Log24

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.

"The transcripts of the 2006 meetings, released after a standard five-year delay,
clearly show some of the nation’s pre-eminent economic minds did not fully understand
the basic mechanics of the economy that they were charged with supervising."

— Binyamin Appelbaum in the Jan. 12 online New York Times

Academics may recall other examples of comfortably ignorant collegiality.

"Examples galore of this feeling must have arisen in the minds of the people who extended the Magic Cube concept to other polyhedra, other dimensions, other ways of slicing.  And once you have made or acquired a new 'cube'… you will want to know how to export a known algorithm , broken up into its fundamental operators , from a familiar cube.  What is the essence of each operator?  One senses a deep invariant lying somehow 'down underneath' it all, something that one can’t quite verbalize but that one recognizes so clearly and unmistakably in each new example, even though that example might violate some feature one had thought necessary up to that very moment.  In fact, sometimes that violation is what makes you sure you’re seeing the same thing , because it reveals slippabilities you hadn’t sensed up till that time….

… example: There is clearly only one sensible 4 × 4 × 4 Magic Cube.  It is the  answer; it simply has the right spirit ."

— Douglas R. Hofstadter, 1985, Metamagical Themas: Questing for the Essence of Mind and Pattern  (Kindle edition, locations 11557-11572)

See also Many Dimensions in this journal and Solomon's Cube.

Tension in the Common Room—

In memory of population geneticist James F. Crow,
who died at 95 on January 4th.

"'Interpenetration'" — Stanley Fish in yesterday evening's online New York Times

"You want Frye's with that?" — A recent humanities graduate

(Continued from Epiphany and from yesterday.)

Detail from the current American Mathematical Society homepage—

Further detail, with a comparison to Dürer's magic square—

The three interpenetrating planes in the foreground of Donmoyer's picture
provide a clue to the structure of the the magic square array behind them.

Group the 16 elements of Donmoyer's array into four 4-sets corresponding to the
four rows of Dürer's square, and apply the 4-color decomposition theorem.
Note the symmetry of the set of 3 line diagrams that result.

Now consider the 4-sets 1-4, 5-8, 9-12, and 13-16, and note that these
occupy the same positions in the Donmoyer square that 4-sets of
like elements occupy in the diamond-puzzle figure below—

Thus the Donmoyer array also enjoys the structural  symmetry,
invariant under 322,560 transformations, of the diamond-puzzle figure.

Just as the decomposition theorem's interpenetrating lines  explain the structure
of a 4×4 square , the foreground's interpenetrating planes  explain the structure
of a 2x2x2 cube .

For an application to theology, recall that interpenetration  is a technical term
in that field, and see the following post from last year—

Yesterday's All About Eve post featured Pope John Paul II
with his close friend and confidant Jerzy Kluger.
Their counterparts Xavier and Magneto in the recent film
"X-Men: First Class," together with Catholic doctrine on telepathy,
suggest  the following meditations.

Douglas Hofstadter on interpenetration—

— as well as Trinity in this journal.

First the punchline—

Then the joke.

    “…the nonlinear characterization of Billy Pilgrim
    emphasizes that he is not simply an established
    identity who undergoes a series of changes but
    all the different things he is at different times.”

This suggests that the above structure
be viewed as illustrating not eight  parts
but rather 8! = 40,320 parts.

"The Cardinal seemed a little preoccupied today."

The New Yorker , May 13, 2002

See also a note of May 14 , 2002.

Literary symbolism, offered without comment—

Log24 post of January 14, 2011

Today's Google Doodle for the 100th birthday of Charles Addams—

A doodle from this year's Feast of the Epiphany—

A doodle based on today's previous post and on a post for Twelfth Night, 2003—

From a post that was written for Twelfth Night—

Bernhard Weiss on the philosophy of Michael Dummett—

" … debates about realism, that is, those debates that ask
whether or not one or another aspect of the world is independent
of the way we represent that aspect to ourselves. For example,
is there a realm of mathematical entities that exists fully formed
independently of our mathematical activity? Are there facts about
the past that our use of the past tense aims to capture?"

Yes and Yes.

• In memory of Anne Tyng, who died last year on Dec. 27,
  see Number and Form.
• In memory of Frederica Sagor Maas, who
  died on Twelfth Night, 2012, see Dogma.
• In memory of time I spent on Wilcox Avenue
  in the Hollywood of the early sixties, see
  Hans Reichenbach on the use of the past tense
  (section 51 of Elements of Symbolic Logic ,
  New York: The Macmillan Company, 1947, 287–98.)

See also The Whirligig of Time in this journal.

A link for Josefine Lyche in memory of Anne Tyng.

"Dreams are sleep's watchful brother, of death's fraternity,
heralds, watchmen of that coming night, and our attitude
toward them may be modeled upon Hades, receiving, hospitable,
yet relentlessly deepening, attuned to the nocturne, dusky, and
with a fearful cold intelligence that gives permanent shelter
in his house to the incurable conditions of human being."

– James Hillman, conclusion of
The Dream and the Underworld  (Harper & Row, 1979)

In memory of Raymond Edward Alan Christopher Paley—

Related material— Mathieu Symmetry.

… que cantaba el rey David.

An example for the Feast of the Epiphany*

For one approach to defining this form, see Diamond Star.

* And for Pomona College