Monday, July 31, 2006  3:17 PM

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Monday, July 31, 2006  2:00 AM

For the feast of
St. Ignatius Loyola...

Final Arrangements,
continued:

 

"Now you has jazz."
- High Society, 1956 

-- Today's online New York Times

Also from today's New York Times: Kurt Kreuger in the 1945 film "Paris Underground."   Kurt Kreuger, a German-born actor who reluctantly played Nazi soldiers in many films about World War II, died July 12 in Beverly Hills, Calif. He was 89.

Log24, Wednesday, July 12, 2006: Band Numbers "Some friends  of mine  are in  this band..." -- David    Auburn,    Proof Seven is Heaven, Eight is a Gate, Nine is a Vine. -- The Prime Powers

Related material:

A Log24 entry commemorating
the murder of six Jesuits
in El Salvador.

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Sunday, July 30, 2006  2:02 PM

Campaign Song

"All things return to the One.
 What does the One return to?"

-- Zen koan, epigraph to
   The Footprints of God,
by Greg Iles of
Natchez, Mississippi

"Literature begins with geography."

-- attributed to Robert Frost

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Sunday, July 30, 2006  2:56 AM

History

From "Today in History," by The Associated Press--

On this date (July 30):

"In 1864, during the Civil War, Union forces tried to take Petersburg, Va., by exploding a mine under Confederate defense lines; the attack failed."

"A nightmare" -- Ulysses

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Saturday, July 29, 2006  5:01 PM

Dark Fields
of the Republic

Today's birthday: Ken Burns

Charley Reese on the republic:

"The republic died at Appomattox, and it's been empire ever since."

Charley Reese on Lincoln:

"Washington and Jefferson created the republic; Lincoln destroyed it."

In closing... 

A link in memory of Donald G. Higman, dead on Feb. 13, 2006, the day after Lincoln's birthday:

On the Graphs of Hoffman-Singleton and Higman-Sims (pdf)

His truth is marching on.

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Saturday, July 29, 2006  2:02 PM

Big Rock

Thanks to Ars Mathematica,  a link to everything2.com:

"In mathematics, a big rock is a result which is vastly more powerful than is needed to solve the problem being considered. Often it has a difficult, technical proof whose methods are not related to those of the field in which it is applied. You say 'I'm going to hit this problem with a big rock.' Sard's theorem is a good example of a big rock."

Another example:

Properties of the Monster Group of R. L. Griess, Jr., may be investigated with the aid of the Miracle Octad Generator, or MOG, of R. T. Curtis.  See the MOG on the cover of a book by Griess about some of the 20 sporadic groups involved in the Monster:


The MOG, in turn, illustrates (via Abstract 79T-A37, Notices of the American Mathematical Society, February 1979) the fact that the group of automorphisms of the affine space of four dimensions over the two-element field is also the natural group of automorphisms of an arbitrary 4x4 array.

This affine group, of order 322,560, is also the natural group of automorphisms of a family of graphic designs similar to those on traditional American quilts.  (See the diamond theorem.)

This top-down approach to the diamond theorem may serve as an illustration of the "big rock" in mathematics.

For a somewhat simpler, bottom-up, approach to the theorem, see Theme and Variations.

For related literary material, see Mathematics and Narrative and The Diamond as Big as the Monster.

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Saturday, July 29, 2006  2:45 AM

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Thursday, July 27, 2006  9:29 PM

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Thursday, July 27, 2006  5:09 PM

Number Sense

The NY lottery numbers for yesterday, 7/26, Jung's birthday, were 726 (mid-day) and 970 (evening).

We may view these numbers as representing the Jungian "sheep" and Freudian "goats" of yesterday's entry Partitions.

For the Jungian coincidence of 726 with 7/26, recall the NY lottery number 911 that was drawn on 9/11 exactly a year after the destruction of the World Trade Center. For more on this coincidence, see For Hemingway's Birthday: Mathematics and Narrative Continued (July 21, 2006).

For 970, Google reveals a strictly skeptical (i.e., like Freud, not Jung) meaning: 970 is the first page of the article "Sources of Mathematical Thinking," in Science, 7 May 1999: Vol. 284. no. 5416, pp. 970 - 974.

That article has been extensively cited in the scholarly literature on the psychology of mathematics.  Its lead author, Stanislas Dehaene, has written a book, The Number Sense.

What sense, if any, is made by 726 and 970?

The mid-day number again (see Hemingway's birthday) illustrates the saying

"Time and chance happeneth to them all."

The evening number again illustrates the saying

"Though truth may be very hard to find in the pages of most books, the page numbers are generally reliable."

-- Steven H. Cullinane,
   Zen and Language Games

These sayings may suit the religious outlook of Susan Blackmore, source (along with Matthew 25:31-46) of the sheep/goats partition in yesterday's entry on that topic.  She herself, apparently a former sheep, is now a goat practicing Zen.

Update of later the same evening--

On Space, Time, Life, the Universe, and Everything:

Note that the "sheep" number 726 has a natural interpretation as a date-- i.e., in terms of time, while the "goat" number 970 has an interpretation as a page number-- i.e., in terms of space.  Rooting, like Jesus and St. Matthew, for the sheep, we may interpret both of today's NY lottery results as dates, as in the next entry, Real Numbers.  That entry may (or may not) pose (and/or answer) The Ultimate Question. Selah.

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Wednesday, July 26, 2006  7:20 PM

Venus at St. Anne's
(Title of the closing chapter
of That Hideous Strength)

Symbol of Venus
and
Symbol of Plato

"What do they
teach them
   at these schools?"
-- C. S. Lewis

Today is the
feast of St. Anne.

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Wednesday, July 26, 2006  1:44 PM

"Mistakes are inevitable and may be either in missing a true signal or in thinking there is a signal when there is not. I am suggesting that believers in the paranormal (called 'sheep' in psychological parlance) are more likely to make the latter kind of error than are disbelievers (called 'goats')."

-- "Psychic Experiences:
     Psychic Illusions,"
     by Susan Blackmore,
     Skeptical Inquirer, 1992

The Club Dumas by Arturo Perez-Reverte One by one, he tore the engravings from the book, until he had all nine.  He looked at them closely.  "It's a pity you can't follow me where I'm going.  As the fourth engraving states, fate is not the same for all." "Where do you believe you're going?" Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them. "To meet someone" was his enigmatic answer. "To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso."

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Wednesday, July 26, 2006  5:00 AM

Jung's Birthday, 5 AM:

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Wednesday, July 26, 2006  4:00 AM

Jung's Birthday, 4 AM:

Jung on the Trinity
and Quaternity

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Wednesday, July 26, 2006  3:00 AM

Jung's Birthday, 3 AM:

The Shape of God:
Deepening the Mystery
of the Trinity

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Monday, July 24, 2006  3:17 PM

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Monday, July 24, 2006  1:00 PM

Discourse Analysis

Edward Rothstein in today's New York Times, reviewing Evil Incarnate (Princeton University Press):

"... the most decisive aspect of the myth is that it is, literally, a myth. Every single example of evil he gives turns out to be evil imagined: there is, he says, no evidence for any of it. Evil, he argues, is not something real, it is a 'discourse,' a 'way of representing things and shaping our experience, not some force in itself.'"

Related material:

A review (pdf) by Steven G. Krantz of Charles Wells's A Handbook of Mathematical Discourse (Notices of the American Mathematical Society, September 2004):

"Ambrose Bierce's Devil's Dictionary is a remarkable and compelling piece of writing because of its searing wit and sardonic take on life. Bierce does not define any new words. He instead gives deadly interpretations of very familiar words. Wells's book does not fit into the same category of literary effort."

For literary efforts perhaps more closely related to Bierce's, see Mathematics and Narrative and the five Log24 entries ending on this date last year.

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Sunday, July 23, 2006  2:56 PM

Dance of the Numbers, continued:

Partitions

Freeman Dyson on the role of the "crank" in the theory of partitions:

"'Each step in the story is a work of art,' Dyson says, 'and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'"

-- Erica Klarreich in
    Science News Online, week of
    June 18, 2005, quoted in
   "In Honor of Freeman Dyson's Birthday:
    Dance of the Numbers"
    (Log24, Dec. 15, 2005)

Paraphrase of Freeman Dyson's remarks in The New York Review of Books, issue dated May 28, 1998:

"Theology is about words; science is about things."

"What is 256 about?"
-- Reply to Freeman Dyson,
    (May 15, 1998)

A partial answer to that rhetorical question: 256 is the cardinality of the power set of an 8-set.

For the role played by 8-sets and by 23 (today's date) in partitions of a different sort, see Geometry of the 4x4 Square.

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Saturday, July 22, 2006  9:00 PM

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Friday, July 21, 2006  1:00 PM

For Hemingway's birthday:

Mathematics and Narrative, continued

"We know many little things about the relation between mathematics and narrative, but lack one big comprehensive insight."

-- John Allen Paulos (pdf)

"On Wednesday, Sept. 11, 2002-- 9/11/02-- the New York State lottery numbers were 911, an eerie coincidence that set many people to thinking or, perhaps more accurately, to not thinking."

--  John Allen Paulos

"Time and chance happeneth to them all."

-- Ecclesiastes 9:11

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Thursday, July 20, 2006  2:00 AM

Bead Game

Those who clicked on Rieff's concept in the previous entry will know about the book that Rieff titled Sacred Order/Social Order: My Life among the Deathworks.

That entry, from Tuesday, July 18, was titled "Sacred Order," and gave as an example the following figure:

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Tuesday, July 18, 2006  1:00 PM

Sacred Order

In memory of Philip Rieff, who died on July 1, 2006:

• An essay from July 16 on Rieff's concept of "the sacred order"
• An example of order-- sacred, since purely mathematical (as was Einstein's "holy geometry book")-- linked to on the date of Rieff's death:
  

Related material:

and

For details, see the
five Log24 entries ending
on the morning of
Midsummer Day, 2006.

Thanks to University Diaries for pointing out the essay on Rieff.

That essay says Rieff had "a dense, knotty, ironic style designed to warn off impatient readers. You had to unpack his aphorisms carefully. And this took a while. As a result, his thinking had a time-release effect." Good for him.  For a related essay (time-release effect unknown), see Hitler's Still Point: A Hate Speech for Harvard.

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Monday, July 17, 2006  6:06 PM

Today is the feast of
St. James McNeill Whistler.

"Nature contains the elements of color and form of all pictures-- as the keyboard contains the notes of all music-- but the artist is born to pick, and choose, and group with science, these elements, that the result may be beautiful--  as the musician gathers his notes, and forms his chords, until he brings forth from chaos, glorious harmony."

-- Whistler, "The Ten O'Clock"

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Sunday, July 16, 2006  3:17 PM

Mathematics and Narrative
continued...

"Now, at the urging of the UC Berkeley cognitive linguist George Lakoff, liberal America's guru of the moment, progressive Democrats are practicing to get their own reluctant mouths around some magical new vocabulary, in the hope of surviving and eventually overcoming the age of Bush."

-- Marc Cooper in The Atlantic Monthly, April 2005, "Thinking of Jackasses: The Grand Delusions of the Democratic Party"

Cooper's "now" is apparently still valid.  In today's New York Times, the leftist Stanley Fish reviews Talking Right, by leftist Geoffrey Nunberg:

"... the right's language is now the default language for everyone.
     On the way to proposing a counterstrategy (it never really arrives), Nunberg pauses to engage in a polite disagreement with his fellow linguist George Lakoff, who has provided a rival account of the conservative ascendancy. Lakoff argues that Republicans have articulated-- first for themselves and then for others-- a conceptual framework that allows them to unite apparently disparate issues in a single coherent worldview ...  woven together not in a philosophically consistent framework but in a narrative 'that creates an illusion of coherence.'
     Once again, the Republicans have such a narrative-- 'declining patriotism and moral standards, the out-of-touch media and the self-righteous liberal elite ... minorities demanding special privileges ... disrespect for religious faith, a swollen government'-- but 'Democrats and liberals have not offered compelling narratives that could compete' with it. Eighty pages later he is still saying the same thing. 'The Democrats need a compelling narrative of their own.'"

Lakoff is the co-author of a book on the philosophy of mathematics, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being.  From Wikipedia's article on Lakoff:

"According to Lakoff, even mathematics itself is subjective to the human species and its cultures: thus 'any question of math's being inherent in physical reality is moot, since there is no way to know whether or not it is.' Lakoff and Rafael E. Nunez (2000) argue at length that mathematical and philosophical ideas are best understood in light of the embodied mind. The philosophy of mathematics ought therefore to look to the current scientific understanding of the human body as a foundation ontology, and abandon self-referential attempts to ground the operational components of mathematics in anything other than 'meat.'"

For a long list of related leftist philosophy, see The Thinking Meat Project.

Democrats seeking narratives may also consult The Carlin Code and The Prime Cut Gospel.