Log24

See the title phrase and Ice 9 in this journal.

From the screenplay of "The Number 23"—

INT. NATHANIEL'S INSTITUTE, STAIRWELL – NIGHT

Agatha climbs a dark staircase. Layers of dust

testify to years of neglect.

INT. 3RD FLOOR CORRIDOR – CONTINUOUS

Agatha finds ROOM 318. A rusting door plaque reads,

"DR. SIRIUS LEARY, M.D. PSYCHIATRY."

For related material, see "Leary + Cuernavaca" and "Prime Cut."

Happy belated 2/3 birthday to Walter Sparrow.

Related material— Two other occurrences of "318" in this journal—
in another horror story, "The Sweet Smell of Avon,"
and in a quote from the Feast of St. Nicholas, 2010—

"When Novelists Become Cubists," by Andre Furlani—

"A symbol comes into being when an artist sees that
it is the only way to get all the meaning in.
Genius always proceeds by faith" (312).

The unparaphrasable architectonic text
"differs from other narrative in that the meaning
shapes into a web, or globe, rather than along a line" (318).

[The references are to page numbers in
 Guy Davenport's The Geography of the Imagination .]

A phrase from today's noon post—

"Le souvenir de ce célèbre orateur"—

a souvenir—

— and a song.

"… 'Mes chers frères, n'oubliez jamais,
  quand vous entendrez vanter le progrès des lumières,
  que la plus belle des ruses du diable
  est de vous persuader qu'il n'existe pas!'

     Le souvenir de ce célèbre orateur
nous conduisit naturellement vers le sujet des académies,
et mon étrange convive m'affirma qu'il ne dédaignait pas,
en beaucoup de cas, d'inspirer la plume, la parole et la conscience
des pédagogues, et qu'il assistait presque toujours en personne,
quoique invisible, à toutes les séances académiques." 

— Baudelaire, "Le Joueur Généreux"

Click to enlarge:

In memory of the longtime co-editor of Series A  of the
Journal of Combinatorial Theory , who died on January 12th,
2012, here is a link to a Log24 post of that date.

* For the title, see January 19th.

"It seems that Hilbert had no taste for philosophers….
Hans Rademacher told this reviewer that, after Heidegger
once lectured in Göttingen, Hilbert gleefully repeated
to everyone the phrase "Das Nichts nichtet die Nichtung ."

— Gian-Carlo Rota, Discrete Thoughts , 2nd ed., p. 233

See January 4th, 2012.

(This link resulted from an application of Heidegger's
philosophy of "the opening" and "the shining" (Die Lichtung ).)

See also The Shining of May 29.

Update of 12:19 AM Feb. 3, 2012—
The undated (but cached by Google on January 4th, 2012)
unsigned post from a deleted weblog linked to above as
"an application" is also available in a version that is signed
(but still undated).

From ShiftLock in this journal—

"Philosophy knows nothing of the opening."
— Heidegger

See also a post of September 25, 2009,
and a film whose opening was on that date.

"Should we arbitrate life and death
at a round table or a square one?"

— Wislawa Szymborska

See also the two previous posts,
Disturbing Archimedes and Tesseract.

Update—

Princeton University Press on a book it will publish in March—

Circles Disturbed: The Interplay of
Mathematics and Narrative

"… brings together important thinkers in mathematics,
history, and philosophy to explore the relationship
between mathematics and narrative.
  The book's title recalls the last words of the great
Greek mathematician Archimedes before he was
slain by a Roman soldier— 'Don't disturb my circles' …."

Related material—

Archimedes's Vicious Circle

The following passage by Tolkien was suggested by a copy of next Sunday's New York Times Book Review  that arrived in the mail today. (See Orson Scott Card's remarks on page 26— "Uncle Orson"— and the Review 's concluding essay "Grand Allusion.")

"Lastly, tengwesta  [system or code of signs] has also become an impediment. It is in Incarnates clearer and more precise than their direct reception of thought. By it also they can communicate easily with others, when no strength is added to their thought: as, for example, when strangers first meet. And, as we have seen, the use of 'language' soon becomes habitual, so that the practice of ósanwe  (interchange of thought) is neglected and becomes more difficult. Thus we see that the Incarnate tend more and more to use or to endeavour to use ósanwe  only in great need and urgency, and especially when lambe  is unavailing. As when the voice cannot be heard, which comes most often because of distance. For distance in itself offers no impediment whatever to ósanwe . But those who by affinity might well use ósanwe  will use lambe  when in proximity, by habit or preference. Yet we may mark also how the 'affine' may more quickly understand the lambe  that they use between them, and indeed all that they would say is not put into words. With fewer words they come swifter to a better understanding. There can be no doubt that here ósanwe  is also often taking place; for the will to converse in lambe  is a will to communicate thought, and lays the minds open. It may be, of course, that the two that converse know already part of the matter and the thought of the other upon it, so that only allusions dark to the stranger need be made; but this is not always so. The affine** will reach an understanding more swiftly than strangers upon matters that neither have before discussed, and they will more quickly perceive the import of words that, however numerous, well-chosen, and precise, must remain inadequate."

* "If a poem catches a student's interest at all, he or she should damned well be able to look up an unfamiliar word in the dictionary…."

   — Elizabeth Bishop, quoted in the essay "Grand Allusion" mentioned above. For a brief dictionary of most of the unfamiliar words in this post's title and in the above passage, see Vinyar Tengwar  39 (July 1998). This is copyrighted but freely available on the Web.

** The word "affine" has connotations not intended by Tolkien. See that word in this journal. See also page 5 of next Sunday's Times Book Review , which contains a full-page ad for the 50th anniversary edition of A Wrinkle in Time . "There is  such a thing as a tesseract."

Weblog posts of two prominent mathematicians today discussed
what appears to be a revolution inspired by the business practices
of some commercial publishers of mathematics.

See Gowers and Cameron.

My own concern is more with the so-called "Non-Euclidean Revolution"
described by Richard Trudeau in a book of that title (Birkhäuser, 1987).

A 1976 document relevant to the concerns in the Trudeau book—

Though not as well known as another document discussing
"self-evident" truths, Cameron's remarks are also of some
philosophical interest.

They apply to finite  geometry, a topic unknown to Euclid,
but nevertheless of considerable significance for the foundations  
of mathematics.

"The hand of the creative artist, laid upon the major premise,
 rocks the foundations of the world." — Dorothy Sayers

Beach with Palms

The following images were suggested by the
"other things" link in yesterday's "287501346" post.

From June 10, 2008—

Two frames from the Jodie Foster film "Contact"—

See Storyline and Time Fold.

The twin topics of autism and of narrowing definitions
suggested the following remarks.

The mystical number "318" in the pilot episode
of Kiefer Sutherland's new series about autism, "Touch,"
is so small that it can easily apply (as the pilot
illustrated) to many different things: a date, a
time, a bus number, an address, etc.

The last 3/18 Log24 post— Defining Configurations—
led, after a false start and some further research,
to the writing of the webpage Configurations and Squares.

An image from that page—

Interpreting this, in an autistic manner, as the number
287501346 lets us search for more specific items
than those labeled simply 318.

The search yields, among other things, an offer of
Night Magic Cologne  (unsold)—

For further mystery and magic, see, from the date
the Night Magic offer closed— May 8, 2010— "A Better Story."
See also the next day's followup, "The Ninth Gate."

See also the links at the end of this morning's post.

— Notices of the American Mathematical Society

See also Rosetta Stone in this  journal.

Princeton University Press on a book it will publish in March—

Circles Disturbed: The Interplay of Mathematics and Narrative

"Circles Disturbed  brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier— 'Don't disturb my circles'— words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds–stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities."

Timeline of the Marvel Cinematic Universe — Norway, March 1942—

"The Red Skull finds the Tesseract, a cube of strange power,
said to be the jewel of Odin’s treasure room, in Tonsberg Norway.
 (Captain America: The First Avenger)"

Tesseracts Disturbed — (Click to enlarge)

Detail of Tesseracts Disturbed —

Narrative of the detail—

See Tesseract in this journal and Norway, May 2010—

The Oslo Version and Annals of Conceptual Art.

"Oh, what a tangled web we weave…"

"Something is happening to our town."

— Mayor of Pleasantville

Related material— Alicia Keys's birthday,
the ending of Midnight in Paris , and Rocket Billie.

See also a Sinatra song uploaded on this date
(Paul Newman's birthday) last year.

"You have a clear and lively voice."
           — Midnight in Paris

Related material— Today's previous post.

Dick Tufeld, Robot Voice in TV’s ‘Lost in Space,’ Dies at 85
    Wed Jan 25, 2012 23:42 from NYT Obituaries  By Bruce Weber

   "Mr. Tufeld possessed one of Hollywood’s most often-heard
   disembodied voices, especially from the 1950s through the 1970s."

In memoriam— A link from the date of Tufeld's death

Rhetorical question—

"Why walk when you can fly?"
— Mary Chapin Carpenter

Rhetorical answer—

Two excerpts from a webpage on random walks—

A drunk man will find his way home,
but a drunk bird may get lost forever.

— Shizuo Kakutani

Now we move to a larger city…

Happy birthday to…

From Labyrinth of the Line (March 2, 2011)—

"… construct the Golay code by taking the 24 points
to be the points of the projective line F₂₃ ∪ {∞}…."

— Robert A. Wilson

A simpler projective line— a Galois geometry
model of the line F₂ ∪ {∞}—

Here we may consider ∞ to be modeled*
by the third square above— the Galois window .

* Update of about 1 AM Jan. 25, 2012—
  This infinity-modeling is of course a poetic conceit,
  not to be taken too seriously. For a serious 
  discussion of points at infinity and finite fields,
  see (for instance) Daniel Bump's "The Group GL(2)."

"Debates about canonicity have been raging in my field
(literary studies) for as long as the field has been
around. Who's in? Who's out? How do we decide?"

— Stephen Ramsay, "The Hermeneutics of Screwing Around"

An example of canonicity in geometry—

"There are eight heptads of 7 mutually azygetic screws, each consisting of the screws having a fixed subscript (from 0 to 7) in common. The transformations of LF(4,2) correspond in a one-to-one manner with the even permutations on these heptads, and this establishes the isomorphism of LF(4,2) and A₈. The 35 lines in S₃ correspond uniquely to the separations of the eight heptads into two complementary sets of 4…."

 — J.S. Frame, 1955 review of a 1954 paper by W.L. Edge,
"The Geometry of the Linear Fractional Group LF(4,2)"

Thanks for the Ramsay link are due to Stanley Fish
(last evening's online New York Times ).

For further details, see The Galois Tesseract.

(Continued)

J. H. Conway in 1971 discussed the role of an elementary abelian group
of order 16 in the Mathieu group M₂₄. His approach at that time was
purely algebraic, not geometric—

For earlier (and later) discussions of the geometry  (not the algebra )
of that order-16 group (i.e., the group of translations of the affine space
of 4 dimensions over the 2-element field), see The Galois Tesseract.

"Design is how it works." —Steve Jobs

Website logo—

Screenshot from How Stuff Works—

(Click image for details.)

From "A Device Worthy of a Gothic Novel,"
Chapter XVI of The Club Dumas,
by Arturo Perez-Reverte (1993),
Vintage International, April 1998….
the basis of the 1999 Roman Polanski film
The Ninth Gate —

Aren't you going to give me a document to sign?"
"A document?"
"Yes. It used to be called a pact. Now it would be a contract
with lots of small print, wouldn't it? 'In the event of litigation,
the parties are to submit to the jurisdiction of the courts of…'
That's a funny thing. I wonder which court covers this."

"Yo sé de un laberinto griego que es una línea única, recta."
 —Borges, "La Muerte y la Brújula"

"I know of one Greek labyrinth which is a single straight line."
—Borges, "Death and the Compass"

From life's box of chocolates…

Happy birthday to Piper Laurie.

* Those who prefer their
souvenirs without sentiment
may consult the quaternions.

In China, the Year of the Dragon
has now begun. See Holy + Field
in this journal.

See Metamagical Themas —

— as well as the pound sign, alias hash .

"The Cardinal seemed a little preoccupied today."

The New Yorker , May 13, 2002

An image suggested by a book at
Princeton University Press—

Click image for details.

See also a somewhat deeper book from Princeton.

Kindergarten Theology

(Log24, St. Bridget's Day, 2008)

(Backstory— Presbyterian in this journal)

Princeton University Press on a book it will publish in March—

Circles Disturbed  brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier–"Don't disturb my circles"–words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds–stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.

Exercise— Discuss the above paragraph's vulgarity.

Discuss also the more robust vulgarity of Marvel Entertainment…

Context— "Marvel" in this journal, and The Cosmic Cube.

(Continued from November 12, 2005 and June 7, 2011)

Related material— "Labyrinth," a fiction
by the late Roberto Bolaño
in the current New Yorker —

"There's no photo credit."

"The 'one' with whom the reader has identified himself
has now become 'the listener, who listens in the snow';
he has become the snow man, and he knows winter
with a mind of winter, knows it in its strictest reality,
stripped of all imagination and human feeling.
But at that point when he sees the winter scene
reduced to absolute fact, as the object not of the mind,
but of the perfect perceptual eye that sees
'nothing that is not there,' then the scene,
devoid of  its imaginative correspondences,
has become 'the nothing that is.'"

—Robert Pack, Wallace Stevens:
An Approach to His Poetry and Thought.
New Brunswick: Rutgers UP, 1958.

"If the fault is with the soul, the sovereigns
Of the soul must likewise be at fault, and first.
If the fault is with the souvenirs, yet these
Are the soul itself. And the whole of the soul, Swenson,
As every man in Sweden will concede,
Still hankers after lions, or, to shift,
Still hankers after sovereign images."

— Wallace Stevens

"Friday night and the lights are low"
— ABBA

See also American Music Award.

(Continued)

See "harmonic analysis" in Mathematical Imagery and elsewhere in this journal.

* Title courtesy of George Steiner.
   For the "thought" part, see Plato's diamond
   in last night's Mathematical Imagery.

From the Crafoord Prize website—

Related meta -mathematical image from Diamond Theory—

Mathematical  image related to combinatorics—

See also permutahedron in this journal.

Those impressed by George Steiner's remark on Hegel in the previous post may consult…

(Click to enlarge.)

(The Christian Examiner.  Volume LXXX. New Series, Volume I.  January, March, May, 1866.
New York: James Miller, Publisher, 522, Broadway.  Boston: Walker, Fuller, & Co.

No. CCLIV, Art. IV.– THE SECRET OF HEGEL.
By C. C. Everett, pp. 196-207.

A review of…

The Secret of Hegel, being the Hegelian System in Origin, Principle, Form, and Matter.
By James Hutchinson Sterling. In two volumes.
London: Longman, Green, Longman, Roberts, & Green. 1865. 8vo, 2 vols.)

On Hegel, from the review—

"He starts not from the beginning, but from the heart, of the world.
There never was a time when this pure Being— which, in its
undivided absoluteness, is indistinguishable from nothing;
as pure, unbroken light is indistinguishable from darkness—
was by itself alone; but this absolute Being is yet the foundation
and the groundwork of whatever is."

For more on Hegel's logic, see Marxists.org.

See also Steiner on chess and Lenin in The New Yorker
(September 7, 1968, page 133).

Perception vs. Inception

Question—

"Where philosophy and literature mesh, where they are litigious toward one another in form or matter, these echoes of origin can be heard. The poetic genius of abstract thought is lit, is made audible. Argument, even analytic, has its drumbeat. It is made ode. What voices the closing movements of Hegel’s Phenomenology  better than Edith Piaf’s non de non , a twofold negation which Hegel would have prized?

This essay is an attempt to listen more closely."

— George Steiner, The Poetry of Thought 

Answer—

Edith Piaf's rien de rien . See also Is Nothing Sacred?

MathWorld.Wolfram.com has an article titled "Square-Triangle Theorem."

An article of my own, whose HTML title was previously "Triangles are Square," has been retitled accordingly.

"On the Internet, nobody knows…"

Related material— Story Theory and the Number of the Beast

In memory of Bach interpreter
Gustav Leonhardt —

Augenmusik

A search for khora  + tao  yields a paper on Derrida—

A check of the above date— Nov. 18, 2010— yields…

Related material on the temptation of physics
for a pure mathematician—

This morning's post on khora  and Cardinal Manning, and,
from Hawking's birthday this year, Big Apple.

Within this  post, by leading us to the apple,
Derrida as usual plays the role of Serpent.

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 —

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 .

"Accentuate the Positive."

— Clint Eastwood, soundtrack album for
"Midnight in the Garden of Good and Evil."

Headline from yesterday evening's New York Times  obituaries—

Frederica Sagor Maas, Silent-Era Scriptwriter, Dies at 111.

For Maas… Past Tense (Jan. 7, 2012) and its link to Dogma.

Related material—

Last night's SNL, this morning's Entertainment Break,
and — in the context of Dogma — Catholics Believe.

From an LA Times  story about Maas on January 7—

"Many of the screenplays she and her husband wrote between 1938 and 1950 were never produced. Hopeless, humiliated and having little money, the couple drove to a hilltop overlooking Hollywood with the intention of committing suicide in their Plymouth. Clutching each other, they started sobbing and realized that 'none of these things mattered. We had each other,' wrote Maas…."

Related material– Saturday night's Derrida at Villanova and Villanueva.

Identity Crisis— Or, Tilting at Whirligigs 

"As Derrida said at Villanova,
"We wait for something we would not like to wait for.
That is another name for death."

— Brian D. Ingraffia, "Is the Postmodern Post-Secular?,"
p. 50 in Postmodern Philosophy and Christian Thought ,
ed. by Merold Westphal, Indiana University Press, 1999, pp. 44-68

See also Derrida at Villanova in this journal.

The link to Ingraffia's remarks was suggested by
this evening's New York Times  obituaries—

Detail of Sylvie Donmoyer picture discussed
here on January 10—

The "13" tile may refer to the 13 symmetry axes
in the 3x3x3 Galois cube, or the corresponding
13 planes through the center in that cube. (See
this morning's post and Cubist Geometries.)

(Continued)

The following is adapted from a 2011 post—

* The title, that of a Fritz Leiber story, is suggested by
   the above picture of the symmetry axes of the square.
   Click "Continued" above for further details. See also
   last Wednesday's Cuber.

Wiener on Paley—

… he was already recognised as the ablest of the group of young English mathematicians who have been inspired by the genius of G H Hardy and J E Littlewood. In a group notable for its brilliant technique, no one had developed this technique to a higher degree than Paley. Nevertheless he should not be though of primarily as a technician, for with this ability he combined creative power of the first order. As he himself was wont to say, technique without 'rugger tactics' will not get one far, and these rugger tactics he practised to a degree that was characteristic of his forthright and vigorous nature.

The Telegraph  today on British mystery author Reginald Hill—

"After National Service between 1955 and 1957,
he went up on a scholarship to St Catherine’s College, Oxford,
where he played rugby…."

Further details—

"Unsheathe your dagger definitions." — James Joyce

Some context— St. Catherine in this journal and her feast day last year.