Thursday, March 8, 2018

Women’s Day: The Hateful Eight

Filed under: General — m759 @ 10:45 AM

The image “http://www.log24.com/log/pix05B/051202-Axe.jpg” cannot be displayed, because it contains errors.

— From Katherine Neville's novel The Eight  (1988)

Related logic —

Nothing Fails Like Success, by Barbara Johnson

Enlarge the above.  Detail:

Barbara Johnson, Nothing Fails Like Success, detail

Friday, May 30, 2014

Matching Theory

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

Some mathematical background for yesterday’s
remarks “For the Bregnans” and “Lost in Translation“—

Matching Theory: A Sampler, from Dénes König
to the Present
,” by Michael D. Plummer, 1991.

See also Matching Theory  by Plummer and Lovász.

Thursday, May 29, 2014

Lost in Translation

Filed under: General — Tags: , — m759 @ 1:45 PM

IMAGE- Original French of text from 'The Shining of May 29'

Translation by Barbara Johnson:

"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 ."

In the original:

"situés sur des lignes ou des colonnes distinctes "

Update of 11:30 PM ET May 29, 2014:

Derrida in 1972 was quoting Philippe Sollers, Nombres
(Paris: Éditions du Seuil , 1968).  Sollers in turn was
perhaps quoting A. Kaufmann, Méthodes et Modèles
de la Recherche Opérationnelle , Paris, Dunod , 1964,
L'Économie d'Entreprise 10 , vol. 2, page 305:

"Le nombre minimal de rangées
(lignes et/ou colonnes) contenant
tous les zéros d'une matrice, est égal
au nombre maximal de zéros
sur des lignes et des colonnes distinctes."

Sunday, September 26, 2010

After the Fall

Filed under: General — m759 @ 10:09 AM

The Harvard Crimson —

Magic of Numbers:
Summing Up the Fall

Published by Timothy J. Walsh on September 24, 2010 at 8:41AM

Each Thursday, The Crimson will compile a series of unique statistics
about Harvard's sports scene. Welcome to the Magic of Numbers—
without the problem sets. We'll do the math for you.


Saturday night's game… Harvard vs. Brown at Providence—

Harvard 14, Brown 29.

Related philosophy about divine providence—


See also, from 2002, a note on "light inclosed in the dark" versus the late Harvard philosopher Barbara Johnson.

For some context on Harvard and "the Magic of Numbers" see Summer Reading from 2007.

Thursday, July 1, 2010

Plato’s Code

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

John Allen Paulos yesterday at Twitter

"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."

The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.

I prefer a different approach to Plato that is
related to the following hoax and hype—


From Dan Brown's novel Angels & Demons  (2000)

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397


Image-- From 'Alchemy,' by Holmyard, the diamond of Aristotle's 4 elements and 4 qualities

This  four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.

For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.

Although an author like Brown might spin the remarks
below into a narrative—  The Plato Code — they are
neither  hoax nor hype.


Image-- From the Diamond in Plato's Meno to Modern Finite Geometry



For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.

Those who prefer  hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's  "The Stone" columnNancy Bauer.

Image-- The Philosophers' Stone according to The New York Times

— The New York Times

Tuesday, February 16, 2010

Mysteries of Faith

Filed under: General,Geometry — m759 @ 9:00 AM

From today's NY Times


Obituaries for mystery authors
Ralph McInerny and Dick Francis

From the date (Jan. 29) of McInerny's death–

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"

Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson

From the date (Feb. 14) of Francis's death–

2x2x2 cube

The EIghtfold Cube

The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.

This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.

For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
  and the death of Coxeter–

Putting Descartes Before Dehors

     Binary coordinates for a 4x2 array  Chess knight formed by a Singer 7-cycle

For a more Protestant meditation,
see The Cross of Descartes


Descartes's Cross

"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke

For further details, click on
the image below–

Quine and Derrida at Notre Dame Philosophical Reviews

Notre Dame Philosophical Reviews

Friday, January 29, 2010

More Glass

Filed under: General — m759 @ 12:00 PM

Part I:

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.' She shows deftly and delicately that the void inside Keats’s urn, Heidegger’s jug, or Wallace Stevens’s jar forms the center around which we tend to organize our worlds."

Harvard University Press on Persons and Things (April 30, 2008), by Barbara Johnson

Part II:

"Did you see more glass?"

Louis Kahn, design for nine large glass cubes forming a Holocaust memorial

Part III:

From the date of Barbara Johnson's death:

"Mathematical relationships were
enough to satisfy him, mere formal
relationships which existed at
all times, everywhere, at once."

Broken Symmetries, 1983


The X's refer to the pattern on the
cover of a paperback edition
  of Nine Stories, by J. D. Salinger.
Salinger died on Wednesday.

"You remember that book he sent me
from Germany? You know–
those German poems.

In Germany, Wednesday was
Holocaust Memorial Day, 2010.

Tuesday, January 26, 2010


Filed under: General,Geometry — Tags: — m759 @ 9:00 PM

From this journal:

Friday December 5, 2008

m759 @ 1:06 PM
Mirror-Play of
the Fourfold

For an excellent commentary
 on this concept of Heidegger,

View selected pages
from the book

Dionysus Reborn:

Play and the Aesthetic Dimension
in Modern Philosophical and
Scientific Discourse

(Mihai I. Spariosu,
Cornell U. Press, 1989)

Related material:
the logo for a
web page

Logo for 'Elements of Finite Geometry'

– and Theme and Variations.

Transition to the
Garden of Forking Paths–

(See For Baron Samedi)–

The Found Symbol
Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–

Pages 354-355
On the mirror-play of the fourfold

Pages 356-357
Shaking up a whole culture

Pages 358-359
Cornerstone and crossroads

Pages 360-361
A deep impression embedded in stone

Pages 362-363
A certain Y, a certain V

Pages 364-365
The world is Zeus's play

Page 366
It was necessary to begin again


Tuesday, September 15, 2009

Tuesday September 15, 2009

Filed under: General — m759 @ 2:02 PM
In memory of
Harvard literature professor
Barbara Ellen Johnson
(Oct. 4, 1947 –
 Aug. 27, 2009)

“…one has to be willing
to tolerate ambiguity,
even to be crazy.”

“Bohr’s words?”

“The party line….”

— Quotation from
Secret Passages linked to on
 the date of Johnson’s death

“Yes and no (what else?).”
Barbara Johnson in
The Wake of Deconstruction

Related material:

Harvard Crimson obituary
and a
Funeral Service obituary
with comments.

For more on ambiguity,
see this journal’s entries of
 March 7, 8, and 9, 2007.

For more on craziness,
see this journal’s entries of
March 10, 2007.

Monday, January 19, 2009

Monday January 19, 2009

Filed under: General — m759 @ 8:48 AM
The Return of
The Purloined Letter

“The letter acts like a signifier precisely to the extent that its function in the story does not require that its meaning be revealed.”

Barbara Johnson, “The Frame of Reference,” an essay on a story by Poe

Sarge in Beetle Bailey 1/19/09: 'They say a picture is worth a thousand words.'

E is for Everlast:

Hilary Swank in 'Million Dollar Baby'

As for Johnson’s title,
“The Frame of Reference,”
see the window above,
Epiphany 2007, and
Church of the
Forbidden Planet.

Happy birthday,
Edgar Allan Poe.

Friday, May 4, 2007

Friday May 4, 2007

Filed under: General — 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.'

Thursday, March 8, 2007

Thursday March 8, 2007

Filed under: General — m759 @ 7:13 PM
Introduction to Logic
for International Women’s Day

“The logic behind such utterances is the logic
of binary opposition, the principle of non-contra-
diction, 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.”

Harvard professor Barbara Johnson
in “Nothing Fails Like Success.”
(See the previous entry, Day Without Logic.)

The 16 Binary Connectives, with Venn Diagrams

Click to enlarge.

Those who value literary theory
more than they value truth
may prefer, on this
International Women’s Day,
the “mandorla” interpretation
of the above diagrams.

For this interpretation, see
Death and the Spirit III,
Burning Bright,
The Agony and the Ya-Ya.

Thursday March 8, 2007

Filed under: General,Geometry — m759 @ 1:00 PM
Day Without

The image “http://www.log24.com/log/pix06A/060804-DWA2.gif” cannot be displayed, because it contains errors.

Symbol of the Dec. 1
Day Without Art

This resembles the following symbol,
due to logician Charles Sanders Peirce,
of the logic of binary opposition:

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

(For futher details on the role
of this symbol in logic, see
Chinese Jar Revisited.)

On this, International Women’s Day,
we might also consider the
widely quoted thoughts on logic of
Harvard professor Barbara Johnson:

Nothing Fails Like Success, by Barbara Johnson


Barbara Johnson, Nothing Fails Like Success, detail

“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.”

It may also be of interest on
International Women’s Day
that in the “box style” I Ching
(suggested by a remark of
Jungian analyst
Marie-Louise von Franz)
the symbol

The image “http://www.log24.com/theory/images/PeirceBox.bmp” cannot be displayed, because it contains errors.
Hexagram 2,
The Receptive.

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.

Thursday, March 17, 2005

Thursday March 17, 2005

Filed under: General — m759 @ 12:00 PM

Readings for
St. Patrick’s Day

Time of this entry: 12:00:36 PM.


  1. A commentary on “Darkening of the Light,” the I Ching, Hexagram 36:
  2. “Here the climax of the darkening is reached. The dark power at first held so high a place that it could wound all who were on the side of good and of the light. But in the end it perishes of its own darkness, for evil must itself fall at the very moment when it has wholly overcome the good, and thus consumed the energy to which it owed its duration.”

  3. Darkness at Noon, by Arthur Koestler

  4. Under Western Eyes, by Joseph Conrad
  5. Narrativity: Theory and Practice, by Philip John Moore Sturgess

    Sturgess’s book deals with the narrative logic of the above novels by Koestler and Conrad, as well as some Irish material:

    Narrativity: Theory and Practice
    Pt. I The Theory of Narrativity
    Introduction 3
    1 Narrativity and its Definitions 5
    2 A Logic of Narrativity 28
    3 Narrativity and Double Logics 68
    4 Narrativity and the Case against Contradiction 93
    5 Narrativity, Structure, and Spatial Form 117
    6 Narrativity and the French Perspective 139
    Pt. II The Practice of Narrativity
    Introduction 161
    7 The Logic of Duplicity and Design in Under Western Eyes 166
    8 A Story of Narrativity in Ulysses 189
    9 Narrative Despotism and Metafictional Mastery: The Case of Flann O’Brien’s At Swim-Two-Birds 235
    10 A Double Logic and the Nightmare of Reason: Arthur Koestler’s Darkness at Noon 260
    Conclusion. A Reading of Maria Edgeworth’s Castle Rackrent 287
    Bibliography and Further Reading 312
    Index 317

These readings are in opposition to the works of Barbara Johnson published by Harvard University Press.

For some background, see The Shining of May 29 (JFK’s birthday).

Discussion question:
In the previous entry, who represents the
Hexagram 36 “dark power” Matory or Summers?

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