Log24

Tuesday, October 10, 2017

Another 35-Year Wait

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

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.

The Lévi-Strauss formula

My "inscape" formula, from a note of Sept. 22, 1982 —

S = f ( f ( X ) ) .

Some mathematics from last year related to the 1982 formula —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also Inscape in this  journal and posts tagged Dirac and Geometry.

Dueling Formulas

Filed under: Uncategorized — Tags: , — m759 @ 12:35 PM

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
 

The Ring of the Diamond Theorem          ::

I prefer Jung. For those who prefer Lévi-Strauss —

     First edition, Cornell University Press, 1970.

A related tale — "A Meaning, Like."

Saturday, April 29, 2017

For the Church of Synchronology*

Filed under: Uncategorized — Tags: — m759 @ 2:00 PM

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.

Saturday, April 8, 2017

A Perfect Nonentity

Filed under: Uncategorized — Tags: — m759 @ 8:25 AM

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."

Wednesday, March 15, 2017

Middle March:

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

The Key to All Mythologies  in a Cartoon Graveyard

This is a sequel to yesterday's post Review, which
suggested a look at Lévi-Strauss's The Raw and The Cooked  
in Derrida's “Structure, Sign, and Play," and then a look at the

Financial Times  of February 26, 2010

"The metaphor for metamorphosis no keys unlock."

Steven H. Cullinane, November 7, 1986

Tuesday, March 14, 2017

Review

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Friday, November 18, 2016

Key to All Mythologies

Filed under: Uncategorized — m759 @ 5:08 AM

(Continued)

Wednesday, October 12, 2016

Elementary Art

Filed under: Uncategorized — m759 @ 12:00 PM

The above cycle may have influenced the design
of Carl Jung's symbol of the self —

Jung's Self-Symbol

http://www.log24.com/log/pix11B/110915-FourDiamondsIcon.gif

Related art by
Steven H. Cullinane

See also Levi-Strauss Formula in this journal.

Thursday, October 6, 2016

Key to All Mythologies…

Filed under: Uncategorized — m759 @ 6:08 PM

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  —

The 1955 Levi-Strauss 'canonic formula' in its original context of permutation groups

I do not recommend trying to make sense of the above "formula."

Related material —

"And six sides to bounce it all off of.

Tuesday, September 27, 2016

Chomsky and Lévi-Strauss in China

Filed under: Uncategorized — m759 @ 7:31 AM

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 —

The larger cases —

The diamond theorem

Tuesday, September 20, 2016

The Diamond Theorem …

Filed under: Uncategorized — m759 @ 11:00 AM

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.

Tuesday, September 6, 2016

Ethno-Aesthetics

Filed under: Uncategorized — m759 @ 3:04 PM

"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 …

IMAGE- Stella Octangula and Claude Levi-Strauss

Related theoretical material — See Hudson + Tetrahedra.

Monday, September 5, 2016

Structural Study

Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

The Lévi-Strauss "canonic formula" of myth in its original 1955 context,
described as that of permutation groups 

The 1955 Levi-Strauss 'canonic formula' in its original context of permutation groups

Related material in this  journal —

Dueling Formulas and Symmetry.

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: Uncategorized — Tags: — m759 @ 4:23 PM

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.

Thursday, May 19, 2016

Kulturkampf

Filed under: Uncategorized — m759 @ 2:27 AM

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.

IMAGE- 'Ratner's Star,' by Don DeLillo (1976)

Above image reposted from Jan. 10, 2014

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

Above images reposted from May 5, 2016

Related material:  The previous post, Dueling Formulas.

Wednesday, May 18, 2016

Dueling Formulas

Filed under: Uncategorized — Tags: , — m759 @ 12:00 AM

Jung's four-diamond formula vs. Levi-Strauss's 'canonical formula'

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 .

Tuesday, May 17, 2016

Bullshit Studies

Filed under: Uncategorized — Tags: , — m759 @ 1:06 AM

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 —

Log24 post titled 'As Is'

[Above photo of Lévi-Strauss and formula added June 6, 2016.]

Thursday, May 5, 2016

Solomon’s Seal

Filed under: Uncategorized — m759 @ 11:00 PM

Excerpt from a post of November 4, 2009

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

For some related material, see a search 
for Solomon Marcus in this  journal.

Thursday, November 12, 2015

The Unbaked, the Baked, and the Half-Baked

Filed under: Uncategorized — Tags: — m759 @ 5:07 PM

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.

Wednesday, April 11, 2012

Steiner’s Systems

Filed under: Uncategorized — m759 @ 12:00 PM

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—

IMAGE- George Steiner on Levi-Strauss viewing man as 'a mythopoetic primate'

Related material—

IMAGE- Daniel Gorenstein quotes Freeman Dyson on physics and the monster group

Also related — Kantor in 1981 on "exquisite finite geometries," and The Galois Tesseract.

Tuesday, December 21, 2010

Savage Solstice

Filed under: Uncategorized — m759 @ 7:20 PM

In memory of kaleidoscope enthusiast Cozy Baker, who died at 86, according to Saturday's Washington Post , on October 19th.

http://www.log24.com/log/pix10B/101221-BrewsterSociety.jpg

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  —

http://www.log24.com/log/pix10B/101221-TristesTropiques.jpg

See also "Levi-Strauss" in this journal and "At Play in the Field."

Sunday, December 19, 2010

Stella

Filed under: Uncategorized — Tags: — m759 @ 8:00 AM

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) —

http://www.log24.com/log/pix10B/101219-MorettiSFHome-Sm.jpg

Detail —

http://www.log24.com/log/pix10B/101219-MorettiStella.jpg

Summary —

IMAGE- Stella Octangula and Claude Levi-Strauss

Thursday, October 21, 2010

St. Ursula’s Day

Filed under: Uncategorized — Tags: — m759 @ 4:07 PM

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

Changing Woman:

“Kaleidoscope turning…

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern within
unalterable structure…”

— 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

Thursday, November 5, 2009

Universal Culture Machines

Filed under: Uncategorized — m759 @ 10:10 AM

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

Parallax illustrated, from Wikipedia-- A star on two background colors, blue and red

and Sesame Street —

http://www.log24.com/log/pix09A/091105-CookieMonster.jpg

Google logo today, Nov. 5, 2009

Click images for historical background.

Wednesday, November 4, 2009

Sinner or Saint?

Filed under: Uncategorized — Tags: — m759 @ 10:31 AM

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

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

http://www.log24.com/log/pix09A/091103-SemioticaSm.jpg

Click to enlarge.

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.

Tuesday, November 3, 2009

Summa Mythologica

Filed under: Uncategorized — Tags: — 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 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."

Levi-Strauss Died…

Filed under: Uncategorized — m759 @ 3:09 PM

… on Friday, October 30, 2009 ………
(known to some as “Devil’s Night”)………
according to The New York Timeshttp://www.log24.com/images/asterisk8.gif

http://www.log24.com/log/pix09A/091103-NYT-LeviStrauss.jpg

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

Black monolith, 1x4x9

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:

“Like all dreamers I confuse
disenchantment with truth.”
— Jean-Paul Sartre

http://www.log24.com/log/pix09A/091103-Cartoon.jpg

Postscript of Nov. 3, 2009:
For more confusion, see
the works of Claude Levi-Strauss.

http://www.log24.com/images/asterisk8.gif 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.

Thursday, September 3, 2009

Thursday September 3, 2009

Filed under: Uncategorized — m759 @ 11:07 AM
Autistic Enchantment

“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

Quaternion rotations in a finite geometry
Click above images for some context.

See also:

Log24 entries of May 30, 2006, as well as “For John Cramer’s daughter Kathryn”– August 27, 2009— and related material at Wikipedia (where Kathryn is known as “Pleasantville”).

Tuesday, June 24, 2008

Tuesday June 24, 2008

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM
Random Walk with
X's and O's

Part I: Random Walk

NY Lottery June 23, 2008: Mid-day 322, Evening 000

Part II: X's

3/22:

Actor contemplating the Chi-rho Page of the Book of Kells

"Shakespeare, Rilke, Joyce,
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
are of central importance,
for whom chiasmus is a
generator of meaning,
tool of discovery and
  philosophical template."
 
— Chiasmus in the
Drama of Life

Part III: O's —

A Cartoon Graveyard
in honor of the late
Gene Persson

Today's Garfield

Garfield cartoon of June 24, 2008

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:

5x5 ultra super magic square

"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah.
"

Wednesday, June 20, 2007

Wednesday June 20, 2007

Filed under: Uncategorized — Tags: — m759 @ 1:06 AM

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)
 

An excerpt:

 

The image “http://www.log24.com/theory/images/PauliSquare.gif” cannot be displayed, because it contains errors.

I do not yet know what Gieser means by "the innermost kernel." The following is my version of a "kernel" of sorts– a diagram well-known to students of anthropologist Claude Levi-Strauss and art theorist Rosalind Krauss:

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.)

Related material:

The "chessboard" of
   Nov. 7, 2006
(as revised Nov. 7, 2012)–

I Ching chessboard. Previous version replaced on Nov. 7, 2012, by original 1989 chessboard arrangement

I Ching chessboard

None of this material really has much to do with the history of physics, except for its relation to the life and thought of physicist Wolfgang Pauli— the "Mephistopheles" of the new book Faust in Copenhagen. (See previous entry.)

"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
 

Friday, May 4, 2007

Friday May 4, 2007

Filed under: Uncategorized — Tags: — m759 @ 5:01 PM

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.'

Saturday, March 24, 2007

Saturday March 24, 2007

Filed under: Uncategorized — m759 @ 2:09 AM
Savage Scrutiny

“They sang desiring an object that was near,
In face of which desire no longer moved,
Nor made of itself that which it could not find…
Three times the concentred self takes hold, three times
The thrice concentred self, having possessed

The object, grips it in savage scrutiny,
Once to make captive, once to subjugate
Or yield to subjugation, once to proclaim
The meaning of the capture, this hard prize,
Fully made, fully apparent, fully found.”

— “Credences of Summer,” VII,
    by Wallace Stevens, from
    Transport to Summer (1947)

Clifford Geertz on Levi-Strauss, from The Cerebral Savage:

“Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns…. “

Related material:

The kaleidoscope puzzle and “Claude Levi-Strauss and the Aesthetic Object,” a videotaped interview with Dr. Boris Wiseman.

Thursday, March 22, 2007

Thursday March 22, 2007

Filed under: Uncategorized — m759 @ 12:00 PM
Chess Letter:
x

Queen sacrifice

Click on a picture
for the meaning of
the chess notation.
 
“Shakespeare, Rilke, Joyce,
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
are of central importance,
for whom chiasmus is a
generator of meaning,
tool of discovery and
  philosophical template.”
 
— Chiasmus in the Drama of Life

Wednesday, November 1, 2006

Wednesday November 1, 2006

Filed under: Uncategorized — Tags: — m759 @ 8:24 AM

The image “http://www.log24.com/log/pix06B/061101-Geertz2.jpg” cannot be displayed, because it contains errors.

Clifford Geertz 

Professor Emeritus,
Institute for Advanced Study

Savage Logic

"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.

Today's New York Times
reports that
Geertz died on Monday,
October 30, 2006.

Related material:

Kaleidoscope Puzzle,

Being Pascal Sauvage,

and Up the River:
 

 

 
The Necessity For Story

by Frederick Zackel

While it's a story that's never been written, a suggested title– Indiana Jones Sails Up The River Of Death–

The image “http://www.log24.com/log/pix04B/041016-Poster2.jpg” cannot be displayed, because it contains errors.

shows how readily we as individuals or we as a culture can automatically visualize a basic story motif. We may each see the particular elements of the story differently, but almost instantaneously we catch its drift.

The hero sails up the river of death to discover what lies within his own heart: i.e., how much moral and physical strength he has.

Indiana Jones sails up the River of Death.

We are following Indiana Jones up the River of Death. We're going to visit with Colonel Kurtz. (You may not want to get off the boat.)

No, I am not mixing up metaphors.

These are the Story.

 

Amen.

Saturday, August 13, 2005

Saturday August 13, 2005

Filed under: Uncategorized — m759 @ 12:04 PM

Kaleidoscope, continued:

In Derrida’s Defense

The previous entry quoted an attack on Jacques Derrida for ignoring the “kaleidoscope” metaphor of Claude Levi-Strauss.  Here is a quote by Derrida himself:

“The time for reflection is also the chance for turning back on the very conditions of reflection, in all the senses of that word, as if with the help of an optical device one could finally see sight, could not only view the natural landscape, the city, the bridge and the abyss, but could view viewing. (1983:19)

— Derrida, J. (1983) ‘The Principle of Reason: The University in the Eyes of its Pupils’, Diacritics 13.3: 3-20.”

The above quotation comes from Simon Wortham,  who thinks the “optical device” of Derrida is a mirror.  The same quotation appears in Desiring Dualisms at thispublicaddress.com, where the “optical device” is interpreted as a kaleidoscope.

Derrida’s “optical device” may (for university pupils desperately seeking an essay topic) be compared with Joyce’s “collideorscape.”  For a different connection with Derrida, see The ‘Collideorscape’ as Différance.

Thursday, August 11, 2005

Thursday August 11, 2005

Filed under: Uncategorized — m759 @ 8:16 AM

Kaleidoscope, continued

From Clifford Geertz, The Cerebral Savage:

"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….  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….  Levi-Strauss generalizes this permutational view of thinking to savage thought in general.  It is all a matter of shuffling discrete (and concrete) images–totem animals, sacred colors, wind directions, sun deities, or whatever–so as to produce symbolic structures capable of formulating and communicating objective (which is not to say accurate) analyses of the social and physical worlds.

…. And the point is general.  The relationship between a symbolic structure and its referent, the basis of its meaning,  is fundamentally 'logical,' a coincidence of form– not affective, not historical, not functional.  Savage thought is frozen reason and anthropology is, like music and mathematics, 'one of the few true vocations.'

Or like linguistics."

Edward Sapir on Linguistics, Mathematics, and Music:

"… linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms.  Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music.  But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest."

— Edward Sapir, "The Grammarian and his Language,"
  American Mercury 1:149-155,1924

From Robert de Marrais, Canonical Collage-oscopes:

"…underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements– and their most general instances are not the regular solids, but crystallographic reflection groups.  You know, those things the non-professionals call . . . kaleidoscopes! *  (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism' **— then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name…)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry  (A polytope is an n-dimensional analog of a polygon or polyhedron.  Chapter V of this book is entitled 'The Kaleidoscope'….)

** … contemporary with the Johns Hopkins hatchet job that won him American marketshare, Derrida was also being subjected to a series of probing interviews in Paris by the hometown crowd.  He first gained academic notoriety in France for his book-length reading of Husserl's two-dozen-page essay on 'The Origin of Geometry.'  The interviews were collected under the rubric of Positions (Chicago: U. of Chicago Press, 1981…).  On pp. 34-5 he says the following: 'the resistance to logico-mathematical notation has always been the signature of logocentrism and phonologism in the event to which they have dominated metaphysics and the classical semiological and linguistic projects…. A grammatology that would break with this system of presuppositions, then, must in effect liberate the mathematization of language…. The effective progress of mathematical notation thus goes along with the deconstruction of metaphysics, with the profound renewal of mathematics itself, and the concept of science for which mathematics has always been the model.'  Nice campaign speech, Jacques; but as we'll see, you reneged on your promise not just with the kaleidoscope (and we'll investigate, in depth, the many layers of contradiction and cluelessness you put on display in that disingenuous 'playing to the house'); no, we'll see how, at numerous other critical junctures, you instinctively took the wrong fork in the road whenever mathematical issues arose… henceforth, monsieur, as Joe Louis once said, 'You can run, but you just can't hide.'…."

Monday, August 25, 2003

Monday August 25, 2003

Filed under: Uncategorized — Tags: — m759 @ 4:24 AM

Words Are Events

August 12 was the date of death of Joseph Patrick Kennedy, Jr., and the date I entered some theological remarks in a new Harvard weblog.  It turns out that August 12 was also the feast day of a new saint… Walter Jackson Ong, of St. Louis University, St. Louis, Missouri, a Jesuit institution.

Today, August 25, is the feast day of St. Louis himself, for whom the aforementioned city and university are named.

The New York Times states that Ong was "considered an outstanding postmodern theorist, whose ideas spawned college courses…."

There is, of course, no such thing as a postmodern Jesuit, although James Joyce came close.

From The Walter J. Ong Project:

"Ong's work is often presented alongside the postmodern and deconstruction theories of Claude Levi-Strauss, Jacques Derrida, Michel Foucault, Hélène Cixous, and others. His own work in orality and literacy shows deconstruction to be unnecessary: if you consider language to be fundamentally spoken, as language originally is, it does not consist of signs, but of events. Sound, including the spoken word, is an event. It takes time. The concept of 'sign,' by contrast, derives primarily not from the world of events, but from the world of vision. A sign can be physically carried around, an event cannot: it simply happens. Words are events."

 

From a commonplace book
on the number 911:

"We keep coming back and coming back
To the real: to the hotel
    instead of the hymns
That fall upon it out of the wind.
    We seek

The poem of pure reality, untouched
By trope or deviation,
    straight to the word,
Straight to the transfixing object,
    to the object

At the exactest point at which
    it is itself,
Transfixing by being purely
    what it is,
A view of New Haven, say,
    through the certain eye,

The eye made clear of uncertainty,
    with the sight
Of simple seeing, without reflection.
    We seek
Nothing beyond reality. Within it,

Everything, the spirit's alchemicana
Included, the spirit that goes
    roundabout
And through included,
    not merely the visible,

The solid, but the movable,
    the moment,
The coming on of feasts
     and the habits of saints,
The pattern of the heavens
     and high, night air."

Wallace Stevens (1879-1955)
An Ordinary Evening in New Haven
IX.1-18, from The Auroras of Autumn,
Knopf, NY (1950)
(Collected Poems, pp. 465-489)
NY Times Obituary (8-3-1955)

 

The web page where I found the Stevens quote also has the following:

 

Case 9 of Hekiganroku:
Joshu's Four Gates

A monk asked Joshu,
"What is Joshu?" (Chinese: Chao Chou)

Joshu said,
"East Gate, West Gate,
 North Gate, South Gate."

Setcho's Verse:

Its intention concealed,
    the question came;
The Diamond King's eye was
    as clear as a jewel.
There stood the gates,
    north, south, east, and west,
But the heaviest hammer blow
    could not open them.

Setcho (980-1052),
Hekiganroku, 9 (Blue Cliff Records)
(translated by Katsuki Sekida,
Two Zen Classics, 1977, p. 172)

 

See also my previous entry for today,
"Gates to the City."

Friday, July 25, 2003

Friday July 25, 2003

Filed under: Uncategorized — m759 @ 5:24 PM

For Jung’s 7/26 Birthday:
A Logocentric Meditation

Leftist academics are trying to pull a fast one again.  An essay in the most prominent American mathematical publication tries to disguise a leftist attack on Christian theology as harmless philosophical woolgathering.

In a review of Vladimir Tasic’s Mathematics and the Roots of Postmodern Thought, the reviewer, Michael Harris, is being less than candid when he discusses Derrida’s use of “logocentrism”:

“Derrida uses the term ‘logocentrism’… as ‘the metaphysics of phonetic writing’….”

Notices of the American Mathematical Society, August 2003, page 792

We find a rather different version of logocentrism in Tasic’s own Sept. 24, 2001, lecture “Poststructuralism and Deconstruction: A Mathematical History,” which is “an abridged version of some arguments” in Tasic’s book on mathematics and postmodernism:

“Derrida apparently also employs certain ideas of formalist mathematics in his critique of idealist metaphysics: for example, he is on record saying that ‘the effective progress of mathematical notation goes along with the deconstruction of metaphysics.’

Derrida’s position is rather subtle. I think it can be interpreted as a valiant sublation of two completely opposed schools in mathematical philosophy. For this reason it is not possible to reduce it to a readily available philosophy of mathematics. One could perhaps say that Derrida continues and critically reworks Heidegger’s attempt to ‘deconstruct’ traditional metaphysics, and that his method is more ‘mathematical’ than Heidegger’s because he has at his disposal the entire pseudo-mathematical tradition of structuralist thought. He has himself implied in an interview given to Julia Kristeva that mathematics could be used to challenge ‘logocentric theology,’ and hence it does not seem unreasonable to try looking for the mathematical roots of his philosophy.”

The unsuspecting reader would not know from Harris’s review that Derrida’s main concern is not mathematics, but theology.  His ‘deconstruction of metaphysics’ is actually an attack on Christian theology.

From “Derrida and Deconstruction,” by David Arneson, a University of Manitoba professor and writer on literary theory:

Logocentrism: ‘In the beginning was the word.’ Logocentrism is the belief that knowledge is rooted in a primeval language (now lost) given by God to humans. God (or some other transcendental signifier: the Idea, the Great Spirit, the Self, etc.) acts a foundation for all our thought, language and action. He is the truth whose manifestation is the world.”

Some further background, putting my July 23 entry on Lévi-Strauss and structuralism in the proper context:

Part I.  The Roots of Structuralism

“Literary science had to have a firm theoretical basis…”

Part II.  Structuralism/Poststructuralism

“Most [structuralists] insist, as Levi-Strauss does, that structures are universal, therefore timeless.”

Part III.  Structuralism and
             Jung’s Archetypes

Jung’s “theories, like those of Cassirer and Lévi-Strauss, command for myth a central cultural position, unassailable by reductive intellectual methods or procedures.”

And so we are back to logocentrism, with the Logos — God in the form of story, myth, or archetype — in the “central cultural position.”

What does all this have to do with mathematics?  See

Plato’s Diamond,

Rosalind Krauss on Art –

“the Klein group (much beloved of Structuralists)”

Another Michael Harris Essay, Note 47 –

“From Krauss’s article I learned that the Klein group is also called the Piaget group.”

and Jung on Quaternity:
      Beyond the Fringe –

“…there is no denying the fact that [analytical] psychology, like an illegitimate child of the spirit, leads an esoteric, special existence beyond the fringe of what is generally acknowledged to be the academic world.”

What attitude should mathematicians have towards all this? 

Towards postmodern French
  atheist literary/art theorists –

Mathematicians should adopt the attitude toward “the demimonde of chic academic theorizing” expressed in Roger Kimball’s essay, Feeling Sorry for Rosalind Krauss.

Towards logocentric German
  Christian literary/art theorists –

Mathematicians should, of course, adopt a posture of humble respect, tugging their forelocks and admitting their ignorance of Christian theology.  They should then, if sincere in their desire to honestly learn something about logocentric philosophy, begin by consulting the website

The Quest for the Fiction of an Absolute.

For a better known, if similarly disrespected, “illegitimate child of the spirit,” see my July 22 entry.

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