested by the
reopening of the investigation into Wood's death.
I had no inkling that these "Jo Lyxe" videos existed until tonight.
The overlapping content of Lyche's mental ramblings and my own seems rather surprising.
Perhaps it is a Norwegian mind-meld, perhaps just a coincidence of interests.
* Update: Google searches by the titles on Dec. 5 show that all three "Lyxe" videos
were uploaded on September 20 and 21, 2011.
** Update: A search shows a track with this title on a Glasgow band's 1994 album.
"I love gazing into things. Can you imagine with me how glorious it is, for example, to see into a dog, in passing— into him… to ease oneself into the dog exactly at his center, the place out of which he exists as a dog, that place in him where God would, so to speak, have sat down for a moment when the dog was complete, in order to watch him at his first predicaments and notions and let him know with a nod that he was good, that he lacked nothing, that no better dog could be made. For a while one can endure being in the middle of the dog, but one has to be sure to jump out in time, before the world closes in around him completely, otherwise one would remain the dog within the dog and be lost to everything else."
— Rainer Maria Rilke, quoted in The New York Times in 1988
Omitting unneeded narrative details,
a madman's knight move —
A novel search in memory of the late
uncrowned crown prince of Albania—
Nabokov, Pale Fire
Related narratives—
Prose Tale and The Meadow.
Oh, and happy birthday to Woody Allen (76 today)—
"Outside of a dog, a book is man's best friend.
Inside of a dog it's too dark to read." —Groucho Marx
Post 2310 in yesterday evening’s Short Story links to two posts
from 2006 inspired by Oxford mathematician Marcus du Sautoy—
|
Thursday, May 25, 2006
|
The first paragraph of
“Zeta Functions of Groups: The Quest for Order
Versus the Flight from Ennui,” by Marcus du Sautoy,
Mathematical Institute, University of Oxford—
“Mathematics is about the search for patterns,
to see order where others see chaos. We are very lucky
to find ourselves studying a subject which is neither so rigid
that the patterns are easy, yet not too complicated
lest our brains fail to master its complexities.
John Cawelti sums up this interplay perfectly in a book*
not about mathematics but about mystery and romance:
‘if we seek order and security, the result is likely to be
boredom and sameness. But rejecting order for the sake
of change and novelty brings danger and uncertainty…
the history of culture can be interpreted as a dynamic
tension between these two basic impulses…
between the quest for order and the flight from ennui.”’
* John G. Cawelti, Adventure, Mystery, and Romance:
Formula Stories as Art and Popular Culture ,
University of Chicago Press, 1976.
[Cawelti cites as his souce on interpreting “the history
of culture” Harry Berger, Jr., “Naive Consciousness and
Culture Change: An Essay in Historical Structuralism,”
Bulletin of the Midwest Modern Language Association ,
Vol. 6, No. 1 (Spring 1973): page 35.]
Here du Sautoy paints mathematicians as seekers of order,
apparently not realizing that the author he approvingly quotes
states that seekers of order face the danger of boredom.
Another danger to seekers
of order is, of course, seeing
order where there is none.
"I need a photo-opportunity,
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard." — Rhymin' Simon
See also Uncertainty and More Uncertainty.
From Thursday's post All Things Fashion—
From today's online New York Times—
The nuclear symbol beneath the op-ed headline
is the most interesting part of this afternoon's front page—
It is possible to project certain characteristics onto another person who does not possess them at all, but the one being projected upon may unconsciously encourage it.
"It frequently happens that the object offers a hook to the projection, and even lures it out. This is generally the case when the object himself (or herself) is not conscious of the quality in question: in that way it works directly upon the unconscious of the projicient. For all projections provoke counter-projections when the object is unconscious of the quality projected upon it by the subject." ["General Aspects of Dream Psychology," CW 8, par. 519.]
For an object that "offers a hook to the projection," see yesterday's Hypercube Rotations—
Central projection
of the hypercube
See also Stallion Gate in this journal.
Suggested by an Oct. 18 piece in the Book Bench section
of the online New Yorker magazine—
Related material suggested by the "Shouts and Murmurs" piece
in The New Yorker , issue dated Oct. 24, 2011—
"a series of e-mails from a preschool teacher planning to celebrate
the Day of the Dead instead of Halloween…"
A search for Coxeter + Graveyard in this journal yields…
Here the tombstone says "GEOMETRY… 600 BC — 1900 AD… R.I.P."
A related search for Plato + Tombstone yields an image from July 6, 2007…
Here Plato's poems to Aster suggested
the "Star and Diamond" tombstone.
The eight-rayed star is an ancient symbol of Venus
and the diamond is from Plato's Meno .
The star and diamond are combined in a figure from
12 AM on September 6th, 2011—
The Diamond Star
See Configurations and Squares.
That webpage explains how Coxeter
united the diamond and the star.
Those who prefer narrative to mathematics may consult
a definition of the Spanish word lucero from March 28, 2003.
R.T. Curtis in a 1990 paper* discussed his method of "symmetric generation" of groups as applied to the Mathieu groups
See Finite Relativity and the Log24 posts Relativity Problem Revisited (Sept. 20) and Symmetric Generation (Sept. 21).
Here is some exposition of how this works with
* "Geometric Interpretations of the ‘Natural’ Generators of the Mathieu groups," Mathematical Proceedings of the Cambridge Philosophical Society (1990), Vol. 107, Issue 01, pp. 19-26.
Background: Jung's Aion in this journal discusses this
figure from finite geometry's diamond theorem—
Fig. A
This resembles a figure that served Jung
as a schema of the Self—
Fig. B
Fig. A, with color variations, serves as the core
of many automatically generated Identicons —
a different sort of self-symbol.
Examples from Sept. 6 at MathOverflow—
A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar—
1. User Submissions. "… you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."
Sounds rather Faustian.
A post of September 1, The Galois Tesseract, noted that the interplay
of algebraic and geometric properties within the 4×4 array that forms
two-thirds of the Curtis Miracle Octad Generator (MOG) may first have
been described by Cullinane (AMS abstract 79T-A37, Notices , Feb. 1979).
Here is some supporting material—
The passage from Carmichael above emphasizes the importance of
the 4×4 square within the MOG.
The passage from Conway and Sloane, in a book whose first edition
was published in 1988, makes explicit the structure of the MOG's
4×4 square as the affine 4-space over the 2-element Galois field.
The passage from Curtis (1974, published in 1976) describes 35 sets
of four "special tetrads" within the 4×4 square of the MOG. These
correspond to the 35 sets of four parallel 4-point affine planes within
the square. Curtis, however, in 1976 makes no mention of the affine
structure, characterizing his 140 "special tetrads" rather by the parity
of their intersections with the square's rows and columns.
The affine structure appears in the 1979 abstract mentioned above—
The "35 structures" of the abstract were listed, with an application to
Latin-square orthogonality, in a note from December 1978—
See also a 1987 article by R. T. Curtis—
Further elementary techniques using the miracle octad generator, by R. T. Curtis. Abstract:
“In this paper we describe various techniques, some of which are already used by devotees of the art, which relate certain maximal subgroups of the Mathieu group M24, as seen in the MOG, to matrix groups over finite fields. We hope to bring out the wealth of algebraic structure* underlying the device and to enable the reader to move freely between these matrices and permutations. Perhaps the MOG was mis-named as simply an ‘octad generator’; in this paper we intend to show that it is in reality a natural diagram of the binary Golay code.”
(Received July 20 1987)
– Proceedings of the Edinburgh Mathematical Society (Series 2) (1989), 32: 345-353
* For instance:
Update of Sept. 4— This post is now a page at finitegeometry.org.
From http://msa-x.msa-x.org/?p=1064 —
"Exit Art New York, The Labyrinth Wall:
From Mythology to Reality" —
From tonight's online New York Times obituaries —
Ms. Ingberman died Wednesday. Related material—
Symmetry (Wednesday), Design (Thursday), Solomon's Labyrinth (Friday).
See also an essay by John Haber —
"Exit Art may yet offer an alternative: shut them up in the labyrinth, with the Minotaur and, as in Iraq, no Ariadne's thread to guide them out. Jeannette Ingberman and Papo Colo line the space with 'The Labyrinth Wall: From Mythology to Reality,' inviting fifty-one artists to cover its sixty-two panels."
— "Marlene Dumas, The Labyrinth Wall, and Emily Jacir"
Haber (ibid .) also describes artist Marlene Dumas, a recent winner of a Royal Swedish Academy Schock Prize. For a fellow Schock winner— mathematician Michael Aschbacher— see Thursday's Design.)
* For another version of the title, see this morning's front page.
Wednesday's Marginal Remarks pictured Robert De Niro
and Sean Penn in "We're No Angels." De Niro appeared
again in a Saturday Night Live sketch linked to
in last night's 9:29 post.
Here are some remarks featuring Penn related to
Peter J. Cameron's description yesterday of Sudoku
as an example of mathematics.
(Recall that the symbol #, known as 'hash,"
can stand for checkmate.)
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"Chess problems are the hymn-tunes of mathematics."
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For a sample chess problem, see a post from Oct. 10, 2005,
the day that the Sudoku remark Cameron describes was
in the news.
Related material: Duende meets Saturday Night Live—
The "duende" link above leads to a post containing the following—
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For the Sudoku part, see this afternoon's Geezer Puzzle and a comment
at Diamond Geezer's weblog this morning by combinatorialist Peter J. Cameron—
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This reminds me of an incident a few years ago when Sir Michael Atiyah was interviewed by a journalist, who asked him what he thought of the Sudoku craze. Sir Michael replied that he was delighted to see so many people doing mathematics every day, and was taken to task by the journalist because "there is no mathematics in it: you don't add the numbers or anything".
Anyway, I consider this a mathematical puzzle; I even have some fancy words for it (a Graeco-Latin square with two disjoint diagonals and some entries prescribed). But don't let that scare anyone off trying the puzzle!
Thanks, DG: I put a link to it right away. |
See also the Pope's schedule today.
From an obituary of choreographer Roland Petit, who died on Sunday, July 10, 2011—
"Ballerina roles had for more than a century been largely made on pale romantically suffering virgins or royal princesses; Petit’s women were liberated and exciting, modern and tangibly real— and yet archaic femmes fatales . Probably his most popular ballet worldwide is Le jeune homme et la mort , in which a young bloke lazing around in his room is visited by an enigmatic, seductive female— at the end of which brief encounter he hangs himself.
The young man’s role was seized upon by the great ballet stars of the next decades, Rudolf Nureyev and Mikhail Baryshnikov notable among them. As with Carmen, the role of La Mort, the death goddess, has been sought out by a pantheon of great ballerinas, in Paris, Russia and the US as well as in Europe." —Ismene Brown at theartsdesk.com
From the philosophy column "The Stone" in Saturday's online New York Times—
Let Be: An Answer to Hamlet’s Question"—
"Jamieson Webster is a psychoanalyst in private practice
in New York. She is the author of
'The Life and Death of Psychoanalysis'
forthcoming from Karnac Books."
Related ART WARS material:
Part I, Midday —
Yesterday's midday NY Lottery "689" suggests (from April 3, 2005)—
| 689 |  |
[fú] blessing, good fortune |
Diagram taken from R. Sing,
“Chinese New Year’s Dragon Teacher’s Guide”
— and the 4-digit midday number suggests a NASA Picture of the Day
that was published (not taken) on 7795 (7/7/95)—
Part II, Evening —
Suggested by yesterday's evening NY Lottery "068"
and by Weltschmerz and the Ursprache —
— Walter Benjamin, “On Language as Such and On the Language of Man” (1916),
Edmund Jephcott, tr., Walter Benjamin, Selected Writings, Volume I: 1913-1926 ,
Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA,
Harvard University Press, 1996, pp. 62-74. The above is page 68.
A more entertaining meditation is suggested by yesterday's 4-digit evening NY number—
a video tribute to a song said to have been released as a single on 7383 (7/3/83)—
Related material— "Dark Side of the Moon" in this journal.
Google Translate version of a recent Norwegian art review—
Josefine Lyche show is working on the basis of crop circles occur in Pewsey, Wiltshire in England for exactly one year ago on 21 June. Three circulars forms of aluminum quote forms from the field in England. With this as a starting point invites Lyche viewer to explore the sacred shapes and patterns through painting, floor work and sculpture. In the monumental painting "Wisdom Luxury Romance" draws Lyche lines to both Matisse and Baudelaire in his poem
From the artist's website, JosefineLyche.com—
WISDOM LUXURY ROMANCE
From elsewhere—
Related material—
From Antichristmas 2002— Aluminum, Your Shiny Friend.
From Sept. 22, 2004— Tribute… in the context of
today's previous entry and of the conclusion of the story
that later became Childhood's End —
"Philosophy seeks not absolute first principles,
nor yet purely immediate insights,
but the self-mediation of the system of truth,
and an insight into this self-mediation."
— Josiah Royce in his article "Axiom" in Encyclopaedia of Religion and Ethics ,
edited by James Hastings (New York: Charles Scribner's Sons, 1910),
Vol. II, pp. 279-282, on page 282.
Related material: Time and Chance (Dec. 17, 2010).
Today is Commencement Day at MIT.
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“To measure the changes — Shing-Tung Yau, To measure the changes:
The smartest are nothing:
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Well, perhaps not quite nothing.
The above pictures were posted here on the day the following book was published—
The lives of the nine Jews in the above book amount to more than Yau's "nothing."
Note, however, that claims by Jews (see Jill Abramson yesterday)
that their secular publications constitute a substitute for religion
and contain only "absolute truth" should be viewed with at least one
raised eyebrow.
Abramson's remark yesterday that her promotion to New York Times executive editor
was like "ascending to Valhalla" had a religious flavor worthy of yesterday's
Feast of the Ascension.
In related news from yesterday's Times—
See also a symbol related to Apollo, to nine, and to "nothing"—
A minimalist 3×3 matrix favicon—
This may, if one likes, be viewed as the "nothing"
present at the Creation. See Jim Holt on physics.
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From Savage Logic— Sunday, March 15, 2009 5:24 PM The Origin of Change A note on the figure
"Two things of opposite natures seem to depend — Wallace Stevens, |
Today is Sonia Kovalevskaya Day in the department of mathematics at Oregon State University in Corvallis.
Some synchronistic background from the end of Women's History Month two years ago—
Two posts from March 31, 2009— Natasha's Dance in this journal and, from a different, but well-written, journal…
Female mad scientists and creative nihilism
(thoughts on Sofia Kovalevskaya).
Background music— A pleasantly elementary version of Maurice Jarre's "Lara's Theme" from Doctor Zhivago .
Cocktail Party Physics yesterday— "Desperately Seeking Sonya"
Related material: Kovalevskaya's Top and Roger Cooke's
The Mathematics of Sonya Kovalevskaya.
See also "Math class is tough, Barbie."
"I need a photo-opportunity,
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard."
— Paul Simon
For Sabato's photo opportunity, click here.
The link is to a weblog post in Spanish published
on St. Thomas Becket's Day, 2010.
See also Helen Lane in this journal. Lane translated
Sabato's "On Heroes and Tombs."
Catherine Elizabeth "Kate" Middleton, born 9 January 1982,
will marry Prince William of Wales on April 29th, 2011.
This suggests, by a very illogical and roundabout process
of verbal association, a search in this journal.
A quote from that search—
“‘Memory is non-narrative and non-linear.’
— Maya Lin in The Harvard Crimson , Friday, Dec. 2, 2005
A non-narrative image from the same
general time span as the bride's birthday—
For some context, see Stevens + "The Rock" + "point A".
A post in that search, April 4th's Rock Notes, links to an essay
on physics and philosophy, "The Discrete and the Continuous," by David Deutsch.
See also the article on Deutsch, "Dream Machine," in the current New Yorker
(May 2, 2011), and the article's author, "Rivka Galchen," in this journal.
Galchen writes very well. For example —
| Galchen on quantum theory—
"Our intuition, going back forever, is that to move, say, a rock, one has to touch that rock, or touch a stick that touches the rock, or give an order that travels via vibrations through the air to the ear of a man with a stick that can then push the rock—or some such sequence. This intuition, more generally, is that things can only directly affect other things that are right next to them. If A affects B without being right next to it, then the effect in question must be in direct—the effect in question must be something that gets transmitted by means of a chain of events in which each event brings about the next one directly, in a manner that smoothly spans the distance from A to B. Every time we think we can come up with an exception to this intuition—say, flipping a switch that turns on city street lights (but then we realize that this happens through wires) or listening to a BBC radio broadcast (but then we realize that radio waves propagate through the air)—it turns out that we have not, in fact, thought of an exception. Not, that is, in our everyday experience of the world. We term this intuition 'locality.' Quantum mechanics has upended many an intuition, but none deeper than this one." |
(Continued from yesterday's Brightness at Noon, Afternoon Delight, and Goodbye Note.)
"The Catholic Church, through the Holy Office, has declared it is not lawful 'to take part in spiritualistic communications or manifestations of any kind, whether through a so-called medium or without one, whether hypnotism is used or not, even with the best of intentions among the participants, whether for the purpose of interrogating the souls of the departed or spiritual beings, whether by listening to their responses or even in idle curiosity, even with the tacit or express protestation of not having anything to do with the evil spirits' (Denzinger 3642*).
Behind the church's attitude toward Spiritualism is the concern that a Catholic would expose himself to the risk of actually dealing with the evil spirit. The assumption is that if fraud or deception are excluded, and manifestations occur that are beyond natural explanation, the active agent in these cases is neither God nor any one of the good spirits (whether angelic or human) but demonic forces that are sure to mislead the Catholic and endanger the integrity of his faith."
* 3642 2182 Qu.: An liceat per Medium, ut vocant, vel sine Medio, adhibito vel non hypnotismo, locutionibus aut manifestationibus spiritisticis quibuscumque adsistere, etiam speciem honestatis vel pietatis praeseferentibus, sive interrogando animas aut spiritus, sive audiendo responsa, sive tantum aspiciendo, etiam cum protestatione tacita vel expressa, nullam cum malignis spiritibus partem se habere velle. Resp.: (cfirm. a S. P'ce, 26 avril): Negative in omnibus.
See also The Ecclesiastical Review , Volume 57,
by Catholic University of America, page 186.
This volume, from Harvard University, was digitized on June 19, 2008.
Katherine Neville, The Eight—
"Continue a search for thirty-three and three.
Veiled forever is the secret door."
See also The Maker's Gift.
* Corrected Dec. 14, 2014, from "Combinatorial."
From University Book Store, Seattle, Washington—
Related material—
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The Use and Abuse
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From a page on Reality Hunger: A Manifesto at DavidShields.com—
"The book's epigraph is a statement from Picasso: 'All art is theft.'"
Update of 3 PM EDT April 7—
"… we get inspiration from everywhere, and there's a bright line between inspiration and slavish imitation. (I was going to throw in the Picasso quote 'All art is theft' here, but I've looked that up in both the Oxford Dictionary of Quotations
— Weblog post by Erin McKean
Escape from Kitsch Mountain
"Why you gotta be so mean?" — Taylor Swift (see last night)
This song includes, as part of the hook, the recurring phrase
"Someday I'll be livin' in a big ol' city."
From a big ol' city—
A Return to Kitsch Mountain
By AUSTIN CONSIDINE
Published in The New York Times on January 16, 2009
As my girlfriend, Larissa, and I approached Gatlinburg, Tenn., this fall, I did my best to prepare her. She hadn’t been to Gatlinburg before, but I had. I understood the town’s complicated reputation both as a gateway to some of the most beautiful country in the United States— the Great Smoky Mountains National Park— and as a flamboyant capital of kitsch….
… It turned out that by 8 or 9 p.m., it was way too late to find a dinner show. The next morning, we had the opposite problem. By the time we woke up and wandered into Gatlinburg, it was noon. All the pancake houses were closed, and I was desolate. I had been thinking about those pancakes since the night before. So we did a little more sightseeing on foot.
Looking at Gatlinburg’s strip with adult eyes, I wondered how much self-awareness was at work there. It would be easy for a city slicker to assume this place misses its own punch lines. In truth, I decided, it merely embraces that special brand of conscious kitsch that forms its own American kind of authenticity. With all its absurdities, Gatlinburg knows what it is and proclaims it loudly, from one flashing signboard to the next….
From Gatlinburg—
Commentary on last night—
Tonight: The After-Party.
In related news…
"The yarns of seamen have a direct simplicity, the whole meaning of which
lies within the shell of a cracked nut. But Marlow was not typical
(if his propensity to spin yarns be excepted), and to him the meaning
of an episode was not inside like a kernel but outside, enveloping the tale
which brought it out only as a glow brings out a haze, in the likeness of
one of these misty halos that sometimes are made visible by
the spectral illumination of moonshine."
– Joseph Conrad in Heart of Darkness , quoted here in
Cold Open (Saturday night, January 29, 2011)
Part I: A search in this journal for Cuernavaca+garden
Part II: This life can be very strange –Steely Dan, 1976
Part III: Owsley Stanley Dies at 76
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.)
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Philosophy versus Stories —
The above uploading was done on December 10th, 2006.
For some context, see the Log24 posts for December 2006.
See also the German version of a nursery rhyme
that one commenter has called "morbid and horrifying"—
"Dein Vater sitzt auf der Schwelle:
Flieg in Himmel aus der Hölle."
The rhyme suggests characters in the novel The Quest for the 36
related to the Triangle Shirtwaist Factory fire often recalled during
women's history month. It also suggests the oeuvre of Stephen King.
“History, Stephen said, is a nightmare
from which I am trying to awake.”
– Ulysses
A search for some background on Dmitri Tymoczko, the subject of yesterday's evening entry on music theory, shows that his name and mine once both appeared in the same web page— "This Week's Finds in Mathematical Physics (Week 234)," by John Baez, June 12, 2006 (linked to by the Wikipedia article on transformational music theory).
In that page, Baez speculates on the possibility of a connection between music theory and Mathieu groups and says—
"For a pretty explanation of M24, also try this:
Steven H. Cullinane, Geometry of the 4 × 4 square, http://finitegeometry.org/sc/16/geometry.html."
I know of no connection* between the groups I discussed there and music theory. For some background on Tymoczko's work, see the helpful survey "Exploring Musical Space," by Julian Hook (Science magazine, 7 July 2006).
* Apart, that is, from the tesseract (see Geometry of the 4 × 4 Square) shown by Tymoczko in a 2010 lecture—
This is perhaps "Chopin's tesseract" from section 8.5 of Tymoczko's new book
A Geometry of Music (Oxford University Press, 2011).
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.
Quotes from the new film "Unknown" —
Related fantasia —
Ad for Posh — Click to enlarge —
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