Sunday, February 2, 2020

Tetrads for McLuhan, or “Blame It on Video”

Filed under: General — Tags: — m759 @ 11:22 PM

"I like to put people on myself by skipping logical steps
in the conversation until they're dizzy." — Jemima Brown
in The Eiger Sanction

Related posts — See "McLuhan Tetrad" in this journal.

Related theology — See  "The Meaning of Perichoresis."
Background — The New Yorker , "On Religion:
Richard Rohr Reorders the Universe," by Eliza Griswold
on February 2, 2020, and a different reordering in posts
tagged Eightfold Metaphysics.

Game of Shadows

Filed under: General — Tags: — m759 @ 2:27 PM

A search in this journal for "Game of Shadows" yields

IMAGE- A Jesuit on words and shadows

“Krauss, Portman; Portman, Krauss.”

Filed under: General — Tags: , , — m759 @ 12:58 AM

Prominent in the oeuvre  of art theorist Rosalind Krauss, the Klein group
is a four-element group named for Felix Christian Klein.

The Klein Four-Group, illustration by Steven H. Cullinane

It is commonly known as the four-group.
Mathematicians sometimes call this group
"V," for its German name, Vierergruppe .

For those who prefer narrative to mathematics

Thursday, January 23, 2020

The Demarcation of Nothing

Filed under: General — Tags: , , , , — m759 @ 3:50 PM

" nothing could be demarcated as 'hors d'oeuvre'…"

Geoffrey Hartman in his Haskins Lecture for 2000
(quoted here on Columbus Day, 2004).

See also May Day 2016 and Gap Dance.

Tuesday, October 15, 2019

A White Stone for Bloom

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

Excerpt from a long poem by Eliza Griswold 
in a recent New Yorker —

Monday, March 25, 2019


Filed under: General — Tags: , , , , — m759 @ 1:46 PM

(Continued from the previous post.)

In-Between "Spacing" and the "Chôra "
in Derrida: A Pre-Originary Medium?

By Louise Burchill

(Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.),  Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010)

"The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance  (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing  (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)."

1  Jacques Derrida, “La Différance,” in Marges – de la philosophie  (Paris: Minuit, 1972), p. 14. Henceforth cited as  D  .

2  Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and  Difference  (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW .

3  Jacques DerridaLe Toucher, Jean-Luc Nancy  (Paris: Galilée, 2000), p. 207.

. . . .

"… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance  consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance  and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus  and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance  that Derrida must, in a 'properly' apotropaic  gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…."

16  Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger  2 (1990): 207-227.

. . . .

… "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.'

For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements )  between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).


For the Church of Synchronology

See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.

Sunday, March 24, 2019

Espacement: Geometry of the Interstice in Literary Theory

Filed under: General — Tags: , , , , — m759 @ 3:28 AM

"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982


Parrhesia  No. 3 • 2007 • 22–32

(Up) Against the (In) Between: Interstitial Spatiality
in Genet and Derrida

by Clare Blackburne

Blackburne — www.parrhesiajournal.org 24 —

"The excessive notion of espacement  as the resurgent spatiality of that which is supposedly ‘without space’ (most notably, writing), alerts us to the highly dynamic nature of the interstice – a movement whose discontinuous and ‘aberrant’ nature requires further analysis."

Blackburne — www.parrhesiajournal.org 25 —

"Espacement  also evokes the ambiguous figure of the interstice, and is related to the equally complex derridean notions of chora , différance , the trace and the supplement. Derrida’s reading of the Platonic chora  in Chora L Works  (a series of discussions with the architect Peter Eisenman) as something which defies the logics of non-contradiction and binarity, implies the internal heterogeneity and instability of all structures, neither ‘sensible’ nor ‘intelligible’ but a third genus which escapes conceptual capture.25 Crucially, chora , spacing, dissemination and différance  are highly dynamic concepts, involving hybridity, an ongoing ‘corruption’ of categories, and a ‘bastard reasoning.’26 Derrida identification of différance  in Margins of  Philosophy , as an ‘unappropriable excess’ that operates through spacing as ‘the becoming-space of time or the becoming-time of space,’27 chimes with his description of chora  as an ‘unidentifiable excess’ that is ‘the spacing which is the condition for everything to take place,’ opening up the interval as the plurivocity of writing in defiance of ‘origin’ and ‘essence.’28  In this unfolding of différance , spacing  ‘insinuates  into  presence an  interval,’29 again alerting us to the crucial role of the interstice in deconstruction, and, as Derrida observes  in Positions ,  its  impact  as  ‘a movement,  a  displacement  that  indicates  an  irreducible alterity’: ‘Spacing is the impossibility for an identity to be closed on itself, on the inside of its proper interiority, or on its coincidence with itself. The irreducibility of spacing is the irreducibility of the other.’30"

25. Quoted in Jeffrey Kipnis and Thomas Leeser, eds., 
Chora L Works. Jacques Derrida and Peter Eisenman  
(New York: The Monacelli Press, 1997), 15.

26. Ibid, 25.

27. DerridaMargins of Philosophy.
(Brighton: The Harvester Press, 1982), 6 and 13.

28. DerridaChora L Works , 19 and 10.

29. Ibid, 203.

30. Derrida, Positions , 94.

Wednesday, December 13, 2017


Filed under: General — Tags: , — m759 @ 2:04 AM

"The philosopher Jerry Fodor was important for the same reason
you’ve probably never heard of him: he was unimpressed,
to put it politely, by the intellectual trends of the day."

—  Stephen Metcalf in The New Yorker , Dec. 12, 2017

See also "The French Invasion," a Dec. 11 Quarterly Conversation
essay about Derrida in Baltimore in 1966, and the Dec. 10 posts
in this  journal tagged Interlacing Derrida. (The deplorable Derrida
trend is apparently still alive in Buffalo.)

According to Metcalf, Fodor's "occasional review-essays in the L.R.B. 
were masterpieces of a plainspoken and withering sarcasm. To Steven
Pinker’s suggestion that we read fiction because ' it supplies us with a
mental catalogue of the fatal conundrums we might face someday,' for
instance, Fodor replied, ' What if it turns out that, having just used the ring
that I got by kidnapping a dwarf to pay off the giants who built me my
new castle, I should discover that it is the very ring that I need in order to
continue to be immortal and rule the world? ' "

In the Fodor-Pinker dispute, my sympathies are with Pinker.

Related material — Google Sutra (the previous Log24 post) and earlier posts
found in a Log24 search for Ring + Bear + Jung —

Four Colours and Waiting for Logos.

Sunday, December 10, 2017


Google search result for Plato + Statesman + interlacing + interweaving

See also Symplectic in this journal.

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

The above symplectic  figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2). See also
related remarks on the notion of  linear  (or line ) complex
in the finite projective space PG(3,2) —

Anticommuting Dirac matrices as spreads of projective lines

Ron Shaw on the 15 lines of the classical generalized quadrangle W(2), a general linear complex in PG(3,2)


Filed under: General — Tags: — m759 @ 4:10 PM

See also The Derrida Reader: Writing Performances, edited by
Julian Wolfreys (U. of Nebraska Press, 1998), pages 112-113,
discussed here in the previous two posts, and this  journal on
1/12-1/13. Related material: Polytropos .


Filed under: General — Tags: — m759 @ 2:55 PM

Derrida quote from the previous post

See also Black + Algebra + Metaphor.

Interlacing, Interweaving

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

The above title should be sung to the following tune

"Right through hell
 there is a path…."
 — Malcolm Lowry,
Under the Volcano

Sunday, November 9, 2014


Filed under: General — Tags: , , , — m759 @ 11:00 AM

The Ideas

“We tell ourselves stories in order to live….
We interpret what we see, select the most workable
of multiple choices. We live entirely, especially if we
are writers, by the imposition of a narrative line upon
disparate images, by the ‘ideas’  with which we have
learned to freeze the shifting phantasmagoria
which is our actual experience.”
— Joan Didion

See Didion and the I Ching  and posts tagged Plato in China .

Wednesday, September 11, 2013

Language Game

Filed under: General — Tags: , — m759 @ 9:29 AM

In which Plato continues to thank the Academy.

From the Academy, a lead balloon for 9/11 —
continued from March First, 2002.

A search today for the name Eisenman
(see previous post) yields the following :

"We need a cameo from Plato, a safecracker,
a wrinkle or two to be ironed out, some ice,
some diamonds, and, above all, laughter
for this irony of ironies."

Jeffrey Kipnis, "Twisting the Separatrix,"
Assemblage  No. 14, April 1991, MIT Press

Friday, February 1, 2013

Get Quotes

Filed under: General — Tags: , — m759 @ 4:01 PM

For Tony Kushner fans:

For logic fans:

IMAGE- NY Times market quotes, American Express Gold Card ad, Kevin Spacey in 'House of Cards' ad

John Searle on Derrida:

On necessity, possibility, and 'necessary possibility'

In the box-diamond notation, the axiom Searle quotes is


"The euclidean property guarantees the truth of this." — Wikipedia

Linking to Euclid

Clicking on "euclidean" above yields another Wikipedia article

"In mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's 'Common Notion 1' in The Elements : things which equal the same thing also equal one another."

Verification: See, for instance, slides on modal logic at Carnegie Mellon University and modal logic at plato.stanford.edu.

Thursday, January 31, 2013

Scholarship in 1961…

Filed under: General,Geometry — m759 @ 12:00 PM

Before Derrida's writings on Plato and on inscription

A remark by the late William Harris:

"Scholarship has many dark ages, and they do not all fall
in the safe confines of remote antiquity."

For more about Harris, see the previous post.

Discussing an approach to solving a geometrical problem 
from section 86e of the Meno , Harris wrote that

"… this is a very important element of method and purpose,
one which must be taken with great seriousness and respect.
In fact it is as good an example of the master describing for us
his method as Plato ever gives us. Tricked by the appearance
of brevity and unwilling to follow through Plato's thought on
the road to Euclid, we have garbled or passed over a unique
piece of philosophical information."

Harris, though not a geometer, was an admirable man.
His remark on the Meno  method is itself worthy of respect.

In memory of Harris, Plato, and pre-Derrida scholarship, here
are some pages from 1961 on the problem Harris discussed.

A pair of figures from the 1961 pages indicates how one view of the
section 86e problem (at right below) resembles the better-known 
demonstration earlier in the Meno  of how to construct
a square of area 2 —

Tuesday, January 17, 2012

Manning and Khora

Filed under: General — m759 @ 1:26 AM

A weblog post from Saturday, Jan. 14, 2012—

"Today is the 120th anniversary of Cardinal Henry Edward Manning's death."

A Reluctant Sinner  (Thanks to Andrew Cusack for the link.)

If Manning is a saint, then Saturday was his feast day.

Some background— Manning in this journal.

See also Saturday's Derrida at Villanova. The link there to
previous posts on that topic leads to a post on Derrida's promotion
of his neologism différance as a version of Plato's khôra.

I prefer Manning's discussion of a closely related concept,
the scholastic philosophers' materia prima .

See Hugh R. King's 1956 paper sneering at the scholastics'
concept, and Heisenberg's much better-informed remarks
on the related concept of potentia

IMAGE- Excerpt from 'The Metaphysical Thought of Thomas Aquinas' by John F. Wippel

For a related fictional account of a religious quest for "possibilities"
and "excluded middles" between "zeroes and ones," see
Ingraffia on The Crying of Lot 49 .

Thursday, October 20, 2011

The Thing Itself

Filed under: General,Geometry — m759 @ 11:29 AM

Suggested by an Oct. 18 piece in the Book Bench section
of the online New Yorker  magazine—



Related material suggested by the "Shouts and Murmurs" piece
in The New Yorker , issue dated Oct. 24, 2011—

"a series of e-mails from a preschool teacher planning to celebrate
the Day of the Dead instead of Halloween…"

A search for Coxeter + Graveyard in this journal yields…

Coxeter exhuming Geometry

Here the tombstone says "GEOMETRY… 600 BC — 1900 AD… R.I.P."

A related search for Plato + Tombstone yields an image from July 6, 2007…

The image “http://www.log24.com/log/pix06A/061019-Tombstones.jpg” cannot be displayed, because it contains errors.

Here Plato's poems to Aster suggested
the "Star and Diamond" tombstone.

The eight-rayed star is an ancient symbol of Venus
and the diamond is from Plato's Meno .

The star and diamond are combined in a figure from
12 AM on September 6th, 2011—

The Diamond Star


See Configurations and Squares.

That webpage explains how Coxeter
united the diamond and the star.

Those who prefer narrative to mathematics may consult
a definition of the Spanish word lucero  from March 28, 2003.

Tuesday, August 30, 2011


Filed under: General — Tags: — m759 @ 11:07 AM

A comment yesterday on the New York Times  philosophy column “The Stone” quoted Karl Barth—

Man is the creature of the boundary between heaven and earth.”

See also Plato’s theory of ideas (or “forms”) and the I Ching

The eight trigrams are images not so much of objects as of states of change. This view is associated with the concept expressed in the teachings of Lao-tse, as also in those of Confucius, that every event in the visible world is the effect of an “image,” that is, of an idea in the unseen world. Accordingly, everything that happens on earth is only a reproduction, as it were, of an event in a world beyond our sense perception; as regards its occurrence in time, it is later than the suprasensible event. The holy men and sages, who are in contact with those higher spheres, have access to these ideas through direct intuition and are therefore able to intervene decisively in events in the world. Thus man is linked with heaven, the suprasensible world of ideas, and with earth, the material world of visible things, to form with these a trinity of the primal powers.

— Richard Wilhelm, Introduction to the I Ching

Thursday, July 15, 2010

Brightness at Noon, continued

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

"What exactly was Point Omega?"

This is Robert Wright in Nonzero: The Logic of Human Destiny.

Wright is discussing not the novel Point Omega  by Don DeLillo,
but rather a (related) concept of  the Jesuit philosopher Pierre Teilhard de Chardin.

My own idiosyncratic version of a personal "point omega"—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

For some other sorts of points, see the drawings
on the wall and Geometry Simplified

Image-- The trivial two-point affine space and the trivial one-point projective space, visualized

The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.

For related darkness  at noon, see Derrida on différance
as a version of Plato's khôra

(Click to enlarge.)

Image-- Fordham University Press on Derrida, differance, and khora

The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institutionDeconstruction in a Nutshell

Image-- A Catholic view of Derrida

For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.

Saturday, June 28, 2008

Saturday June 28, 2008

Filed under: General — Tags: — m759 @ 12:00 PM
The God Factor

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

The following poem of Emily Dickinson is quoted here in memory of John Watson Foster Dulles, a scholar of Brazilian history who died at 95 on June 23.  He was the eldest son of Secretary of State John Foster Dulles, a nephew of Director of Central Intelligence Allen Dulles, brother of Roman Catholic Cardinal Avery Dulles, and a grandson of Presbyterian minister Allen Macy Dulles, author of The True Church.

I asked no other thing,   
No other was denied.   
I offered Being for it;   
The mighty merchant smiled.   
Brazil? He twirled a button,           
Without a glance my way:   
"But, madam, is there nothing else   
That we can show to-day?"

"He twirled a button…."

Plato's diamond figure from the 'Meno'

The above figure
of Plato
(see 3/22)
was suggested by
Lacan's diamond
Lacan's lozenge - said by some to symbolize Derrida's 'differance'
(losange or poinçon)
as a symbol —
according to Frida Saal
of Derrida's
which is, in turn,
"that which enables and
results from Being itself"
—  according to
Professor John Lye

I prefer Plato and Dulles
to Lacan and Lye.

Wednesday, October 24, 2007

Wednesday October 24, 2007

Filed under: General — Tags: , — m759 @ 9:26 AM
A Story for Dobbs

Internet Movie Database on screenwriter Lem Dobbs:

Son of painter R.B. (Ron) Kitaj.

Took his pseudonym from the character Humphrey Bogart played
in 'The Treasure of the Sierra Madre.'"

Bogart and Robert Blake in The Treasure of the Sierra Madre

Click for details.

NY Lottery Oct. 21, 2007: Mid-day 512, Evening 430

October 21 was the day
that R. B. Kitaj died.
For what Kitaj called
"midrashic glosses"
on the numbers and
the lucky sums, see
4/30, 5/12, and
Eight is a Gate.

Screenwriter Joan Didion:

"We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling."

David Cohen on R. B. Kitaj:

"He has come to be fascinated… by the kabbalah, finding in it parallels to the world of art and ideas. Every morning, after a long walk, he winds up at a Westwood café surrounded by pretty UCLA students where he studies the writings of Emmanuel Levinas, before working for an hour on his memoirs."

Levinas Adieu:

Levinas, and Derrida, on the Adieu

Click for source.

"There is no teacher
but the enemy.

— Orson Scott Card,  
Ender's Game

Tuesday, June 19, 2007

Tuesday June 19, 2007

Filed under: General — m759 @ 11:49 AM
Let No Man Write
My Epitaph

— Title of a novel
by Willard Motley

“Recall the passage in the Odyssey when he [Ulysses] encounters the Cyclops Polyphemos. Trying to disguise himself, to hide himself, Ulysses calls himself Outis– nobody, no man, personne. Here, in a strategy of simple erasure, the Subject masks his singularity behind no one, das Man (here in a sense that does not depend on the Heidggerian distinction between the authentic Dasein and the inauthentic das Man). In French, Outis is translated as personne, meaning no one, no particular subject.”

— Jacques Derrida, “Summary of Impromptu Remarks,” pp. 39-45 in Anyone, ed. by Cynthia Davidson (New York: Rizzoli International, 1991)

“In A GOOD YEAR, more than one reference is made to the secret of comedy. It’s all in the timing, two characters explain.” —Review at epinions.com

Time of this entry:


Wednesday, December 13, 2006

Wednesday December 13, 2006

Filed under: General — m759 @ 9:29 AM

 Best Wishes for a
C. S. Lewis


 C.S. Lewis

Image of Lewis from
Into the Wardrobe

What on earth
  is a concrete

— Robert M. Pirsig, author of Zen and the Art of Motorcyle Maintenance

For one approach to an answer, click on the picture at left.

Update of 4:23 PM:

The Lewis link above deals with the separation of Heaven from Hell.  The emphasis is on Heaven.  A mysterious visitor to this website, “United States,” seems to be seeking equal time for Hell.  And so…


Based on Xanga footprints of Dec. 13, 2006
from m759’s site-visitor “United States”
(possibly a robot; if so, a robot with strange tastes).

TIME OF     DATE OF             PAGE VISITED   

1217 040520  Parable
1218 060606  The Omen
1220 051205  Don’t Know Much About History
1225 030822  Mr. Holland’s Week (And in Three Days…)
1233 030114  Remarks on Day 14 (What is Truth?)
1238 040818  Train of Thought (Oh, My Lolita)
1244 020929  Angel Night (Ellis Larkins)
1249 040715  Identity Crisis (Bourne and Treadstone)
1252 050322  Make a Differance (Lacan, Derrida, Reba)
1255 050221  Quarter to Three on Night of HST’s death
1256 040408  Triple Crown on Holy Thursday
1258 040714  Welcome to Mr. Motley’s Neighborhood
1258 030221  All About Lilith
0103 040808  Quartet (for Alexander Hammid)
0104 030106  Dead Poet in the City of Angels
0109 030914  Skewed Mirrors (Readings on Aesthetics)
0110 050126  A Theorem in Musical Form
0125 021007  Music for R. D. Laing
0138 020806  Butterflies & Popes (Transfiguration)
0140 060606  The Omen (again)
0156 030313  ART WARS: Perennial Tutti-Frutti
0202 030112  Ask Not (A Bee Gees Requiem)
0202 050527  Drama of the Diagonal, Part Deux
0202 060514  STAR WARS continued (Eclipse and Venus)
0207 030112  Ask Not (again… Victory of the Goddess)
0207 030221  All About Lilith (again… Roll credits.)

“How much story do you want?”
— George Balanchine

Monday, October 9, 2006

Monday October 9, 2006

Filed under: General,Geometry — m759 @ 9:00 AM
To Apollo
The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
Balanchine's Birthday

Art Theory for Yom Kippur

A Form

A Form, continued

Deep Game
Gameplayers of Zen
And So To Bed
Translation Plane for Rosh Hashanah
Derrida Dead
The Nine
From Tate to Plato
Art History
A Miniature Rosetta Stone
High Concept
High Concept, Continued
Analogical Train of Thought
Today's Sermon: Magical Thinking
Seven is Heaven, Eight is a Gate
Nine is a Vine
Apollo and Christ
Hamilton's Whirligig
On Beauty
Sunday Morning
New Haven
Washington Ballet
Catholic Schools Sermon
The Logic of Apollo
Game Boy
Art Wars Continued: The Krauss Cross
Art Wars Continued: Pandora's Box
The Pope in Plato's Cave
Today's Birthdays
Symbology 101

Friday, March 31, 2006

Friday March 31, 2006

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

Women's History Month continues…
Ontology Alignment

"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally.  To understand who Michael Laski is you must have a feeling for that kind of compulsion."

— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)

"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.

— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996

"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….

Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real."

— Rebecca Goldstein,
Mathematics and
the Character of Tragedy

Thursday, August 11, 2005

Thursday August 11, 2005

Filed under: General,Geometry — 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, June 6, 2005

Monday June 6, 2005

Filed under: General — m759 @ 1:00 PM

Order and Disorder

From “Connoisseur of Chaos,”
by Wallace Stevens, in
Parts of a World, 1942:


A.  A violent order is a disorder; and
B.  A great disorder is an order.
    These Two things are one. (Pages of illustrations.)               


A.  Well, an old order is a violent one. This proves nothing.
    Just one more truth, one more
    Element in the immense disorder of truths.

B.  It is April as I write. The wind
    Is blowing after days of constant rain.
    All this, of course, will come to summer soon.
    But suppose the disorder of truths should ever come
    To an order, most Plantagenet, most fixed. . . .
    A great disorder is an order.
    Now, A And B are not like statuary, posed
    For a vista in the Louvre. They are things chalked
    On the sidewalk so that the pensive man may see.


    The pensive man . . . He sees that eagle float
    For which the intricate Alps are a single nest.

Related material:
Derrida on Plato on writing says ‘In order for these contrary values (good/evil, true/false, essence/appearance, inside/outside, etc.) to be in opposition, each of the terms must be simply EXTERNAL to the other, which means that one of these oppositions (the opposition between inside and outside) must already be accredited as the matrix of all possible opposition.’ “

Peter J. Leithart

See also

Skewed Mirrors,
Sept. 14, 2003

“Evil did not  have the last word.”
Richard John Neuhaus, April 4, 2005

Lps. The keys to. Given! A way a lone
a last a loved a long the


“There is never any ending to Paris.”
— Ernest Hemingway

Tuesday, April 5, 2005

Tuesday April 5, 2005

Filed under: General,Geometry — Tags: — m759 @ 3:17 PM
Art History:
The Pope of Hope

At the Vatican on
Shakespeare's Birthday
(See Log24.net,
Oct. 4, 2002)

See also the iconology
what Dan Brown in
The Da Vinci Code
  calls "symbology" —
of Pandora's Box
at Log24.net,
March 10, 2005:

The image “http://www.log24.com/log/pix05/050310-Nell2.jpg” cannot be displayed, because it contains errors.


"Man and woman are a pair of locked caskets,
each containing the key to the other."

Baroness Karen Blixen

"Karol Wojtyla had looked into
the heart of darkness–
and at the heart of darkness
discovered reason
for an indomitable hope.

He lived on the far side of
the greatest catastrophe
in human history,
the death of the Son of God,
and knew that evil
did not have the last word.
This is the key…."

Richard John Neuhaus,
April 4, 2005

The image “http://www.log24.com/log/pix05/050405-JoyceGeometry.gif” cannot be displayed, because it contains errors.

Finnegans Wake, p. 293,
"the lazily eye of his lapis"


The image “http://www.log24.com/log/pix05/050403-StPetersSq3.jpg” cannot be displayed, because it contains errors.


Perette Elizabeth Michelli on the Ovato Tondo:


"Notice how the Pope turns out to be
at the center of the breaking and
redefining of the Classical system."

"Derrida on Plato on writing says 'In order for these contrary values (good/evil, true/false, essence/appearance, inside/outside, etc.) to be in opposition, each of the terms must be simply EXTERNAL to the other, which means that one of these oppositions (the opposition between inside and outside) must already be accredited as the matrix of all possible opposition.' "

Peter J. Leithart

See also

Skewed Mirrors
Sept. 14, 2003

"Evil did not  have the last word."
Richard John Neuhaus, April 4, 2005

Lps. The keys to. Given! A way a lone
a last a loved a long the


"There is never any ending to Paris."
— Ernest Hemingway

For the first word, see Louis Armand on
Lethe, erinnerung, and riverrun.

See also the following passage,
linked to on the Easter Vigil, 2005:

  You will find to the left of the House of Hades
    a spring,
  And by the side thereof standing
    a white cypress.
  To this spring approach not near.
  But you shall find another,
    from the lake of Memory
  Cold water flowing forth, and there are
    guardians before it.
  Say, "I am a child of Earth and starry Heaven;
  But my race is of Heaven alone.
    This you know yourselves.
  But I am parched with thirst and I perish.
    Give me quickly
  The cold water flowing forth
    from the lake of Memory."

Tuesday, March 22, 2005

Tuesday March 22, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 4:01 PM

Make a Différance

From Frida Saal's
Lacan The image “http://www.log24.com/log/pix05/050322-Diamond.gif” cannot be displayed, because it contains errors. Derrida:

"Our proposal includes the lozenge (diamond) in between the names, because in the relationship / non-relationship that is established among them, a tension is created that implies simultaneously a union and a disjunction, in the perspective of a theoretical encounter that is at the same time necessary and impossible. That is the meaning of the lozenge that joins and separates the two proper names. For that reason their respective works become totally non-superposable and at the same time they were built with an awareness, or at least a partial awareness, of each other. What prevails between both of them is the différance, the Derridean signifier that will become one of the main issues in this presentation."


From a Contemporary Literary Theory website:

"Différance is that which all signs have, what constitutes them as signs, as signs are not that to which they refer: i) they differ, and hence open a space from that which they represent, and ii) they defer, and hence open up a temporal chain, or, participate in temporality. As well, following de Sassure's famous argument, signs 'mean' by differing from other signs. The coined word 'différance' refers to at once the differing and the deferring of signs. Taken to the ontological level†, the differing and deferring of signs from what they mean, means that every sign repeats the creation of space and time; and ultimately, that différance is the ultimate phenomenon in the universe, an operation that is not an operation, both active and passive, that which enables and results from Being itself."

From a text purchased on
Make a Difference Day, Oct. 23, 1999:

The image “http://www.log24.com/log/pix05/050322-Fig39.gif” cannot be displayed, because it contains errors.22. Without using the Pythagorean Theorem prove that the hypotenuse of  an isosceles right triangle will have the length The image “http://www.log24.com/log/pix05/050322-Sqtr2.gif” cannot be displayed, because it contains errors.  if the equal legs have the length 1.  Suggestion: Consider the similar triangles in Fig. 39.
23.  The ancient Greeks regarded the Pythagorean Theorem as involving areas, and they proved it by means of areas.  We cannot do so now because we have not yet considered the idea of area.  Assuming for the moment, however, the idea of the area of a square, use this idea instead of similar triangles and proportion in Ex. 22 above to show that x = The image “http://www.log24.com/log/pix05/050322-Sqtr2.gif” cannot be displayed, because it contains errors. .


— Page 98 of Basic Geometry, by George David Birkhoff, Professor of Mathematics at Harvard University, and Ralph Beatley, Associate Professor of Education at Harvard University (Scott, Foresman 1941)

Though it may be true, as the president of Harvard recently surmised, that women are inherently inferior to men at abstract thought — in particular, pure mathematics*  — they may in other respects be quite superior to men:

The image “http://www.log24.com/log/pix05/050322-Reba2.jpg” cannot be displayed, because it contains errors.

The above is from October 1999.
See also Naturalized Epistemology,
from Women's History Month, 2001.

* See the remarks of Frida Saal above and of Barbara Johnson on mathematics (The Shining of May 29, cited in Readings for St. Patrick's Day).

† For the diamond symbol at "the ontological level," see Modal Theology, Feb. 21, 2005.  See also Socrates on the immortality of the soul in Plato's Meno, source of the above Basic Geometry diamond.

Sunday, December 12, 2004

Sunday December 12, 2004

Filed under: General — Tags: — m759 @ 7:59 PM

Ideas, Stories, Values:
Literati in Deep Confusion

Joan Didion, The White Album:

“We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas‘ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”

Interview with Joseph Epstein:

“You can do in stories things that are above those in essays,” says Epstein.  “In essays and piecework, you are trying to make a point, whereas in stories you are not quite sure what the point is. T.S. Eliot once said of Henry James, ‘He had a mind so fine no idea could violate it,’ which, I think, is the ultimate compliment for an author. Stories are above ideas.”

Harvard President Lawrence H. Summers, Sept. 12, 2004:

“You are entering a remarkable community, the Harvard community. It is a community built on the idea of searching for truth… on the idea of respect for others….

… we practice the values we venerate. The values of seeking truth, the values of respecting others….”

Paul Redding on Hegel:

“… Hegel discusses ‘culture’ as the ‘world of self-alienated spirit.’ The idea seems to be that humans in society not only interact, but that they collectively create relatively enduring cultural products (stories, dramas, and so forth) within which they can recognise their own patterns of life reflected.”

The “phantasmagoria” of Didion seems related to the “phenomenology” of Hegel…

From Michael N. Forster,  Hegel’s Idea of a Phenomenology of Spirit:

“This whole system is conceived, on one level at least, as a defense or rational reworking of the Christian conception of God.  In particular, its three parts are an attempt to make sense of the Christian idea of a God who is three in one — the Logic depicting God as he is in himself, the Philosophy of Nature God the Son, and the Philosophy of Spirit God the Holy Spirit.”

and, indeed, to the phenomenology of narrative itself….

From Patrick Vert,
The Narrative of Acceleration:

“There are plenty of anecdotes to highlight the personal, phenomenological experience of railway passage…

… a unique study on phantasmagoria and the history of imagination. The word originates [in] light-projection, the so-called ghost-shows of the early 19th century….

… thought becomes a phantasmagorical process, a spectral, representative location for the personal imagination that had been marginalized by scientific rationalism….

Truly, ‘immediate experience is [or becomes] the phantasmagoria of the idler’ [Walter Benjamin, The Arcades Project.  Cambridge: Harvard University Press, 1999.  Page 801.]….

Thought as phantasm is a consequence of the Cartesian split, and… a further consequence to this is the broad take-over of perceptual faculty…. What better example than that of the American railway?  As a case-study it offers explanation to the ‘phantasmagoria of the idler’….

This phantasmagoria became more mediated over time…. Perception became increasingly visually oriented…. As this occurred, a narrative formed to encapsulate the phenomenology of it all….”

For such a narrative, see
the Log24.net entries of

November 5, 2002, 2:56 AM,
November 5, 2002, 6:29 AM,
January 3, 2003, 11:59 PM,
August 17, 2004, 7:29 PM,
August 18, 2004, 2:18 AM,
August 18, 2004, 3:00 AM, and
November 24, 2004, 10:00 AM.

Tuesday, April 6, 2004

Tuesday April 6, 2004

Filed under: General — Tags: , — m759 @ 10:00 PM

Ideas and Art, Part III

The first idea was not our own.  Adam
In Eden was the father of Descartes…

— Wallace Stevens, from
Notes Toward a Supreme Fiction

“Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito.”

Descartes, Meditationes III, 5

“Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God.”

Descartes, Meditations III, 5

Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.

You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.

— Wallace Stevens, from
Notes Toward a Supreme Fiction

“… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse.”

Descartes, Meditationes III, 11

“… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike.”

Descartes, Meditations III, 11

“Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective.”

Descartes, Meditationes III, 15

“And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act].”

Descartes, Meditations III, 15

Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction,”

The Quest for the Fiction of the Absolute:

“Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: “The poem goes from the poet’s gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?” The poet, the creator-figure, the shadowy god-figure, is elided, evading us, “as in a senseless element.”  The poet seeks to find the transcendent in the immanent, the general in the particular, trying “by a peculiar speech to speak / The peculiar potency of the general.” In playing on the senses of “peculiar” as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract.”

Brian Cronin in Foundations of Philosophy:

“The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight.”

— From Ch. 2, Identifying Direct Insights

Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction“:

“The fourth canto returns to the theme of opposites. ‘Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.’  Change resulting from a meeting of opposities is at the root of Taoism: ‘Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things’ (Tao Te Ching 42) ….”

From an entry of March 7, 2004

From the web page

Introduction to the I Ching–
By Richard Wilhelm

“He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the ‘great primal beginning’ of all that exists, t’ai chi — in its original meaning, the ‘ridgepole.’ Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t’ai chi was represented by the circle divided into the light and the dark, yang and yin,


This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites.”

The t’ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that

“W.J.T. Mitchell calls ‘iconology’
a study of the ‘logos’
(the words, ideas, discourse, or ‘science’)
of ‘icons’ (images, pictures, or likenesses).
It is thus a ‘rhetoric of images’
(Iconology: Image, Text, Ideology, p. 1).”

A variation on the t’ai chi symbol appears in a log24.net entry for March 5:

The Line,
by S. H. Cullinane

See too my web page Logos and Logic, which has the following:

“The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics.”

— Simone Weil, Oeuvres Choisies, ed. Quarto, Gallimard, 1999, p. 100

 Logos Alogos,
by S. H. Cullinane 

In the conclusion of Section 3, Canto X, of “Notes,” Stevens says

“They will get it straight one day
at the Sorbonne.
We shall return at twilight
from the lecture
Pleased that
the irrational is rational….”

This is the logoi alogoi of Simone Weil.

In “Notes toward a Supreme Fiction,”
Wallace Stevens lists three criteria
for a work of the imagination:

It Must Be Abstract

The Line,
by S.H. Cullinane 

It Must Change

 The 24,
by S. H. Cullinane

It Must Give Pleasure

by S. H. Cullinane

Related material:

Logos and Logic.


Friday, July 25, 2003

Friday July 25, 2003

Filed under: General,Geometry — m759 @ 11:59 PM

Realism in Literature:
Under the Volcano

Mexican Volcano Blast
Scares Residents


Filed at 11:13 p.m. EDT Friday, July 25, 2003

PUEBLA, Mexico (AP) — Mexico’s Popocatepetl volcano shot glowing rock and ash high into the air Friday night, triggering a thunderous explosion that panicked some residents in nearby communities.

Here are 3 webcam views of the volcano.   Nothing to see at the moment.

Literary background:

Malcolm Lowry’s Under the Volcano,

Plato, Pegasus, and the Evening Star,

A Mass for Lucero,

Shining Forth,

and, as background for today’s earlier entry on Platonism and Derrida,

The Shining of May 29.


For more on Plato and Christian theology, consult the highly emotional site

Further Into the Depths of Satan:

“…in The Last Battle on page 170 [C. S.] Lewis has Digory saying, ‘It’s all in Plato, all in Plato.’ Now, Lewis calls Plato ‘an overwhelming theological genius’ (Reflections on the Psalms, p. 80)….”

The title “Further Into the Depths of Satan,” along with the volcano readings above, suggests a reading from a related site:

Gollum and the Mystery of Evil:

“Gollum here clearly represents Frodo’s hidden self. It is ‘as if we are witnessing the darkest night of the soul and one side attempting to master the other’ (Jane Chance 102). Then Frodo, whose finger has been bitten off, cries out, and Gollum holds the Ring aloft, shrieking: ‘Precious, precious, precious! My Precious! O my Precious!’ (RK, VI, 249). At this point, stepping too near the edge, he falls into the volcano, taking the Ring with him. With this, the mountain shakes.’ “

In the above two-step vignette, the part of Gollum is played by the author of “Further Into the Depths of Satan,” who called  C. S. Lewis a fool “that was and is extremely useful to his father the devil.”

See Matthew 5:22: “…whosoever shall say, Thou fool, shall be in danger of hell fire.” 

Friday July 25, 2003

Filed under: General — 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.

Monday, March 24, 2003

Monday March 24, 2003

Filed under: General — m759 @ 12:52 PM

Orwell’s question, according to
an admirer of leftist Noam Chomsky:

“When so much of the BS is right out in the open,
why is it that we know so little about it?
Why don’t we see what’s right in front of our eyes?”

Deep Chomsky:
Lying, Truth-Telling,
and the Social Order

“First of all, I’d like to thank the Academy….”
— Quotation attributed to Plato

The New Yorker of March 31, 2003, discusses leftist academic Noam Chomsky.  The online edition provides a web page listing pro-Chomsky links.

Chomsky’s influence is based in part on the popularity of his half-baked theories on linguistics, starting in the 1950’s with “deep structure” and “transformational,” or “generative,” grammar.

Chomsky has abandoned many of his previous ideas and currently touts what he calls The Minimalist Program.

For some background on Chomsky’s recent linguistic notions, see the expository essay “Syntactic Theory,” by Elly van Gelderen of the Arizona State University English Department.  Van Gelderen lists her leftist political agenda on her “Other Interests” page.  Her department may serve as an example of how leftists have converted many English departments in American universities to propaganda factories.

Some attacks on Chomsky’s scholarship:

The Emperor’s New Linguistics

The New Grammarians’ Funeral

Beyond Chomsky

Could Chomsky Be Wrong? 

Forty-four Reasons Why the Chomskians Are Mistaken

Call for Papers, Chomsky 2003

Chomsky’s (Mis)Understanding of Human Thinking

Anatomy of a Revolution… Chomsky in 1962

…Linguistic Theory: The Rationality of Noam Chomsky

A Bibliography

Some attacks on Chomsky’s propaganda:

LeftWatch.com Chomsky page

Destructive Generation excerpt

The Sick Mind of Noam Chomsky

Partners in Hate: Noam Chomsky and the Holocaust Deniers

Chomsky and Plato’s Diamond

Like another purveyor of leftist nonsense, Jacques Derrida, Chomsky is fond of citing Plato as a precedent.  In particular, what Chomsky calls “Plato’s problem” is discussed in Plato’s Meno.  For a look at the diamond figure that plays a central role in that dialogue, see Diamond Theory.  For an excellent overview of related material in Plato, see Theory of Forms.

Sunday, September 22, 2002

Sunday September 22, 2002

Filed under: General,Geometry — Tags: , , , — m759 @ 8:02 PM

Force Field of Dreams

Metaphysics and chess in today’s New York Times Magazine:

  • From “Must-See Metaphysics,” by Emily Nussbaum:

    Joss Whedon, creator of a new TV series —

    “I’m a very hard-line, angry atheist” and
    “I want to invade people’s dreams.”

  • From “Check This,” by Wm. Ferguson:

    Garry Kasparov on chess —

    “When the computer sees forced lines,
    it plays like God.”

Putting these quotations together, one is tempted to imagine God having a little game of chess with Whedon, along the lines suggested by C. S. Lewis:

As Lewis tells it the time had come for his “Adversary [as he was wont to speak of the God he had so earnestly sought to avoid] to make His final moves.” (C. S. Lewis, Surprised by Joy, Harcourt, Brace, and World, Inc., 1955, p. 216) Lewis called them “moves” because his life seemed like a chess match in which his pieces were spread all over the board in the most disadvantageous positions. The board was set for a checkmate….

For those who would like to imagine such a game (God vs. Whedon), the following may be helpful.

George Steiner has observed that

The common bond between chess, music, and mathematics may, finally, be the absence of language.

This quotation is apparently from

Fields of Force:
Fischer and Spassky at Reykjavik
. by George Steiner, Viking hardcover, June 1974.

George Steiner as quoted in a review of his book Grammars of Creation:

“I put forward the intuition, provisional and qualified, that the ‘language-animal’ we have been since ancient Greece so designated us, is undergoing mutation.”

The phrase “language-animal” is telling.  A Google search reveals that it is by no means a common phrase, and that Steiner may have taken it from Heidegger.  From another review, by Roger Kimball:

In ”Grammars of Creation,” for example, he tells us that ”the classical and Judaic ideal of man as ‘language animal,’ as uniquely defined by the dignity of speech . . . came to an end in the antilanguage of the death camps.”

This use of the Holocaust not only gives the appearance of establishing one’s credentials as a person of great moral gravity; it also stymies criticism. Who wants to risk the charge of insensitivity by objecting that the Holocaust had nothing to do with the ”ideal of man as ‘language animal’ ”?

Steiner has about as clear an idea of the difference between “classical” and “Judaic” ideals of man as did Michael Dukakis. (See my notes of September 9, 2002.)

Clearly what music, mathematics, and chess have in common is that they are activities based on pure form, not on language. Steiner is correct to that extent. The Greeks had, of course, an extremely strong sense of form, and, indeed, the foremost philosopher of the West, Plato, based his teachings on the notion of Forms. Jews, on the other hand, have based their culture mainly on stories… that is, on language rather than on form. The phrase “language-animal” sounds much more Jewish than Greek. Steiner is himself rather adept at the manipulation of language (and of people by means of language), but, while admiring form-based disciplines, is not particularly adept at them.

I would argue that developing a strong sense of form — of the sort required to, as Lewis would have it, play chess with God — does not require any “mutation,” but merely learning two very powerful non-Jewish approaches to thought and life: the Forms of Plato and the “archetypes” of Jung as exemplified by the 64 hexagrams of the 3,000-year-old Chinese classic, the I Ching.

For a picture of how these 64 Forms, or Hexagrams, might function as a chessboard,

click here.

Other relevant links:

“As you read, watch for patterns. Pay special attention to imagery that is geometric…”


from Shakhmatnaia goriachka

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