The groups generated as above are affine groups in finite geometries.
What other results are known from this area of research,
which might be called "groups generated by permutations of
congruent subarrays"? (Search phrase: "congruent subarrays")
Click image to enlarge.
"As McCarthy peers through the screen, or veil,
of technological modernity to reveal the underlying
symbolic structures of human experience,
The Making of Incarnation weaves a set of stories
one inside the other, rings within rings, a perpetual
motion machine." — Amazon.com description
of a novel published on All Souls' Day (Dia de los
Muertos), 2021.
The McCarthy novel is mentioned in The New York Times today —
For a simpler perpetual motion machine, see T. S. Eliot's "Chinese jar."
Return of the well-dressed man with a beard —
See also this journal on the above April 27, 2016,
art date: "Local and Global."
On "Indiana Jones and the Dial of Destiny" —
"… second unit began shooting the tuk-tuk chase in Morocco.
'It’s scripted as Tangier in the movie, but it was actually shot in Fez'…."
— https://www.lucasfilm.com/news/indiana-jones-duncan-broadfoot/
See as well, from 12 AM ET Sept. 10, "Plan 9 from Death Valley."
For other remarks about Archimedes and Death, see Hidden Structure.
|
Monday, May 8, 2017
New Pinterest Board
|
The face at lower left above is that of an early Design edgelord.
A product of that edgelord's school —
See a design by Prince-Ramus in today's New York Times —
Remarks quoted here on the above San Diego date —
A related void —
|
From "Knight to Move," by Fritz Leiber "… You were talking about basic games. Well, the chessboard is clearly a spider’s web with crisscross strands—in Go you even put the pieces on the intersections. The object of the game is to hunt down and immobilize the enemy King, just as a spider paralyzes its victim and sometimes wraps it in its silk. But here’s the clincher: the Knight, the piece most characteristic of chess, has exactly eight crooked moves when it stands in the clear—the number of a spider’s crooked legs, and eyes too! This suggests that all chess-playing planets are Spider-infiltrated from way back. It also suggests that all the chessplayers here for the tournament are Spiders—your shock battalion to take over 61 Cygni 5.” Colonel von Hohenwald sighed. “I was afraid you’d catch on, dear,” he said softly. “Now you’ve signed your abduction warrant at the very least. You may still be able to warn your HQ, but before they can come to your aid, this planet will be in our hands.” He frowned. “But why did you spill this to me, Erica? If you had played dumb—” “I spilled it to you,” she said, “because I wanted you to know that your plot’s been blown––and that my side has already taken countermeasures! We’ve made a crooked Knight’s move too. Has the significance of track games never occurred to you, Colonel? The one-dimensional track, sinuously turning, obviously symbolizes the snake. The pieces are the little bugs and animals the snake has swallowed. As for the dice, well, one of the throws is called Snake Eyes. So be assured that all the k’ta’hra players here are Snakes, ready to counter any Spider grab at 61 Cygni 5.” The Colonel’s mouth almost gaped. |
"Having seen Labyrinth at St. Mark's-in-the-Valley Episcopal Church,
it's time to have a rest at this restaurant."
— https://restaurantguru.com/Bar-Le-Cote-Los-Olivos-California
"It's wine country , after all." — "All the Old Knives"
"Infinity Cube" … hinged plaything, for sale —
"Eightfold Cube" … un hinged concept, not for sale—
See as well yesterday's Trickster Fuge ,
and a 1906 discussion of the eightfold cube:
|
Margaret Atwood on Lewis Hyde's "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159) What is "the next world"? It might be the Underworld…. 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." (254) 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. |
"Drop me a line" — Request attributed to Emma Stone
"If it’s possible to be two things at once,
I was both pathologically insecure and
intoxicated by the power that my newly
discovered desirability to men seemed
to have conferred on me."
Possible ‽
Ask Mark Wahlberg.
* See as well the September 1982 Kate Bush album.
Addendum of 10:50 AM June 11 —
My own concerns in September 1982 were
rather different —
A review by Robert Ghrist of a paper on aperiodic
Wang tilings suggests a search in this journal for Wang tiles.
A resulting image seems appropriate for today's posts,
which include a reference to a renowned Prada-wearer.
"She's like the wind." — Song lyric. See as well Hexagram 57.
"Another story" —
See also Sontag's own account of the Mann meeting.
Related material —
It would seem that Moser is deeply confused about two different
meetings of Sontag with Mann — discussing Doctor Faustus
in 1947, and, later, as a U. of Chicago student, discussing
The Magic Mountain with Mann in 1949 on the Feast of the
Holy Innocents — coincidentally, also the date of her dies natalis
(in the Catholic sense) in 2004.
Related dramatic dialogue from FUBAR —
Hero — I guess I'll take the pill, and get it over with. (Dramatic music playing.)
Villain — This will be fun. (Music intensifies.) Cheers … Nothing's happening.
Hero — Come to think of it, I might have taken the antidote.
Read more at: https://tvshowtranscripts.ourboard.org/… .
Related synchronology check —
"He stopped at a bench where people could catch buses
from Somewhere to Elsewhere." — John Crowley, 1981
Hat tip to Stephanie Dick, now at Simon Fraser U.
"When the men on the chessboard
get up and tell you where to go . . . ."
Don't take the Brown acid!
Abstract: Boolean functions on a triangular grid.
Note: It seems that the above rearrangement of a square array
of hyperplanes to a triangular array of hyperplanes, which was
rather arbitrarily constructed to have nice symmetries, will
answer a question posed here on Dec. 15, 2015.
The reference to "Magic: The Gathering" in the previous post
suggests a review of "gathering" tales that I personally prefer —
From the American Mathematical Society today —
Robert Earl Tubbs (1954-2023)
May 15, 2023
"Tubbs, associate professor of mathematics at
the University of Colorado Boulder, died April 11, 2023,
at the age of 69. He received his PhD in 1981 from
Penn State University under the supervision of
W. Dale Brownawell. His research interests included
number theory, especially transcendental number theory,
the intellectual history of mathematical ideas and mathematics,
and the humanities."
This journal on the dies natalis of Tubbs had the third of three
posts tagged "Space and Form." Those posts dealt with European
cultural history related to Tubbs's interests. The "Space and Form"
posts, along with today's previous Log24 post, suggest a review of
the Nov. 10, 2021 post titled European Culture. An image from that post —
Those who share Cassirer's enthusiasm for myth may regard the
above Josefine Lyche version of my work as a sort of "secret writing,"
to quote a phrase of Cassirer's I find very distasteful. But there is nothing
secret about it, although there is some resemblance to written characters.
This post's title was suggested by a Salinger quote in the European Culture post.
Update on the next day, May 17 —
Further reading in Cassirer's Mythical Thought indicates that in the
passages above, on Schelling, he may be presenting a parody of
Schelling when he writes "a poem hidden behind a wonderful
secret writing." Later, on page 10, he asks, sensibly,
"… is there, perhaps, a means of retaining the question
put forward by Schelling's Philosophie der Mythologie
but of transferring it from the sphere of a philosophy of
the absolute to that of critical philosophy?"
There has reportedly been "an upsurge of interest" in Cassirer —
"The history of the length of movies takes place in two dimensions—
on the axis of the ordinary and the axis of the extraordinary, or,
of the rule and the exception."
— Richard Brody, The New Yorker , April 24, "In Praise of the Long Movie."
The Ordinary —
The Extraordinary —
A version of "News of the World" I prefer —
For those who prefer facts to Harvard bullshit —
From the previous post, "The Large Language Model,"
a passage from Wikipedia —
"… sometimes large models undergo a 'discontinuous phase shift'
where the model suddenly acquires substantial abilities not seen
in smaller models. These are known as 'emergent abilities,' and
have been the subject of substantial study." — Wikipedia
Compare and contrast
this with the change undergone by a "small space model,"
that of the finite affine 4-space A with 16 points (a Galois tesseract ),
when it is augmented by an eight-point "octad." The 30 eight-point
hyperplanes of A then have a natural extension within the new
24-point set to 759 eight-point octads, and the 322,560 affine
automorphisms of the space expand to the 244,823,040 Mathieu
automorphisms of the 759-octad set — a (5, 8, 24) Steiner system.
For a visual analogue of the enlarged 24-point space and some remarks
on analogy by Simone Weil's brother, a mathematician, see this journal
on September 8 and 9, 2022.
"… sometimes large models undergo a 'discontinuous phase shift'
where the model suddenly acquires substantial abilities not seen
in smaller models. These are known as 'emergent abilities,' and
have been the subject of substantial study." — Wikipedia
See also the first five episodes of "Mrs. Davis."
Blocking Groups —
A Harvard phrase for a process analogous
to that of the Hogwarts Sorting Hat.
Hat tip to IG's @marrific:
New York:
“The experience of being hailed by ‘inanimate’ matter—
by objects beautiful or odd, by a refrain, by a piece of cake,
or a buzz from your phone—is widespread.”
— Jane Bennett, quoted in The New Yorker on Feb. 28, 2023
Los Angeles (click to enlarge):
See earlier instances of "working backwards" in this journal.
Alan Rickman as Metatron in "Dogma" —
Alan Rickman as Severus Snape at Hogwarts —
Page three hundred and ninety-four —
See also today's previous post.
From my RSS feeds last night —
This journal on Wednesday, December 28, 2022 —
For those who prefer a "liturgical, ecstatic style" —
The title refers to a post discussing a date,
that of last year's Feast of St. Thomas Becket.
Related material —
https://www.nytimes.com/2023/01/09/movies/ruggero-deodato-dead.html .
From a link target in this journal on April 4, 2004 —
"Puzzle begun I write in the day's space . . . ."
Today's link targets —
Valéry and Rilke, Stevens and Borges . . . and Zeno.
The title is from . . .
https://booksonthewall.com/blog/samuel-beckett-quote-fail-better/ .
This post was suggested by yesterday's Feast of St. Thomas Becket —
A Beckett-related flashback linked to here yesterday —
"To get inside the systems of this work,
whether LeWitt's or Judd's or Morris's,
is precisely to enter
a world without a center,
a world of substitutions and transpositions
nowhere legitimated by the revelations
of a transcendental subject. This is the strength
of this work, its seriousness, and its claim to modernity."
"The novelist Cormac McCarthy has been a fixture around
the Santa Fe Institute since its embryonic stages in the
early 1980s. Cormac received a MacArthur Award in 1981
and met one of the members of the board of the MacArthur
Foundation, Murray Gell-Mann, who had won the Nobel Prize
in physics in 1969. Cormac and Murray discovered that they
shared a keen interest in just about everything under the sun
and became fast friends. When Murray helped to found the
Santa Fe Institute in 1984, he brought Cormac along, knowing
that everyone would benefit from this cross-disciplinary
collaboration." — https://www.santafe.edu/news-center/news/
cormac-and-sfi-abiding-friendship
Joy Williams, review of two recent Cormac McCarthy novels —
"McCarthy has pocketed his own liturgical, ecstatic style
as one would a coin, a ring, a key, in the service of a more
demanding and heartless inquiry through mathematics and
physics into the immateriality, the indeterminacy, of reality."
A Demanding and Heartless Coin, Ring, and Key:
COIN
RING
"We can define sums and products so that the G-images of D generate
an ideal (1024 patterns characterized by all horizontal or vertical "cuts"
being uninterrupted) of a ring of 4096 symmetric patterns. There is an
infinite family of such 'diamond' rings, isomorphic to rings of matrices
over GF(4)."
KEY
"It must be remarked that these 8 heptads are the key to an elegant proof…."
— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.
For those who prefer a "liturgical, ecstatic style" —
"If the window is this matrix of ambi- or multivalence,
and the bars of the windows-the grid-are what help us
to see, to focus on, this matrix, they are themselves
the symbol of the symbolist work of art. They function as
the multilevel representation through which the work of art
can allude, and even reconstitute, the forms of Being."
— Page 59, Rosalind Krauss, "Grids," MIT Press,
October , Vol. 9 (Summer, 1979), pp. 50-64
Related material —
Click the above image for a related Log24 post of 15 years ago today.
A related literary remark —
"Imagine Raiders of the Lost Ark set in 20th-century London, and then
imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture…."
— Doug Thorpe in an Amazon.com book review, not of Dark Materials.
"The book I came back to
George Eliot’s Middlemarch. I couldn’t cope with it
as a student; it wasn’t until I was grown up, and married,
and a parent, and trying to teach it myself, that I realised
its majestic scope and depth." — Philip Pullman in
The Guardian, Fri 23 Dec 2022 05.00 EST
Another instance of scope and depth —
"The Amber Spyglass" Log24 post of Wednesday.
See also other references here to Middlemarch.
"Borrow ends at 10:31 AM" —
A different 10|31 —
. . . as well as starring in Alpha Dog and in . . .
The above obituary reports a death that happened on July 23.
Also on that date . . . Myth Space and Date Note.
Or: The Sontag Puzzlement
Wikipedia on "Heavenly Creatures" —
"Juliet introduces Pauline to the idea of 'the Fourth World',
a Heaven without Christians where music and art are
celebrated. Juliet believes she will go there when she dies.
Certain actors and musicians have the status of saints in
this afterlife, such as singer Mario Lanza, with whom
both girls are obsessed."
Related material — Sontag + Camp .
|
OPINION DYNAMICS ON DISCOURSE SHEAVES By JAKOB HANSEN AND ROBERT GHRIST arXiv:2005.12798 (math) [Submitted on 26 May 2020] Funding: This work was funded by the Office of the Assistant Secretary of Defense Research & Engineering through a Vannevar Bush Faculty Fellowship, ONR N00014-16-1-2010. HANSEN — Department of Mathematics, University of Pennsylvania, Philadelphia, PA (jhansen@math.upenn.edu) GHRIST — Department of Mathematics and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA (ghrist@math.upenn.edu) |
See as well this journal on the above date (26 May 2020) —
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" . . .
Some may prefer their own, less collective, manifestations.
Magic Mikes Continues:
"I get no kick from champagne…." — Cole Porter
See too another item with the BRC "Waking Dreams" date —
From the new URL mythspace.org, which forwards to . . .
http://m759.net/wordpress/?tag=mythspace —
|
From Middlemarch (1871-2), by George Eliot, Ch. III — "Dorothea by this time had looked deep into the ungauged reservoir of Mr. Casaubon's mind, seeing reflected there in vague labyrinthine extension every quality she herself brought; had opened much of her own experience to him, and had understood from him the scope of his great work, also of attractively labyrinthine extent. For he had been as instructive as Milton's 'affable archangel;' and with something of the archangelic manner he told her how he had undertaken to show (what indeed had been attempted before, but not with that thoroughness, justice of comparison, and effectiveness of arrangement at which Mr. Casaubon aimed) that all the mythical systems or erratic mythical fragments in the world were corruptions of a tradition originally revealed. Having once mastered the true position and taken a firm footing there, the vast field of mythical constructions became intelligible, nay, luminous with the reflected light of correspondences. But to gather in this great harvest of truth was no light or speedy work." |
See also the term correspondence in this journal.
Oxford University Press Blog
|
Note the above Oxford University Press date. Also on that date —
Tuesday September 29, 2009
|
"Is a puzzlement." — Oscar Hammerstein II
“Not games. Puzzles. Big difference. That’s a whole other matter.
All art — symphonies, architecture, novels — it’s all puzzles.
The fitting together of notes, the fitting together of words have
by their very nature a puzzle aspect. It’s the creation of form
out of chaos. And I believe in form.”
— Stephen Sondheim, in Stephen Schiff,
“Deconstructing Sondheim,”
The New Yorker, issue of March 8, 1993, p. 76
Cartoon version of George Eliot, author of Middlemarch ,
and Ada Lovelace, programming pioneer —
See as well an earlier vision of a data cube for mythologies
by Claude Lévi-Strauss —
Tonight is Replacement Eve —
"The metaphor for metamorphosis no keys unlock" — Cullinane, 1986
Related remarks —
From a Log24 search for "Notation+Levi-Strauss" —
"There is such a thing as a four-set."
— Motto adapted from a 1962 young-adult novel.
|
Tuesday, November 3, 2009 Filed under: General,Geometry — Tags: Glasperlenspiel, Solomon Marcus — m759 @ 10:10 PM Book review by Jadran Mimica in Oceania, Vol. 74, 2003: "In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopoeic dynamics [fx(a) : fy(b) :: fx(b) : fa-1(y)] that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object." So there. At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.) I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth: "…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created." |
The above title is from Northrop Frye —
"Is it possible* that understanding the nature of clarity and order
can cast suspicion on the very ideas of clarity and order?"
— Douglas Sadao Aoki, University of Alberta, "The Thing Never
Speaks for Itself: Lacan and the Pedagogical Politics of Clarity,"
Harvard Educational Review , Vol. 70, No. 3, Fall 2000,
Copyright © by President and Fellows of Harvard College.
Related scholarly citation by Aoki —
The cited source:
* For the diamond as a symbol of possibility , see modal diamond box .
In memory of an editor/author who reportedly died on September 12 . . .
Vide an anthology he edited that was published on November 1, 2013,
and two Log24 posts from that date —
See the title phrase in this journal.
See also posts from last August tagged Storyville.
See Josh Lederman's AP story on this year's
colorful White House Halloween decorations.
Orange and black are also the Princeton colors.
See as well The Crosswicks Curse.
* "Story space" is a phrase from Log24 on September 12.
Click the image below for "Story Theory and the Number of the Beast"
(the latter, a Heinlein novel).
See also "Story Space."
In today's online New York Times , Kathryn Harrison reviews a new novel:
MATRIX
By Lauren Groff
From the online New York Times Book Review on May 24, 2018 —
From this journal on May 24, 2018 —
Further remarks by Lauren Groff on May 24, 2018 —
"Something invisible and pernicious seems to be preventing
even good literary men from either reaching for books with
women’s names on the spines, or from summoning women’s
books to mind when asked to list their influences. I wonder
what such a thing could possibly be."
Quentin Tarantino?
"It seems no coincidence that all of these titles
are written by women, for a primary angle of
Gunpowder Milkshake is one that tries its best
to promote 'feminism'… in a Quentin Tarantino
sort of way."
Or Lévi-Strauss?
See Log24 posts on The Matrix of Lévi-Strauss.
A phrase from the previous post : "modern society's mythical figures."
A mythical figure from Claude Lévi-Strauss —
The above image is from a study of Lévi-Strauss's "Canonical Formula" …
See a Log24 search for Beadgame Space.
This post might be regarded as a sort of “checked cell”
for the above concepts listed as tags . . .
Related material from a Log24 search for Structuralism —
The following passage is from Amanda Gefter’s Trespassing
on Einstein’s Lawn (Bantam Books, 2014).
| “You know the story of Plato’s cave?” my father asked. “All the prisoners are chained up in the cave and they can’t see the real world outside, only the shadows on the wall? That’s supposed to be a negative thing, like they’ll never know reality. But the truth is, you have to be stuck inside a limited reference frame for there to be any reality at all! If you weren’t chained to your light cone, you’d see nothing. The H-state.”
I nodded. “You’d have no information. You need the broken symmetry, the shadow, to have information and information gives rise to the world. It from bit.” I couldn’t help but grin with excitement. The message was clear: having a finite frame of reference creates the illusion of a world, but even the reference frame itself is an illusion. Observers create reality, but observers aren’t real. There is nothing ontologically distinct about an observer, because you can always find a frame in which that observer disappears: the frame of the frame itself, the boundary of the boundary. “If physicists discover an invariant someday, the game will be up,” my father mused. “That would rule out the hypothesis that the universe is really nothing.” That was true. But so far, at least, every last invariant had gone the way of space and time, rendered relative and observer-dependent. Spacetime, gravity, electromagnetism, the nuclear forces, mass, energy, momentum, angular momentum, charge, dimensions, particles, fields, the vacuum, strings, the universe, the multiverse, the speed of light— one by one they had been downgraded to illusion. As the surface appearance of reality fell away, only one thing remained. Nothing. |
My path to Gefter’s father’s musing led from a quotation attributed,
probably falsely, to John Archibald Wheeler on page 52 of Octavio
Paz’s Claude Lévi-Strauss: An Introduction (Cornell, 1970) —
“There is a point at which
‘something is nothing and nothing is something.’ “
The quote may actually be by AP writer John Barbour reporting
on a 1967 American Physical Society talk by Wheeler, “The End
of Time.”
Gefter mentions Wheeler 369 times:
See as well Introduction to Quantum Woo.
For an account by R. T. Curtis of how he discovered the Miracle Octad Generator,
see slides by Curtis, “Graphs and Groups,” from his talk on July 5, 2018, at the
Pilsen conference on algebraic graph theory, “Symmetry vs. Regularity: The first
50 years since Weisfeiler-Leman stabilization” (WL2018).
See also “Notes to Robert Curtis’s presentation at WL2018,” by R. T. Curtis.
Meanwhile, here on July 5, 2018 —
| Simultaneous perspective does not look upon language as a path because it is not the search for meaning that orients it. Poetry does not attempt to discover what there is at the end of the road; it conceives of the text as a series of transparent strata within which the various parts—the different verbal and semantic currents—produce momentary configurations as they intertwine or break apart, as they reflect each other or efface each other. Poetry contemplates itself, fuses with itself, and obliterates itself in the crystallizations of language. Apparitions, metamorphoses, volatilizations, precipitations of presences. These configurations are crystallized time: although they are perpetually in motion, they always point to the same hour—the hour of change. Each one of them contains all the others, each one is inside the others: change is only the oft-repeated and ever-different metaphor of identity.
— Paz, Octavio. The Monkey Grammarian |
The 2018 Log24 post containing the above Paz quote goes on to quote
remarks by Lévi-Strauss. Paz’s phrase “series of transparent strata”
suggests a review of other remarks by Lévi-Strauss in the 2016 post
“Key to All Mythologies.“
For the title, see Zero: Both Real and Imaginary (a Log24 search).
The title was suggested by the previous post, by Zorro Ranch,
by the classic 1967 film The Producers , and by . . .
Related material —
Vanity Fair on Sept. 8, 2017, celebrated the young actress
who played Beverly Marsh in the 2017 film version of
Stephen King's IT . See a post from her 12th birthday —
"Winter's Game" — that touches upon Maori themes.
More generally, see Bester + Deceivers in this journal.
And for the Church of Synchronology . . .
See posts related to the above Vanity Fair date.
(From his “Structure and Form: Reflections on a Work by Vladimir Propp.”
Translated from a 1960 work in French. It appeared in English as
Chapter VIII of Structural Anthropology, Volume 2 (U. of Chicago Press, 1976).
Chapter VIII was originally published in Cahiers de l’Institut de Science
Économique Appliquée , No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).)
The structure of the matrix of Lévi-Strauss —
Illustration from Diamond Theory , by Steven H. Cullinane (1976).
The relevant field of mathematics is not Boolean algebra, but rather
Galois geometry.
Wikipedia on film producer Lorenzo di Bonaventura
(Harvard AB (1980) in Intellectual History*) —
“His tenure at Warner Bros. included discovering and
shepherding The Matrix into production, and the
purchase of the rights to the Harry Potter books by
J. K. Rowling.”
From the previous post —
“But he enters into the central myth of
this book at another, higher level as well;
for he is an artist, a potter . . . .“
— Wendy Doniger O’Flaherty on
Claude Lévi-Strauss, author of
The Jealous Potter
* See as well “What is Intellectual History?” and
Magic for Liars .
Four Quartets
. . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.
A Permanent Order of Wondertale Elements
| In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both “in time” (it consists of a succession of events) and “beyond” (its value is permanent). With regard to Propp’s theories my analysis offers another advantage: I can reconcile much better than Propp himself his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108). If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns). |
… Or by congruent quarter-sections.
Some context for what Heidegger called
das Spiegel-Spiel des Gevierts
From Helen Lane's translation of El Mono Gramático ,
a book by Nobel winner Octavio Paz first published
in Barcelona by Seix Barral in 1974 —
|
Simultaneous perspective does not look upon language as a path because it is not the search for meaning that orients it. Poetry does not attempt to discover what there is at the end of the road; it conceives of the text as a series of transparent strata within which the various parts—the different verbal and semantic currents—produce momentary configurations as they intertwine or break apart, as they reflect each other or efface each other. Poetry contemplates itself, fuses with itself, and obliterates itself in the crystallizations of language. Apparitions, metamorphoses, volatilizations, precipitations of presences. These configurations are crystallized time: although they are perpetually in motion, they always point to the same hour—the hour of change. Each one of them contains all the others, each one is inside the others: change is only the oft-repeated and ever-different metaphor of identity.
— Paz, Octavio. The Monkey Grammarian |
A related 1960 meditation from Claude Lévi-Strauss taken from a
Log24 post of St. Andrew's Day 2017, "The Matrix for Quantum Mystics":
"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss
I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets
(from The Matrix Meets the Grid) —
.
The Hamilton watch from "Interstellar" (2014) —
On the above date — Nov. 17, 2016 —
* See posts tagged Broomsday 2014.
Scholia on the title — See Quantum + Mystic in this journal.
"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss, 1976
I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets (from
The Matrix Meets the Grid) —
.
From a Log24 post of June 26-27, 2017:
A work of Eddington cited in 1974 by von Franz —
See also Dirac and Geometry and Kummer in this journal.
Ron Shaw on Eddington's triads "associated in conjugate pairs" —
For more about hyperbolic and isotropic lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.
For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.
David Brooks in The New York Times today —
"We once had a unifying national story, celebrated each Thanksgiving.
It was an Exodus story. Americans are the people who escaped oppression,
crossed a wilderness and are building a promised land. The Puritans brought
this story with them. Each wave of immigrants saw themselves in this story.
The civil rights movement embraced this story.
But we have to admit that many today do not resonate with this story. . . .
Today, we have no common national narrative, no shared way
of interpreting the flow of events. Without a common story,
we don’t know what our national purpose is. We have no
common set of goals or ideals.
We need a new national narrative."
From a post of August 15, 2010 —
For some background, see Java Jive and Today's Theology.
Related readings —
From 1928:
From the previous post:
"Thus, instead of Propp's chronological scheme,
in which the order of succession of events
is a feature of the structure . . .
another scheme should be adopted, which would present
a structural model defined as the group of transformations
of a small number of elements. This scheme would appear
as a matrix . . . ."
— Claude Lévi-Strauss, 1960
| Claude Lévi-Strauss
From his “Structure and Form: To maintain. as I have done. that the permutability of contents is not arbitrary amounts to saying that, if the analysis is carried to a sufficiently deep level, behind diversity we will discover constancy. And, of course. the avowed constancy of form must not hide from us that functions are also permutable. The structure of the folktale as it is illustrated by Propp presents a chronological succession of qualitatively distinct functions. each constituting an independent genre. One can wonder whether—as with dramatis personae and their attributes— Propp does not stop too soon, seeking the form too close to the level of empirical observation. Among the thirty-one functions that he distinguishes, several are reducible to the same function reappearing at different moments of the narrative but after undergoing one or a number of transformations . I have already suggested that this could be true of the false hero (a transformation of the villain), of assigning a difficult task (a transformation of the test), etc. (see p. 181 above), and that in this case the two parties constituting the fundamental tale would themselves be transformations of each other. Nothing prevents pushing this reduction even further and analyzing each separate partie into a small number of recurrent functions, so that several of Propp’s functions would constitute groups of transformations of one and the same function. We could treat the “violation” as the reverse of the “prohibition” and the latter as a negative transformation of the “injunction.” The “departure” of the hero and his “return” would appear as the negative and positive expressions of the same disjunctive function. The “quest” of the hero (hero pursues someone or something) would become the opposite of “pursuit” (hero is pursued by something or someone), etc.
In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both “in time” (it consists of a succession of events) and “beyond” (its value is permanent). With regard to Propp’s theories my analysis offers another advantage: I can reconcile much better than Propp himself his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108) If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns). These critical remarks are certainly valid for the method used by Propp and for his conclusions. However. it cannot be stressed enough that Propp envisioned them and in several places formulated with perfect clarity the solutions I have just suggested. Let us take up again from this viewpoint the two essential themes of our discussion: constancy of the content (in spite of its permutability) and permutability of functions (in spite of their constancy). * Translated from a 1960 work in French. It appeared in English as Chapter VIII |
See also “Lévi-Strauss” + Formula in this journal.
Some background related to the previous post —
The title refers to today's earlier post "The 35-Year Wait."
A check of my activities 35 years ago this fall, in the autumn
of 1982, yields a formula I prefer to the nonsensical, but famous,
"canonical formula" of Claude Lévi-Strauss.
My "inscape" formula, from a note of Sept. 22, 1982 —
S = f ( f ( X ) ) .
Some mathematics from last year related to the 1982 formula —
See also Inscape in this journal and posts tagged Dirac and Geometry.
Continued from the previous post and from posts
now tagged Dueling Formulas —
The four-diamond formula of Jung and
the four-dot "as" of Claude Lévi-Strauss:
Simplified versions of the diamonds and the dots —
::
I prefer Jung. For those who prefer Lévi-Strauss —
First edition, Cornell University Press, 1970.
A related tale — "A Meaning, Like."
A book cover from Amazon.com —
See also this journal on the above date, September 27, 2016 —
Chomsky and Levi-Strauss in China,
Or: Philosophy for Jews.
Some other remarks related to the figure on the book cover —
Field Theology and Galois Window.
* See Synchronology in this journal.
The title is from Hume:
"And were all my perceptions removed by death,
and could I neither think, nor feel, nor see, nor love,
nor hate, after the dissolution of my body, I should
be entirely annihilated, nor do I conceive what is
further requisite to make me a perfect nonentity."
— Book I, Part IV, Section vi of
A Treatise of Human Nature
"What is further requisite" — Perhaps …
This four-dot notation ("as") is from a search for Lévi-Strauss in this journal.
See also "That I Am."
The above cycle may have influenced the design
of Carl Jung's symbol of the self —
Related art by
Steven H. Cullinane
See also Levi-Strauss Formula in this journal.
According to Octavio Paz and Claude Lévi-Strauss
"Poetry…. conceives of the text as a series of transparent strata
within which the various parts—the different verbal and semantic
currents— produce momentary configurations as they intertwine
or break apart, as they reflect each other or efface each other.
Poetry contemplates itself, fuses with itself, and obliterates itself
in the crystallizations of language. Apparitions, metamorphoses,
volatilizations, precipitations of presences. These configurations
are crystallized time…."
— Octavio Paz in The Monkey Grammarian (written in 1970)
"Strata" also seem to underlie the Lévi-Strauss "canonic formula" of myth
in its original 1955 context, described as that of permutation groups —
I do not recommend trying to make sense of the above "formula."
Related material —
Or: Philosophy for Jews
From a New Yorker weblog post dated Dec. 6, 2012 —
"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."
Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).
Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…
The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)
The matrix at left below represents the feminine yin principle
and the diamond at right represents the masculine yang .
From a post of Sept. 22,
"Binary Opposition Illustrated" —
A symbol of the unity of yin and yang —
Related material:
A much more sophisticated approach to the "deep structure" of the
Meno diagram —
As the Key to All Mythologies
For the theorem of the title, see "Diamond Theorem" in this journal.
"These were heavy impressions to struggle against,
and brought that melancholy embitterment which
is the consequence of all excessive claim: even his
religious faith wavered with his wavering trust in his
own authorship, and the consolations of the Christian
hope in immortality seemed to lean on the immortality
of the still unwritten Key to all Mythologies."
— Middlemarch , by George Eliot, Ch. XXIX
Related material from Sunday's print New York Times —
Sunday's Log24 sermon —
See also the Lévi-Strauss "Key to all Mythologies" in this journal,
as well as the previous post.
"Lévi-Strauss is an infatuated aesthetician."
— Boris Wiseman, Lévi-Strauss, Anthropology and Aesthetics ,
Cambridge University Press, 2007, p. 27
Last night's link from the Piper Laurie image leads to …
Related theoretical material — See Hudson + Tetrahedra.
The Lévi-Strauss “canonic formula” of myth in its original 1955 context,
described as that of permutation groups —
Related material in this journal —
Dueling Formulas and Symmetry.
According to McLuhan
Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—
"The American mind is not even close to being amenable
to the ideogram principle as yet. The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D. AB:CD.
It can see AB relations. But relations in four terms are still
verboten. This amounts to deep occultation of nearly all
human thought for the U.S.A.
I am trying to devise a way of stating this difficulty as it exists.
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."
For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)
A relation in four terms —
A : B :: C : D as Model : Crutch :: Metaphor : Ornament —
See also Dueling Formulas and Symmetry.
From a check tonight of The New York Review of Books —
These NYRB stories from May 15 and May 13 suggest a
review of images on Ratner's Star and on the Eye of God.
Above image reposted from Jan. 10, 2014
|
I. The structures in the Diamond Puzzle…
Click on image for Jungian background. II: The structure on a recent cover of Semiotica…
|
Above images reposted from May 5, 2016
Related material: The previous post, Dueling Formulas.
Note the echo of Jung's formula in the diamond theorem.
An attempt by Lévi-Strauss to defend his formula —
"… reducing the life of the mind to an abstract game . . . ." —
For a fictional version of such a game, see Das Glasperlenspiel .
The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.
This suggests a review of another noted four-set.
The above image is from a study of Lévi-Strauss's "Canonical Formula" …
Midrash —
[Above photo of Lévi-Strauss and formula added June 6, 2016.]
Excerpt from a post of November 4, 2009 —
|
I. The structures in the Diamond Puzzle…
Click on image for Jungian background. II: The structure on a recent cover of Semiotica…
|
For some related material, see a search
for Solomon Marcus in this journal.
A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —
The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .
Some may view the above web page as illustrating the
Glasperlenspiel passage quoted here in Summa Mythologica —
“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”
A less poetic meditation on the above web page* —
"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."
Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955: "…three different readings
become possible: left to right, top to bottom, front
to back."
* For the underlying mathematics, see a June 21, 1983, research note.
Consider the trichotomy of the title as applied to the paragraph
by Adam Gopnik in the previous post (The Raw, the Cooked,
and the Spoiled).
The following quotation seems to place Gopnik's words
among the half -baked.
"L'axe qui relie le cru et le cuit est caractéristique du passage
à la culture; celui qui relie le cru et le pourri, du retour à la nature,
puisque la cuisson accomplit la transformation culturelle du cru
comme la putréfaction en achève la transformation naturelle."
— Claude Lévi-Strauss, Paroles données, p.54, Plon, 1984,
as quoted in a weblog.
See also Lévi-Strauss's bizarre triangle culinaire (French Wikipedia) —
The source of this structuralist nonsense —
Lévi-Strauss, Claude. 1969. “Le triangle culinaire.”
L’Arc no. 26: 19-29.
Background— George Steiner in this journal
and elsewhere—
"An intensity of outward attention —
interest, curiosity, healthy obsession —
was Steiner’s version of God’s grace."
— Lee Siegel in The New York Times ,
March 12, 2009
(See also Aesthetics of Matter in this journal on that date.)
Steiner in 1969 defined man as "a language animal."
Here is Steiner in 1974 on another definition—
Related material—
Also related — Kantor in 1981 on "exquisite finite geometries," and The Galois Tesseract.
In memory of kaleidoscope enthusiast Cozy Baker, who died at 86, according to Saturday's Washington Post , on October 19th.
This journal on that date — Savage Logic and Savage Logic continued.
See this journal on All Saints' Day 2006 for some background to those posts—
“Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of ‘the odds and ends left over from psychological or historical process.’
These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the ‘residue of events… fossil remains of the history of an individual or a society.’) Such images are inevitably embodied in larger structures– in myths, ceremonies, folk taxonomies, and so on– for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that ‘it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,’ Levi-Strauss generalizes this permutational view of thinking to savage thought in general.”
– Clifford Geertz, “The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss,” in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.
Related material —
See also "Levi-Strauss" in this journal and "At Play in the Field."
In the spirit of last night's SNL Hanukkah version of "It's a Wonderful Life" —
A Geometric Merkabah for Hanukkah from December 1, and…
"The Homepage of Contemporary Structuralism" (click to enlarge) —
Detail —
Summary —
Mathematics and Narrative continued
A search for Ursula in this journal yields a story…
“The main character is a slave woman who discovers new patterns in the mosaics.”
Other such stories: Plato’s Meno and Changing Woman —
|
“Kaleidoscope turning…
Shifting pattern within — Roger Zelazny, Eye of Cat |
Philosophical postscript—
“That Lévi-Strauss should have been able to transmute the romantic passion of Tristes Tropiques into the hypermodern intellectualism of La Pensée Sauvage is surely a startling achievement. But there remain the questions one cannot help but ask. Is this transmutation science or alchemy? Is the ‘very simple transformation’ which produced a general theory out of a personal disappointment real or a sleight of hand? Is it a genuine demolition of the walls which seem to separate mind from mind by showing that the walls are surface structures only, or is it an elaborately disguised evasion necessitated by a failure to breach them when they were directly encountered? Is Lévi-Strauss writing, as he seems to be claiming in the confident pages of La Pensée Sauvage, a prolegomenon to all future anthropology? Or is he, like some uprooted neolithic intelligence cast away on a reservation, shuffling the debris of old traditions in a vain attempt to revivify a primitive faith whose moral beauty is still apparent but from which both relevance and credibility have long since departed?”
— Clifford Geertz, conclusion of “The Cerebral Savage: On the Work of Claude Lévi-Strauss“
"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…."
– Don DeLillo, Point Omega
Capitalized, the letter omega figures in the theology of two Jesuits, Teilhard de Chardin and Gerard Manley Hopkins. For the former, see a review of DeLillo. For the latter, see James Finn Cotter's Inscape and "Hopkins and Augustine."
The lower-case omega is found in the standard symbolic representation of the Galois field GF(4)—
A representation of GF(4) that goes beyond the standard representation—
Here the four diagonally-divided two-color squares represent the four elements of GF(4).
The graphic properties of these design elements are closely related to the algebraic properties of GF(4).
This is demonstrated by a decomposition theorem used in the proof of the diamond theorem.
To what extent these theorems are part of "a saga of created reality" may be debated.
I prefer the Platonist's "discovered, not created" side of the debate.
University of California anthropologist Alan Dundes:
"One could well argue that binary opposition is a universal. Presumably all human societies, past and present, made some kind of distinction between 'Male and Female,' 'Life and Death,' 'Day and Night' (or Light and Dark), etc." –"Binary Opposition in Myth: The Propp/Levi-Strauss Debate in Retrospect," Western Folklore, Winter 1997
To Levi-Strauss, I prefer Clifford Geertz —
"…what Levi-Strauss has made for himself is an infernal culture machine." –"The Cerebral Savage"
— and Heinrich Zimmer —
"…all opposition, as well as identity, stems from Maya. Great Maya is wisdom and increase, stability and readiness to assist, compassion and serenity. Queen of the World, she is alive in every nuance of feeling and perception; feelings and perceptions are her gestures. And her nature can be sensed only by one who has comprehended that she is the unity of opposites." —The King and the Corpse
And then there are more up-to-date culture machines.
Levi-Strauss, obtuse and boring, is an opposite, of sorts, to the smart and funny Dundes. The latter, in the binary opposition posed in yesterday's Log24 title "Sinner or Saint?," is definitely on the side of the saints. (See selected Log24 entries for the date of his death– Warren Beatty's birthday.)
Today's happy birthdays — Elke Sommer —
and Sesame Street —
Google logo today, Nov. 5, 2009
Click images for historical background.
As noted here yesterday, Claude Levi-Strauss may have died on Devil's Night, on Halloween, or on All Saints' Day. He was apparently a myth-transformer to the end.
The Independent says today he died on Sunday, All Saints' Day. Its eulogy, by Adam Kuper, is well-written, noting that linguist Roman Jakobson was a source of Levi-Strauss's theory of oppositions in myth, and observing that
"… binary oppositions tend to accumulate to form structures…."
Yes, they do. Examples:
I. The structures in the Diamond Puzzle…
Click on image for Jungian background.
II: The structure on a recent cover of Semiotica…
The Semiotica article by mathematical linguist Solomon Marcus is a defense of the Levi-Strauss canonic formula mentioned here yesterday.
It is available online for $40.
A less expensive, and possibly more informative, look at oppositions in linguistics is available for free online in a 1984 master's thesis (pdf, 8+ mb)–
"Language, Linguistics, and Philosophy: A Comparison of the Work of Roman Jakobson and the Later Wittgenstein, with Some Attention to the Philosophy of Charles Saunders Peirce," by Miles Spencer Kimball.
Book review by Jadran Mimica in Oceania, Vol. 74, 2003:
"In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopeic dynamics
[fx(a) : fy(b) :: fx(b) : fa-1(y)]
that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object."
So there.
At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.)
I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth:
"…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created."
… on Friday, October 30, 2009 ………
(known to some as “Devil’s Night”)………
according to The New York Times
…
A search in this journal for “Levi-Strauss” yields various entries, the most recent being “Autistic Enchantment” (Sept. 3, 2009).
Related material:
Today’s New York Times on autism
(A Powerful Identity, a Vanishing Diagnosis)
and Log24 on enchantment.
An instance of the latter (from Feb. 15, 2008):
Door
Step:
“Many dreams have been
brought to your doorstep.
They just lie there
and they die there.”
— Lyricist Ray Evans,
who died at 92
one year ago today
Associated Press –
Feb. 15, 2008
Today in History –
Thought for Today:
Postscript of Nov. 3, 2009:
For more confusion, see
the works of Claude Levi-Strauss.
But according to The Telegraph, Levi-Strauss
died on Saturday, Oct. 31, All Hallows’ Eve.
According to Le Monde, he may have died
even later, on Sunday, Nov. 1, All Saints’ Day.
“Music and mathematics are among the pre-eminent wonders of the race. Levi-Strauss sees in the invention of melody ‘a key to the supreme mystery’ of man– a clue, could we but follow it, to the singular structure and genius of the species. The power of mathematics to devise actions for reasons as subtle, witty, manifold as any offered by sensory experience and to move forward in an endless unfolding of self-creating life is one of the strange, deep marks man leaves on the world. Chess, on the other hand, is a game in which thirty-two bits of ivory, horn, wood, metal, or (in stalags) sawdust stuck together with shoe polish, are pushed around on sixty-four alternately coloured squares. To the addict, such a description is blasphemy. The origins of chess are shrouded in mists of controversy, but unquestionably this very ancient, trivial pastime has seemed to many exceptionally intelligent human beings of many races and centuries to constitute a reality, a focus for the emotions, as substantial as, often more substantial than, reality itself. Cards can come to mean the same absolute. But their magnetism is impure. A mania for whist or poker hooks into the obvious, universal magic of money. The financial element in chess, where it exists at all, has always been small or accidental.
To a true chess player, the pushing about of thirty-two counters on 8×8 squares is an end in itself, a whole world next to which that of a mere biological or political or social life seems messy, stale, and contingent. Even the patzer, the wretched amateur who charges out with his knight pawn when the opponent’s bishop decamps to R4, feels this daemonic spell. There are siren moments when quite normal creatures otherwise engaged, men such as Lenin and myself, feel like giving up everything– marriage, mortgages, careers, the Russian Revolution– in order to spend their days and nights moving little carved objects up and down a quadrate board. At the sight of a set, even the tawdriest of plastic pocket sets, one’s fingers arch and a coldness as in a light sleep steals over one’s spine. Not for gain, not for knowledge or reknown, but in some autistic enchantment, pure as one of Bach’s inverted canons or Euler’s formula for polyhedra.”
— George Steiner in “A Death of Kings,” The New Yorker, issue dated September 7, 1968, page 133
“Examples are the stained-glass windows of knowledge.” —Nabokov
Click above images for some context.
Part I: Random Walk
Part II: X's
3/22:
Part III: O's —
A Cartoon Graveyard
in honor of the late
Gene Persson †
Today's Garfield —
See also
Midsummer Eve's Dream:
"The meeting is closed
with the lord's‡ prayer
and refreshments are served."
† Producer of plays and musicals
including Album and
The Ruling Class
‡ Lower case in honor of
Peter O'Toole, star of
the film version of
The Ruling Class.
(This film, together with
O'Toole's My Favorite Year,
may be regarded as epitomizing
Hollywood's Jesus for Jews.)
Those who prefer
less randomness
in their religion
may consult O'Toole's
more famous film work
involving Islam,
as well as
the following structure
discussed here on
the date of Persson's death:
"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah."
Kernel
Mathematical Reviews citation:
MR2163497 (2006g:81002) 81-03 (81P05)
Gieser, Suzanne The innermost kernel. Depth psychology and quantum physics. Wolfgang Pauli's dialogue with C. G. Jung. Springer-Verlag, Berlin, 2005. xiv+378 pp. ISBN: 3-540-20856-9
A quote from MR at Amazon.com:
"This revised translation of a Swedish Ph. D. thesis in philosophy offers far more than a discussion of Wolfgang Pauli's encounters with the psychoanalyst Carl Gustav Jung…. Here the book explains very well how Pauli attempted to extend his understanding beyond superficial esotericism and spiritism…. To understand Pauli one needs books like this one, which… seems to open a path to a fuller understanding of Pauli, who was seeking to solve a quest even deeper than quantum physics." (Arne Schirrmacher, Mathematical Reviews, Issue 2006g)
The four-group is also known as the Vierergruppe or Klein group. It appears, notably, as the translation subgroup of A, the group of 24 automorphisms of the affine plane over the 2-element field, and therefore as the kernel of the homomorphism taking A to the group of 6 automorphisms of the projective line over the 2-element field. (See Finite Geometry of the Square and Cube.)
The "chessboard" of
Nov. 7, 2006
(as revised Nov. 7, 2012)–
(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
May '68 Revisited
"At his final Paris campaign rally… Mr. Sarkozy declared himself the candidate of the 'silent majority,' tired of a 'moral crisis in France not seen since the time of Joan of Arc.'
'I want to turn the page on May 1968,' he said of the student protests cum social revolution that rocked France almost four decades ago.
'The heirs of May '68 have imposed the idea that everything has the same worth, that there is no difference between good and evil, no difference between the true and the false, between the beautiful and the ugly and that the victim counts for less than the delinquent.'
Denouncing the eradication of 'values and hierarchy,' Mr. Sarkozy accused the Left of being the true heirs and perpetuators of the ideology of 1968."
— Emma-Kate Symons, Paris, May 1, 2007, in The Australian
Related material:
From the translator's introduction to Dissemination, by Jacques Derrida, translated by Barbara Johnson, University of Chicago Press, 1981, page xxxi —
"Both Numbers and 'Dissemination' are attempts to enact rather than simply state the theoretical upheavals produced in the course of a radical reevaluation of the nature and function of writing undertaken by Derrida, Sollers, Roland Barthes, Julia Kristeva and other contributors to the journal Tel Quel in the late 1960s. Ideological and political as well as literary and critical, the Tel Quel program attempted to push to their utmost limits the theoretical revolutions wrought by Marx, Freud, Nietzsche, Mallarme, Levi-Strauss, Saussure, and Heidegger."
This is the same Barbara Johnson who has served as the Frederic Wertham Professor of Law and Psychiatry in Society at Harvard.
Johnson has attacked "the very essence of Logic"–
"… the logic of binary opposition, the principle of non-contradiction, often thought of as the very essence of Logic as such….
Now, my understanding of what is most radical in deconstruction is precisely that it questions this basic logic of binary opposition….
Instead of a simple 'either/or' structure, deconstruction attempts to elaborate a discourse that says neither 'either/or', nor 'both/and' nor even 'neither/nor', while at the same time not totally abandoning these logics either."
— "Nothing Fails Like Success," SCE Reports 8, 1980
Such contempt for logic has resulted, for instance, in the following passage, quoted approvingly on page 342 of Johnson's translation of Dissemination, from Philippe Sollers's Nombres (1966):
"The minimum number of rows– lines or columns– that contain all the zeros in a matrix is equal to the maximum number of zeros located in any individual line or column."
For a correction of Sollers's Johnson's damned nonsense, click here.
Update of May 29, 2014:
The error, as noted above, was not Sollers's, but Johnson's.
See also the post of May 29, 2014 titled 'Lost in Translation.'
Powered by WordPress
