The phrase "the mathematical concept of invariance of symmetry"
in the previous post suggests a Google search . . .
For those who prefer narrative to mathematics, the search result
"The Time Invariance of Snow" is not without interest.
See also "Snow Queen" in this journal.
Mathematics:
From Log24 "Pyramid Game" posts —
The letter labels, but not the tetrahedron, are from Whitehead’s
The Axioms of Projective Geometry (Cambridge U. Press, 1906), page 13.
Narrative:
The tortoise of the previous post suggests . . .
"Is it the good turtle soup
or merely the mock?"
Related material from the above
Toronto premiere date —
Midrash from Philip Pullman . . .
"The 1929 Einstein-Carmichael Expedition"
I prefer the 1929 Emch-Carmichael expedition —
This is from . . .
“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer
(Ch. 14 (pp. 693-746) of Handbook of Combinatorics,
Vol. I, MIT Press, 1995, edited by Ronald L. Graham,
Martin Grötschel, and László Lovász, Section 16 (p. 716))
Related literary notes — On April 28 The New York Times
reported a death from the above date (Tuesday, April 26, 2022).
See a followup in the Times today on "New York literary royalty."
Modernism, Fiction and Mathematics
by Nina Engelhardt
(Edinburgh Critical Studies in Modernist Culture)
From a review by Johann A. Makowsky in
Notices of the American Mathematical Society,
November 2020, pp. 1589-1595 —
"Engelhardt’s goal in this study is to put the interplay
between fiction and mathematical conceptualizations
of the world into its historical context. She sees her work
as a beginning for further studies on the role of mathematics,
not only modern, in fiction in the wider field of literature and
science. It is fair to say that in her book Nina Engelhardt does
succeed in giving us an inspiring tour d’horizon of this interplay."
Another such tour —
On the title of Westworld Season 4 Episode 5, "Zhuangzi" —
A song for Teddy: "Across my dreams, with nets of wonder . . ."
See Zhuangzi also in the 2022 Black Rock CIty manifesto, "Waking Dreams" . . .
The above title is from a July 1 review by Brent Simon of
the recent film "Code Name: Banshee."
Example of a narrative template —
The "He's a mad scientist and I'm his beautiful daughter" plot,
as in "Ant-Man" (2015) and in . . .
Plot twist —
"It was a bright cold day in April . . ."
"Solomon Golomb’s classic book Shift Register Sequences,
published in 1967—based on his work in the 1950s—
went out of print long ago. But its content lives on. . . ."
For part of that content, see Stencils .
A :Log24 post from the date of Golomb's death —
See as well other posts on Mathematics and Narrative.
Examples of Narrative:
Example of Mathematics:
From the month — November 1985 — in the second example above —
* Addicts of narrative might consult "Friends of Nemo."
** See Mathematics + Narrative in this journal and . . .
"As the chaos grew . . . ." —
“To conquer, three boxes* have to synchronize and join together into the Unity.”
―Wonder Woman in Zack Snyder’s Justice League
See also The Unity of Combinatorics and The Miracle Octad Generator.
* Cf. Aitchison’s Octads —
Mathematics: This journal on September 1, 2011 —
Posts tagged September Morn.
Narrative: Also on September 1, 2011 —
See as well Nabokov’s Magic Carpet.
Mathematics: See Tetrahedron vs. Square in this journal
(Notes on two different models of schoolgirl space ).
Narrative: Replacing the square from the above posts by
a related cube …
… yields a merchandising inspiration —
Dueling Holocrons:
Jedi Cube vs. Sith Tetrahedron —
* See also earlier posts on Mathematics and Narrative.
"Leonardo was something like what we now call a Conceptual artist,
maybe the original one. Ideas — experiments, theories — were
creative ends in themselves."
— Holland Cotter in the online New York TImes this evening
From other Log24 posts tagged Tetrahedron vs. Square —
* Phrase from the previous post, "Overarching Narrative."
In memory of a retired co-director of Galerie St. Etienne
who reportedly died on October 17 . . .
"It is… difficult to mount encyclopedic exhibitions
without an overarching art-historical narrative…."
— Jane Kallir, director of Galerie St. Etienne, in
https://www.tabletmag.com/jewish-arts-and-culture/
visual-art-and-design/269564/the-end-of-middle-class-art
An overarching narrative from the above death date —
See as well the previous post
and "Dancing at Lughnasa."
"There is such a thing as a desktop."
— Saying adapted from a 1962 young-adult novel.
"Here, modernism is defined as an autonomous body
of ideas, having little or no outward reference, placing
considerable emphasis on formal aspects of the work
and maintaining a complicated—indeed, anxious—
rather than a naïve relationship with the day-to-day
world, which is the de facto view of a coherent group
of people, such as a professional or discipline-based
group that has a high sense of the seriousness and
value of what it is trying to achieve. This brisk definition…."
— Jeremy Gray, Plato's Ghost: The Modernist
Transformation of Mathematics , Princeton, 2008
"Even as the dominant modernist narrative was being written,
there were art historians who recognized that it was inaccurate.
The narrative was too focused on France . . . . Nor was it
correct to build the narrative so exclusively around formalism;
modernism was far messier, far more multifaceted than that."
— Jane Kallir, https://www.tabletmag.com/
jewish-arts-and-culture/visual-art-and-design/
269564/the-end-of-middle-class-art,
quoted here on the above date — Sept. 11, 2018.
From some related Log24 posts —
See also "Overarching + Tesseract" in this journal. From the results
of that search, some context for the "inscape" of the previous post —
See also Clifford in this journal, in particular
The Matrix for Quantum Mystics
(Log24, St. Andrew's Day, 2017).
Mathematics —
See (for instance) a research group at Ghent University.
For those who prefer narrative . . .
See also . . .
See also, in this journal, 23-cycle.
Update of Sept. 6, 2018, 9:05 AM ET: "The Cubist Method" —
Multifaceted narrative by James Joyce —
Multifaceted structures in pure mathematics, from Plato and R. T. Curtis —
For Cady Heron
"Why you gotta be so mean?" — Taylor Swift
* See references to that Greek island in this journal.
Excerpts from a post of May 25, 2005 —
Above is an example I like of mathematics….
Here is an example I like of narrative:
.
Kate felt quite dizzy. She didn't know exactly what it was
that had just happened, but she felt pretty damn certain that
it was the sort of experience that her mother would not have
approved of on a first date.
"Is this all part of what we have to do to go to Asgard?"
she said. "Or are you just fooling around?"
"We will go to Asgard...now," he said.
At that moment he raised his hand as if to pluck an apple,
but instead of plucking he made a tiny, sharp turning movement.
The effect was as if he had twisted the entire world through a
billionth part of a billionth part of a degree. Everything
shifted, was for a moment minutely out of focus, and then
snapped back again as a suddenly different world.
— Douglas Adams, The Long Dark Tea-Time of the Soul
Image from a different different world —
Hat-tip to a related Feb. 26 weblog post
at the American Mathematical Society.
See also posts tagged May 19 Gestalt.
In memory of weather buff Stephen Fybish,
who reportedly died at 80 on August 30.
The Eye of Harvey meets the Eye of Shangri-La —
Today's New York Times on Fybish —
"Winter was his favorite season. He liked to taste the snow,
'since that’s one of the purer forms of water that we’re likely
to encounter here in the Big Apple,' he said."
— Sam Roberts
See Captain America's special breakfast
in posts tagged Aesthetic Distance.
See as well Taylor Swift in the previous post and
The School of the New York Times on creating
great branded content:
Quoted here on St. Stephen's Day, 2008 —
“Wayne C. Booth’s lifelong
study of the art of rhetoric
illuminated the means
by which authors seduce,
cajole and lie to their readers
in the service of narrative.”
— New York Times, Oct. 11, 2005
Booth was a native of American Fork, Utah.
“That corpse you planted
last year in your garden,
Has it begun to sprout?
Will it bloom this year?
Or has the sudden frost
disturbed its bed?”
— T. S. Eliot, “The Waste Land“
Click the book for a video.
Mathematics —
Hudson's parametrization of the
4×4 square, published in 1905:
A later parametrization, from this date in 1986:
A note from later in 1986 shows the equivalence of these
two parametrizations:
Narrative —
Posts tagged Memory-History-Geometry.
The mathematically challenged may prefer the narrative of the
Creation Matrix from the religion of the Transformers:
"According to religious legend, the core of the Matrix
was created from Solomus, the god of wisdom,
trapped in the form of a crystal by Mortilus, the god
of death. Following the defeat of Mortilus, Solomus
managed to transform his crystal prison into the Matrix—
a conduit for the energies of Primus, who had himself
transformed into the life-giving computer Vector Sigma."
The images in the previous post do not lend themselves
to any straightforward narrative. Two portions of the
large image search are, however, suggestive —
Cross and Boolean lattice.
The improvised cross in the second pair of images
is perhaps being wielded to counteract the
Boole of the first pair of images. See the heading
of the webpage that is the source of the lattice
diagram toward which the cross is directed —
Update of 10 am on August 16, 2016 —
See also Atiyah on the theology of
(Boolean) algebra vs. (Galois) geometry:
The novel Blood on Snow , set in Oslo, was published
by Knopf on April 7, 2015. This journal on that date —
|
Log24 on Tuesday, April 7, 2015 Filed under: Uncategorized — m759 @ 7:00 PM Seven years ago in this journal —
|
A related image —
Continued from June 8, 2016.
A book by Northrop Frye pictured in the previous post
suggests a Log24 search for "The Great Code."
That search yields …
"Icy white and crystalline"
— Johnny Mercer
Jews on Style continues …
From a Washington Post obituary this morning —
"For the past 30 years, while teaching at New York University’s
law school, Dr. Bruner explored the idea of storytelling as a
fundamental way of understanding the nature of the world
around us. He believed that the choices we make in telling
stories 'become so habitual that they finally become recipes
for structuring experience itself, for laying down routes into
memory,' he said in 1987.
'This is a mode of cognition,' Gardner said, 'at least as
important as STEM' — the science, technology, engineering
and mathematics model of instruction that has gained
currency in recent years.
'He made narrative a form of thinking,' Gardner added.
Jerome Seymour Bruner was born Oct. 1, 1915,
in New York City to Jewish immigrants from Eastern Europe."
Related material —
Principles before Personalities — AA Saying .
Principles —
See Schoolgirl Problem in Wikipedia.
Personalities —
See Alexandra Alter in the May 26 online New York Times :
"With the proliferation of 'girl' titles,
there are signs that the trend may have peaked;
it already seems ripe for parody."
Update of 12:40 PM ET on Wednesday, June 1, 2016 —
A note for the Church of Synchronology …
See a post from this journal on the date of the Alter piece, May 26:
(Click image for the rest of the post .)
Madeleine L'Engle meets Captain America —
This is from a Jan. 27, 2012, post on mathematics and narrative.
Related literary criticism by the late Florence King —
"Given all the historical personages the author whistles in,
one more won't hurt. Nicolas Boileau, the 17th-century
French literary critic, gave writers a piece of advice that
Ms. Neville could use: 'Make not your tale of accidents
too full / too much variety will make it dull / Achilles' rage
alone, when wrought with skill /Abundantly does a whole
"Iliad" fill.' "
— NY Times review of The Eight , a novel by Katherine Neville
(Continued from Dec. 13, 2014.)
David Lavery's enthusiasm today for the Marvel Comics
"Infinity Stones" suggests a review of The Foundation Stone
mentioned in the post Narrative Metaphysics of 12/13/2014.
See as well "Many Dimensions" in this journal.
From "Guardians of the Galaxy" —
"Then the Universe exploded into existence…"
For those who prefer a more traditional approach :
See also Symplectic Structure and Stevens's Rock.
Mathematics: Galois-Plane Models.
Narrative: "The Dreaming Jewels."
"We live entirely, especially if we are writers, by the imposition
of a narrative line upon disparate images…." — Joan Didion
Narrative Line:
Disparate images:
Exercise:
Can the above narrative line be imposed in any sensible way
upon the above disparate images?
Raiders of the Lost Archetype
“… an unexpected development: the discovery of a lost archetype….”
— “The Lost Theorem,” by Lee Sallows, Mathematical Intelligencer, Fall 1997
Related material:
A scene from the 1954 film:
A check of this journal on the above MetaFilter date — Jan. 24, 2012 —
yields a post tagged “in1954.” From another post with that tag:
Backstory: Posts tagged Root Circle.
"Richard Hughes’s celebrated short novel is
a masterpiece of concentrated narrative."
— New York Review of Books on
A High Wind in Jamaica
As perhaps were, in their way, parts of the life
of the late Patrice Wymore Flynn, who reportedly
died at 87 on Saturday.
Deep backstory: See Colony of Santiago (Jamaica).
For the "mathematics" part of this post's title, see
Saturday's Log24 post on Kummer-surface terms
and a post of September 23, 2012.
Or: The Confessions of Nat Tate
“A convincing lie is, in its own way, a tiny, perfect narrative.”
— William Boyd, “A Short History of the Short Story” (2006)
“A novel written in the first-person singular has certain powerful
narrative advantages, especially when it takes the form of a ‘confession.'”
— William Boyd, “Memoir of a Plagiarist” (1994)
From a Log24 post yesterday —
For Little Man Tate —
Related material — Wechsler in this journal and an earlier Siri Hustvedt
art novel, from 2003 —
Mark and Lucille, Bill and Violet, Al and Regina, etc., etc., etc. —
Mathematics:
A review of posts from earlier this month —
Wednesday, September 4, 2013
|
Narrative:
Aooo.
Happy birthday to Stephen King.
… from yesterday— Bling Ring and Church Logic.
Related narratives— Get Quotes (source of image below)
as well as Helprin's Doors and Trickster.
"Why history?
Well, the essence of history is story ,
and a good story is an end in itself."
— Barry Mazur, "History of Mathematics as a tool,"
February 17, 2013
This journal on February 17, 2013:FROM Christoph Waltz"Currently in post-production": The Zero Theorem. For Christoph WaltzRaiders of the Lost Tesseract continues… SOCRATES: Is he not better off in knowing his ignorance? |
See also today's previous post.
See Snakes on a Projective Plane by Andrew Spann (Sept. 26, 2006):
Click image for some related posts.
"…what he was trying to get across was not that he was the Soldier of a Power that was fighting across all of time to change history, but simply that we men were creatures with imaginations and it was our highest duty to try to tell what it was really like to live in other times and places and bodies. Once he said to me, 'The growth of consciousness is everything… the seed of awareness sending its roots across space and time. But it can grow in so many ways, spinning its web from mind to mind like the spider or burrowing into the unconscious darkness like the snake. The biggest wars are the wars of thought.' "
— Fritz Leiber, Changewar , page 22
"… both marveled at early Ingmar Bergman movies."
One of the friends' "humor was inspired by
surrealist painters and Franz Kafka."
"Most of Marvel's fictional characters operate in
a single reality known as the Marvel Universe…."
Related material: The Cosmic Cube.
Angels & Demons meet Hudson Hawk
Dan Brown's four-elements diamond in Angels & Demons :
The Leonardo Crystal from Hudson Hawk :
Mathematics may be used to relate (very loosely)
Dan Brown's fanciful diamond figure to the fanciful
Leonardo Crystal from Hudson Hawk …
"Giving himself a head rub, Hawk bears down on
the three oddly malleable objects. He TANGLES
and BENDS and with a loud SNAP, puts them together,
forming the Crystal from the opening scene."
— A screenplay of Hudson Hawk
Happy birthday to Bruce Willis.
Primes Are Forever
"If diamonds are a girl's best friend,
prime numbers are a mathematician's….
A Mersenne prime is of the form 2P-1,
where the variable P is itself a prime—
making the Mersenne an elite sort of prime,
a James Bond among spies."
— Anonymous author at
Fox News, Feb. 5, 2013
The author notes that the smaller
Mersenne primes include 7.
Related Material
April is Math Awareness Month.
This year's theme is "mathematics and art."
Update of 2:56 PM Feb. 7:
See also Paul Bateman and, in this journal, the date of Bateman's death.
For mathematics rather than narrative, see (for instance)…
.
In diamond-narrative news today…
"Among the low points of his career was his performance
in the disastrous 1985 remake of “King Solomon’s Mines….”
— David Belcher in today's online New York Times
Two narratives in memory of my seventh-grade
history teacher, who died on January 27, 2012—
1. On the history of Liberia
(subject of a paper I wrote in seventh grade), and
2. Comic-book history (from the above date)
Princeton University Press on a book it will publish in March—
Circles Disturbed: The Interplay of Mathematics and Narrative
"Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier— 'Don't disturb my circles'— words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds–stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities."
Timeline of the Marvel Cinematic Universe — Norway, March 1942—
"The Red Skull finds the Tesseract, a cube of strange power,
said to be the jewel of Odin’s treasure room, in Tonsberg Norway.
(Captain America: The First Avenger)"
Tesseracts Disturbed — (Click to enlarge)
Detail of Tesseracts Disturbed —
Narrative of the detail—
See Tesseract in this journal and Norway, May 2010—
Mathematics —
(Some background for the Galois tesseract )
Narrative —
An essay on science and philosophy in the January 2012
Notices of the American Mathematical Society .
Note particularly the narrative explanation of the double-slit experiment—
"The assertion that elementary particles have
free will and follow Quality very closely leads to
some startling consequences. For instance, the
wave-particle duality paradox, in particular the baffling
results of the famous double slit experiment,
may now be reconsidered. In that experiment, first
conducted by Thomas Young at the beginning
of the nineteenth century, a point light source
illuminated a thin plate with two adjacent parallel
slits in it. The light passing through the slits
was projected on a screen behind the plate, and a
pattern of bright and dark bands on the screen was
observed. It was precisely the interference pattern
caused by the diffraction patterns of waves passing
through adjacent holes in an obstruction. However,
when the same experiment was carried out much
later, only this time with photons being shot at
the screen one at a time—the same interference
pattern resulted! But the Metaphysics of Quality
can offer an explanation: the photons each follow
Quality in their actions, and so either individually
or en masse (i.e., from a light source) will do the
same thing, that is, create the same interference
pattern on the screen."
This is from "a Ph.D. candidate in mathematics at the University of Calgary."
His essay is titled "A Perspective on Wigner’s 'Unreasonable Effectiveness
of Mathematics.'" It might better be titled "Ineffective Metaphysics."
See also this journal on October 10, 2010.
Related material: Duende meets Saturday Night Live—
The "duende" link above leads to a post containing the following—
|
|
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—
|
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.
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.
From 6/22, 2010 —
I would argue that at least sometimes, lottery numbers may be regarded,
according to Bernstein's definition, as story statements.
From 7/02, 2010 —
Apollo's 13: A Group Theory Narrative —
I. At Wikipedia —
II. Here —
See Cube Spaces and Cubist Geometries.
The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
subcubes in the 27-part (Galois) 3×3×3 cube–
A note from 1985 describing group actions on a 3×3 plane array—
Undated software by Ed Pegg Jr. displays
group actions on a 3×3×3 cube that extend the
3×3 group actions from 1985 described above—
Pegg gives no reference to the 1985 work on group actions.
Thanks to David Lavery for the following dialogue on the word "narrative" in politics—
"It's like – does this fit into narrative?
It's like, wait, wait, what about a platform? What about, like, ideas?
What about, you know, these truths we hold to be self-evident?
No, it's the narrative."
"Is narrative a fancy word for spin?"
Related material —
Church Logic (Log24, October 29) —
What sort of geometry
is the following?
"What about, you know, these truths we hold to be self-evident?"
Some background from Cambridge University Press in 1976 —
Commentary —
The Church Logic post argues that Cameron's implicit definition of "non-Euclidean" is incorrect.
The four-point, six-line geometry has as lines "all subsets of the point set" which have cardinality 2.
It clearly satisfies Euclid's parallel postulate. Is it, then, not non-Euclidean?
That would, according to the principle of the excluded middle (cf. Church), make it Euclidean.
A definition from Wikipedia that is still essentially the same as it was when written on July 14, 2003—
"Finite geometry describes any geometric system that has only a finite number of points. Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points…."
This definition would seem to imply that a finite geometry (such as the four-point geometry above) should be called non -Euclidean whether or not it violates Euclid's parallel postulate. (The definition's author, unlike many at Wikipedia, is not anonymous.)
See also the rest of Little Gidding.
The Story of N
Roberta Smith in the New York Times of July 7, 2006—
Art Review
"… The show has an endgame, end-time mood, as if we are looking at the end of the end of the end of Pop, hyperrealism and appropriation art. The techniques of replication and copying have become so meticulous that they are beside the point. This is truly magic realism: the kind you can't see, that has to be explained. It is also a time when artists cultivate hybridism and multiplicity and disdain stylistic coherence, in keeping with the fashionable interest in collectivity, lack of ego, the fluidity of individual identity. But too often these avoidance tactics eliminate the thread of a personal sensibility or focus.
I would call all these strategies fear of form, which can be parsed as fear of materials, of working with the hands in an overt way and of originality. Most of all originality. Can we just say it? This far from Andy Warhol and Duchamp, the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.
Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible. With a few exceptions, forms of collage and assemblage dominate this show: the putting together (or simply putting side by side) of existing images and objects prevails. The consistency of this technique in two and three dimensions should have been a red flag for the curators. Collage has driven much art since the late 1970's. Lately, and especially in this exhibition, it often seems to have become so distended and pulled apart that its components have become virtually autonomous and unrelated, which brings us back to square one. This is most obvious in the large installations of graphic works whose individual parts gain impact and meaning from juxtaposition but are in fact considered distinct artworks."
Margaret Atwood on art and the trickster—
"The pleasures of fabulation, the charming and playful lie— this line of thought leads Hyde* to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning 'to join,' 'to fit,' and 'to make.' If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart."
* Lewis Hyde, Trickster Makes This World: Mischief, Myth, and Art, Farrar Straus & Giroux, January 1998
Smith mentions "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."
Atwood mentions "a seamless whole."
For some related remarks, see "A Study in Art Education" and the central figure pictured above. (There "N" can stand for "number," "nine," or "narrative.")
Narrative Sequence
In today's New York Times, Michiko Kakutani reviews a summer thriller by Kevin Guilfoile. The Thousand is in the manner of Dan Brown's 2003 The Da Vinci Code or of Katherine Neville's 1988 The Eight .
From the review—
What connects these disparate events, it turns out, is a sinister organization called the Thousand, made up of followers of the ancient Greek mathematician and philosopher Pythagoras (yes, the same Pythagoras associated with the triangle theorem that we learned in school).
As Mr. Guilfoile describes it, this organization is part Skull and Bones, part Masonic lodge, part something much more twisted and nefarious….
The plot involves, in part,
… an eccentric artist’s mysterious masterwork, made up of thousands of individually painted tiles that may cohere into an important message….
Not unlike the tiles in the Diamond Theory cover (see yesterday's post) or, more aptly, the entries in this journal.
"List, list, O, list!"
— Hamlet's father's ghost
"Ordering and patterning are not wholly narrative activities."
— James E. Giles, 1986
"See also… the true story 0, 1, 2, 3…" 
— Log24, January 9, 2009
For some non-narrative patterning of this list, see (for instance)
Apostol's Modular Functions and Dirichlet Series in Number Theory.
"By groping toward the light we are made to realize
how deep the darkness is around us."
— Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
A 1973 review of Koestler's book—
"Koestler's 'call girls,' summoned here and there
by this university and that foundation
to perform their expert tricks, are the butts
of some chilling satire."
Examples of Light—
Felix Christian Klein (1849- June 22, 1925) and Évariste Galois (1811-1832)
Klein on Galois—
"… in France just about 1830 a new star of undreamt-of brilliance— or rather a meteor, soon to be extinguished— lighted the sky of pure mathematics: Évariste Galois."
— Felix Klein, Development of Mathematics in the 19th Century, translated by Michael Ackerman. Brookline, Mass., Math Sci Press, 1979. Page 80.
"… um 1830 herum in Frankreich als ein neuer Stern von ungeahntem Glanze am Himmel der reinen Mathematik aufleuchtet, um freilich, einem Meteor gleich, sehr bald zu verlöschen: Évariste Galois."
— Felix Klein, Vorlesungen Über Die Entwicklung Der Mathematick Im 19. Jahrhundert. New York, Chelsea Publishing Co., 1967. (Vol. I, originally published in Berlin in 1926.) Page 88.
Examples of Darkness—
Martin Gardner on Galois—
"Galois was a thoroughly obnoxious nerd,
suffering from what today would be called
a 'personality disorder.' His anger was
paranoid and unremitting."
Gardner was reviewing a recent book about Galois by one Amir Alexander.
Alexander himself has written some reviews relevant to the Koestler book above.
See Alexander on—
The 2005 Mykonos conference on Mathematics and Narrative
A series of workshops at Banff International Research Station for Mathematical Innovation between 2003 and 2006. "The meetings brought together professional mathematicians (and other mathematical scientists) with authors, poets, artists, playwrights, and film-makers to work together on mathematically-inspired literary works."
The Unfolding
A post for Florencio Campomanes,
former president of the World Chess Federation.
Campomanes died at 83 in the Philippines
at 1:30 PM local time (1:30 AM Manhattan time)
on Monday, May 3, 2010.
From this journal on the date of his death —
"There is such a thing as a tesseract."
– Madeleine L'Engle
Image by Christopher Thomas at Wikipedia —
Unfolding of a hypercube and of a cube —
Related material from a story of the Philippines —
Romancing the
Non-Euclidean Hyperspace
Backstory —
Mere Geometry, Types of Ambiguity,
Dream Time, and Diamond Theory, 1937
For the 1937 grid, see Diamond Theory, 1937.
The grid is, as Mere Geometry points out, a non-Euclidean hyperspace.
For the diamonds of 2010, see Galois Geometry and Solomon’s Cube.
Saturday's post quoted a mathematical narrative with the following opening sentence–
"Let G be a finite, primitive subgroup of
If that narrative were a novel, its opening might win a Bulwer-Lytton prize.
As might the opening of another nonfiction narrative—
"What are we are doing?"
A partial answer to this profound metaphysical question
for fans of the classic film "Dark City"
(which was written in part by one "Lem Dobbs")–
Part I — Fiction —
Wednesday August 4, 2004Shell Beach “It was a dark and stormy night….” – Opening of A Wrinkle in Time, a classic novel by Madeleine L’Engle. For those who seek religious significance in the name of Hurricane Alex: “Alex Proyas directs this futuristic thriller about a man waking up to find he is wanted for brutal murders he doesn’t remember. Haunted by mysterious beings who stop time and alter reality, he seeks to unravel the riddle of his identity.” – Description of the 1998 film Dark City
[See also June 14, 2005.] |
Part II — Nonfiction —
Part III — Fiction —
"The bench on which Dobbs was sitting
was not so good."
— B. Traven, opening sentence
of The Treasure of the Sierra Madre
The Magic Lyre
(Click image for context.)
See also Saturday's post—
as well as Solemn Dance
and Mazur at Delphi.
(This last is apparently based on
a talk given by Barry Mazur at Delphi
in 2007 and may or may not appear in
a book, Mathematics and Narrative,
to be published in 2010.)
Suggested tune for the lyre–
"Send me the pillow
that you dream on,"
in memory of Hank Locklin,
who died on this date last year.
A graphic novel reviewed in the current Washington Post features Alfred North Whitehead and Bertrand Russell–
Related material:
Whitehead on Fano’s finite projective three-space:
“This is proved by the consideration of a three dimensional geometry in which there are only fifteen points.”
—The Axioms of Projective Geometry , Cambridge University Press, 1906
Further reading:
See Solomon’s Cube and the link at the end of today’s previous entry, then compare and contrast the above portraits of Whitehead and Russell with Charles Williams’s portraits of Sir Giles Tumulty and Lord Arglay in the novel Many Dimensions .
The dimensions of the "bricks" in the R. T. Curtis
"Miracle Octad Generator": 2×4.
For those who prefer narrative to mathematics . . .
From the above Baez essay —
"And when the hero arrives, there should be
a little flourish of trumpets, like:
And now we come to a key player:
the group of deck transformations."
This remark and Baez's statement that
"Ideally the tricks I’m suggesting here
will be almost invisible…."
suggest a non-mathematical "deck transformation"
that some will prefer —
In the March 21 Netflix series "3 Body Problem,"
the deck of the ship Judgment Day is transformed
in a spectacular manner by an invisible trick.
The New York Times this afternoon —
" William Beecher, who as a reporter for The New York Times
revealed President Richard M. Nixon’s secret bombing campaign
over Cambodia during the Vietnam War, and who later won a
Pulitzer Prize at The Boston Globe, died on Feb. 9 at his home
in Wilmington, N.C. He was 90." — Clay Risen, 2:28 PM
Also on Feb. 9 —
Another Beecher narrative —
Religious meditation from the Church of Synchronology . . .
A search for Varda in this journal yields a passage from
a site called "saint-lucy.com" . . .
The European Film Academy award date above suggests a review —
Narrative Metaphysics, Log24, December 13, 2014.
"The present article elaborates on a talk presented at the first
'Mathematics and Narrative' conference (Mykonos, July 12-15, 2005)."
— Leo Corry on his "Calculating the Limits of Poetic License"
"In this article I seek to clarify the role played by poetic license
in the triangular relationship involving mathematics, the history
of mathematics and mathematics in fiction."
— Leo Corry, https://www.tau.ac.il/~corry/publications/articles.html . . .
|
html/ |
"Calculating the Limits of Poetic License: Fictional Narrative and the History of Mathematics", Configurations 15 (3) (2007), 195-226. (German translation: "Berechnungen zur Grenze der poetischen Freiheit: Fiktionales Erzählen und die Geschichte der Mathematik", in Andrea Albrecht et al (eds.) Zahlen, Zeichen und Figuren: Mathematische Inspirationen in Kunst und Literatur, Berlin: De Gruyter (2011), pp. 564-599.) |
See also tonight's previous post.
|
From Chapter 23, "Poetry," by Adam Parkes, in Writing in 1910–11, the English poet and critic T. E. Hulme claimed that the two major traditions in poetry, romanticism and classicism, were as different as a well and a bucket. According to the romantic party, Hulme explained, humankind is “intrinsically good, spoilt by circumstance”; that is, our nature is “a well, a reservoir full of possibilities.” For the classical party, however, human nature is “like a bucket”; it is “intrinsically limited, but disciplined by order and tradition to something fairly decent” (Hulme 1987: 117). But it was not only that romanticism and classicism were as dissimilar as a well and a bucket; their contents were different, too. To draw water from the well of romanticism was, in effect, to pour a “pot of treacle over the dinner table,” while the classical bucket was more likely to be full of little stones – or jewels, perhaps. Romanticism, in Hulme’s view, was the result of displaced religious fervor; it represented the return of religious instincts that the “perverted rhetoric of Rationalism” had suppressed, so that “concepts that are right and proper in their own sphere are spread over, and so mess up, falsify and blur the clear outlines of human experience” (Hulme 1987: 118). Classicism, by contrast, traded in dry goods – dry, hard goods, to be precise. Hulme left little doubt as to which side he was on. “It is essential to prove,” he argued, “that beauty may be in small, dry things. The great aim is accurate, precise and definite description. . . . I prophesy that a period of dry, hard, classical verse is coming” (Hulme 1987: 131–3). If by “dry, hard, classical verse” Hulme meant poems looking like the fragments of Sappho, he didn’t have to wait long to see his prophecy fulfilled.
The hard sand breaks,
Far off over the leagues of it, 228
playing on the wide shore, So wrote Hilda Doolittle in “Hermes of the Ways,” the first poem that she signed “H. D., Imagiste” at the behest of her fellow American expatriate Ezra Pound. From Pound’s perspective, the Imagist movement that he co-founded in 1912 with H. D. and the English poet Richard Aldington was finished well before the First World War began in August 1914; throughout this war-torn decade, however, Imagism continued to spawn the poetry of “small, dry things” whose coming Hulme had predicted a few years before. Indeed, modernist poets weren’t content merely to break down the extended heroic narratives – the “spilt religion,” as Hulme put it – of their treacly nineteenthcentury predecessors; they insisted on breaking down small things into ever-smaller particles and subparticles. This logic of disintegration is clearly at work in poems like “Hermes of the Ways,” where each line is metrically unique, creating a sense of perpetual freshness – an apotheosis of modernity, as it were. REFERENCE Hulme, T. E. (1987). Speculations: Essays on Humanism and the Philosophy of Art, ed. Herbert Read. London and New York: Routledge and Kegan Paul. First published 1924. |
Compare and contrast:
Jeremy Gray,
Plato's Ghost: The Modernist Transformation of Mathematics,
Princeton University Press, first edition Sept. 22, 2008 —
"Here, modernism is defined as an autonomous body of ideas,
having little or no outward reference, placing considerable emphasis
on formal aspects of the work and maintaining a complicated—
indeed, anxious— rather than a naïve relationship with the
day-to-day world, which is the de facto view of a coherent group
of people, such as a professional or discipline-based group
that has a high sense of the seriousness and value of what it is
trying to achieve. This brisk definition…."
(Quoted at the webpage Solomon's Cube.)
Loki Season 2, Episode 5, minus spoilers . . .
"… then he learns to control his time slipping.
It's not about where, when, or why. It's about who."
Midrash for fans of narrative . . .
Sometimes tattoos are more useful than Post-It notes.
From the University of Chicago Press…
The Nutshell:
Related Narrative:
………………………………………………………………………………………………………..
A function (in this case, a 1-to-1 correspondence) from finite geometry:
This correspondence between points and hyperplanes underlies
the symmetries discussed in the Cullinane diamond theorem.
Academics who prefer cartoon graveyards may consult …
Cohn, N. (2014). Narrative conjunction’s junction function:
A theoretical model of “additive” inference in visual narratives.
Proceedings of the Annual Meeting of the Cognitive Science
Society, 36. See https://escholarship.org/uc/item/2050s18m .
Related narrative —
This post was suggested by the Möbius Dick air date —
August 4, 2011 — in this journal.
Related narrative: Bosch by Snaith . See also . . .
Neil Welliver, great American painter, father of Titus Welliver
Titus Welliver Says "Losing His Way" Led Him Back to Painting
Nima Arkani-Hamed, as quoted by Peter Woit yesterday —
|
I think the subject has not been so exciting for many, many decades, and at the same time our ability to experimentally address and solidly settle some of these very big questions has never been more uncertain. I don’t think it’s a normal time, it’s an inflection point in the history of the development of our subject, and it requires urgency… The confluence of the technical expertise for doing so and the enthusiasm amongst the young people who are willing to do it exists now and I very much doubt it will exist in 10 or 15 years from now. If we are going to do it, we have to start thinking about doing it now. |
See as well an inflection-point-related post in this journal —
True Grid: "Rosetta Stone" as a Metaphor
in Mathematical Narratives .
From Wednesday, St. Bridget's Day, 2023 —
Poetic meditation from The New Yorker today —
"If the tendency of rhyme, like that of desire,
is to pull distant things together
and force their boundaries to blur,
then the countervailing force in this book,
the one that makes it go, is the impulse
toward narrative, toward making sense of
the passage of time."
"The literary attack on the concept of a remembered self
comes principally from three directions:
(1) the brokenness of memory,
(2) the difficulty of affirming that all memories pertain to
the same self; and
(3) the impossibility of pretending that a subject is an object.
All three of these attacks tend to dissolve the self, to expose it
as fictitious, artificial, quaintly contrived."
"Literary and Psychological Models of the Self,” pp. 19 – 40 in
Neisser, U., & Fivush, R. (Eds.) (1994). The Remembering Self:
Construction and Accuracy in the Self-Narrative (Emory Symposia
in Cognition). Cambridge: Cambridge University Press.
See also The Thing and I.
"He played with history and narrative techniques." — Obituary headline
|
* See his New York Times obituary, online today —
| Number | Space |
| Arithmetic | Geometry |
| Discrete | Continuous |
Related literature —
From a "Finite Fields in 1956" post —
The Nutshell:
Related Narrative:
"A good public narrative can, at the best of times,
transform an art theft into a lucky break for the gallery."
From a search in this journal for Goya —
Related quotations —
"So we beat on, boats against the current…." — F. Scott Fitzgerald
"There grows a tree in Paradise…." — Joan Baez
Related narrative — River of Death.
From "When Novelists Become Cubists," by Andre Furlani—
"The architectonics of a narrative," Davenport says,
"are emphasized and given a role to play in dramatic effect
when novelists become Cubists; that is, when they see
the possibilities of making a hieroglyph, a coherent symbol,
an ideogram of the total work. A symbol comes into being
when an artist sees that it is the only way to get all the meaning in."
* See "Starlight Like Intuition" by Delmore Schwartz.
The "Twelve" of the title may be regarded as cube edges.
C. S. Lewis on myth —
"The stories I am thinking of always have a very simple narrative shape—
a satisfactory and inevitable shape, like a good vase or a tulip."
The image and quote are from posts tagged Spectral Valhalla.
"With the Tablet of Ahkmenrah and the Cube of Rubik,
my power will know no bounds!"
— Kahmunrah in a novelization of Night at the Museum:
Battle of the Smithsonian , Barron's Educational Series
Scholium —
Abstracting from narrative to structure, and from structure
to pure number, the Tablet of Ahkmenrah represents the
number 9 and the Cube of Rubik represents the number 27.
Returning from pure abstract numbers to concrete representations,
9 yields the structures in Log24 posts tagged Triangle.graphics,
and 27 yields a Galois cube .
See also . . .
http://m759.net/wordpress/?s=Prism .
Further searching, on the wider Web, yields . . .
"Blair has multiple sclerosis, a condition Didion shared."
— Susan Burton, review of Mean Baby , NY Times 15 May 2022
Another recent narrative about Didion and MS —
|
March 3rd, 2022 by Emily Carmichael |
From the "Mathematics and Narrative" link in the previous post —
An image reposted here on March 12, 2022, the reported date of death
for Vera Diamantova —
Helen Mirren with plastic Gankyil .
|
"… Wade’s entire life is built around the squid attack. In the episode’s opening, we see that 34 years ago, young Wade was at a carnival in Hoboken, New Jersey, proselytizing as a Jehovah’s Witness when the squid emitted a psychic blast that killed three million people in the New York area. Just before the attack, a girl led him into a house of mirrors, feigning interest in hooking up with him in order to steal his clothes, leaving him naked and humiliated in the fairground attraction. But the cruel prank also saved his life, as mirrors can apparently repel the squid's psychic blast." |
Related literary remarks —
|
"It may have been by chance, and it may have had the side effect of being easy to read, but this way of putting a novel together offered a bridge between the miniaturist in Doerr and the seeker of world-spanning connections. He could focus on the details of every piece in the narrative, but there was pleasure, too, in placing them against each other. Sometimes he would lay out all these micro chapters on the floor so he could see them and discover the resonances between characters across space and time. 'That’s the real joy,' Doerr said, 'the visceral pleasure that comes from taking these stories, these lives, and intersecting them, braiding them.'" — "A version of this article appears in print on Sept. 20, 2021, Section C, Page 4 of the New York edition with the headline: Bringing His Readers To Higher Ground." |
The online New York Times today reporting a Jan. 29 death:
"Mr. Dylan asked Mr. Lay to back him on the title track
of his album “Highway 61 Revisited.” In addition to
playing drums, Mr. Lay played a toy whistle on the song’s
memorable opening."
— Richard Sandomir, Feb. 5, 2022, 2:06 p.m. ET
The above link yields a March 11, 2019, YouTube upload:
Some may prefer the theology of Hexagram 61.
“‘Oracle, why did you write
The Grasshopper Lies Heavy?
What are we supposed to learn?'”
— Philip K. Dick
“She began throwing the coins.“
Other remarks from the above
YouTube upload date — March 11, 2019 —
"Redgrave proceeded to focus on the end of Blue Nights ,
and Didion’s determination to maintain momentum after
the death of Quintana, when she and Redgrave mounted
their production of The Year of Magical Thinking . Here,
St John the Divine became a setting in the narrative of
Blue Nights yet again – this time, as Quintana’s final resting
place in St Ansgar’s Chapel within the cathedral."
The feast of St. Ansgar is Feb. 3. See that date this year.
Related song lyric from "Finian's Rainbow" —
Necessity,
That's the maximum that a minimum thing could be,
There's nothing lower than less unless it's Necessity.
Related material — Disparate Images :
Joan Didion, The White Album :
“We tell ourselves stories in order to live….
We interpret what we see, select the most workable
of multiple choices. We live entirely, especially if we
are writers, by the imposition of a narrative line upon
disparate images, by the ‘ideas’ with which we have
learned to freeze the shifting phantasmagoria which
is our actual experience.
Or at least we do for a while. I am talking here about
a time when I began to doubt the premises of all the
stories I had ever told myself, a common condition
but one I found troubling.”
Flashback:
Detail of Instagram story last night by marrific:
Quoted here on today's date — Joan Didion's birthday —
Joan Didion, The White Album :
“We tell ourselves stories in order to live….
We interpret what we see, select the most workable
of multiple choices. We live entirely, especially if we
are writers, by the imposition of a narrative line upon
disparate images, by the ‘ideas’ with which we have
learned to freeze the shifting phantasmagoria which
is our actual experience.Or at least we do for a while. I am talking here about
a time when I began to doubt the premises of all the
stories I had ever told myself, a common condition
but one I found troubling.”
Friday March 31, 2006
|
The above title is from Wallace Stevens.
Related meditations — This journal on March 9, 2021, and . . .
See as well recent posts in this journal
now tagged The Chinese Room Experiment.
For the source of the above Wallace Stevens phrase, see (for instance) . . .
The above weblog post on Stevens is dated November 17, 2010.
Posts in this weblog on that same date and its eve are now tagged . . .
Related Scholarly Remarks:
From the Wikipedia Manual of Style —
|
Writing About Fiction . . .
An in-universe perspective describes the narrative |
Scholium:
Related art:
“… What is your dream—your ideal? What is your News from Nowhere,
or, rather, What is the result of the little shake your hand has given to
the old pasteboard toy with a dozen bits of colored glass for contents?
And, most important of all, can you present it in a narrative or romance
which will enable me to pass an idle hour not disagreeably? How, for instance,
does it compare in this respect with other prophetic books on the shelf?”
— Hudson, W. H.. A Crystal Age (p. 2). Open Road Media. Kindle Edition.
See as well . . .
The lexicographic Golay code
contains, embedded within it,
the Miracle Octad Generator.
Epigraph from Google —
Related narratives — the recent film Fast Color * and
a not-so-recent** film . . .
* “Parents need to know that Fast Color is a sci-fi drama
about a family of women who have the ability to deconstruct
objects with their minds.”
** See the not-so-recent writer.
| “… the walkway between here and there would be colder than a witch’s belt buckle. Or a well-digger’s tit. Or whatever the saying was. Vera had been hanging by a thread for a week now, comatose, in and out of Cheyne-Stokes respiration, and this was exactly the sort of night the frail ones picked to go out on. Usually at 4 a.m. He checked his watch. Only 3:20, but that was close enough for government work.”
— King, Stephen (2013-09-24). |
Related narrative — November 13, 2014.
Reflection in the door of 794 Lexington Avenue,
New York City, November 2019 —
The object reflected —
To enlarge the image, click the above view of Lexington Ave. traffic.
Related narratives —
The life stories of “Germany’s oldest bookseller,” who reportedly died
around New Year’s 2021, and of her uncle, who had an art-book store
and gallery at 794 Lexington Avenue starting in 1923.
“In a sense, we would see that change arises from
the structure of the object.”
— Nima Arkani-Hamed, quoted in
“A Jewel at the Heart of Quantum Physics,”
by Natalie Wolchover, Quanta Magazine , Sept. 17, 2013.
For those who prefer less barbaric entertainment —
From a post of Tuesday, May 7, 2019 —
“Honored in the Breach:
Graham Bader on Absence as Memorial”
Artforum International , April 2012
| . . . .
“In the wake of a century marked by inconceivable atrocity, the use of emptiness as a commemorative trope has arguably become a standard tactic, a default style of public memory. The power of the voids at and around Ground Zero is generated by their origin in real historical circumstance rather than such purely commemorative intent: They are indices as well as icons of the losses they mark. Nowhere is the negotiation between these two possibilities–on the one hand, the co-optation of absence as tasteful mnemonic trope; on the other, absence’s disruptive potential as brute historical scar–more evident than in Berlin, a city whose history, as Andreas Huyssen has argued, can be seen as a ‘narrative of voids.’ Writing in 1997, Huyssen saw this tale culminating in Berlin’s post-wall development, defined equally by an obsessive covering-over of the city’s lacunae–above all in the elaborate commercial projects then proliferating in the miles-long stretch occupied until 1989 by the Berlin Wall–and a carefully orchestrated deployment of absence as memorial device, particularly in the ‘voids’ integrated by architect Daniel Libeskind into his addition to the Berlin Museum, now known as the Jewish Museum Berlin.” |
See also Breach in this journal, as well as Void.
* Literary background — The word “Purloined” in this journal.
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