"I know no writing— except perhaps Henry James's introductory essays— which conveys so clearly and with such an absence of fuss the excitement of the creative artist."

— Graham Greene on A Mathematician's Apology , review in The Spectator , 20 December 1940

"The mere quality and play of an ironic consciousness in the designer left wholly alone, amid a chattering unperceiving world, with the thing he has most wanted to do, with the design more or less realised— some effectual glimpse of that might, by itself, for instance, reward one's experiment."

— Henry James, "Prefaces to the New York Edition," in The Figure in the Carpet and Other Stories, Penguin Books, 1986, with introduction and notes by Frank Kermode

"What? You've found a pattern?"

— Greg Egan, "Wang's Carpets"

See also Notes on Mathematics and Narrative, with its discussion of the tiles of the creative artist Patrick Blackburn in the recent (August 2010) Pythagorean novel The Thousand  and the discussion of Wang tiles in Modal Logic,  a  book from November 2002 whose author also happens to be named Patrick Blackburn.

(Credit for the Greene bibliographic information is due to Janelle Robyn Humphreys, whose doctoral thesis, Shadows of Another Dimension, was published in 2009 by the University of Wollongong.)

The history of mathematics continues…

PRESS RELEASE The Academician Professor Nicolaos Artemiadis will give a speech entitled "The Exploration of the Universe through the Mathematical Science" during a public session of the Academy of Athens (the speech will be in Greek). The public session will be held on Tuesday, January 26th, 2010, at 19:00 at the Academy of Athens.

For some background on Professor Artemiadis, see two notes of July 2005 (the month an international conference on "Mathematics and Narrative" was held in Greece).

A post related by synchronicity to Artemiadis's Jan. 26 speech— Symbology.

Other philosophical remarks— "The Pediment of Appearance."

From the last link within the last link of yesterday’s entry:

“Review the concepts of integritas, consonantia, and claritas in Aquinas….”

Review also the properties of the number six that appears in today’s date.

For such properties, see the page of Log24 entries that end on September 6, 2006, with “Hamlet’s Transformation.”

Happy Feast of the Transfiguration.

Special Topics

From a review by Liesl Schillinger in the Aug. 13 New York Times of a new novel by Marisha Pessl:

“… Special Topics in Calamity Physics tells the story of a wise newcomer who joins a circle of students who orbit a charismatic teacher with a tragic secret. The newcomer, a motherless waif named Blue van Meer, spent most of her life driving between college towns with her genius poli-sci professor father, Gareth….  Gareth is fond of making oracular statements, which his daughter laps up as if they were Churchill’s: ‘Everyone is responsible for the page-turning tempo of his or her Life Story,’ he tells her. And, he cautions, ‘never try to change the narrative structure of someone else’s story.’

…. Heeding Gareth van Meer’s dictum that the most page-turning read known to man is the collegiate curriculum, with its ‘celestial, sweet set of instructions, culminating in the scary wonder of the Final Exam,’ Pessl structures Blue’s mystery like a kind of Great Books class…. A professor is all-powerful, Gareth liked to tell his daughter, he puts ‘a veritable frame around life,’ and ‘organizes the unorganizable. Nimbly partitions it into modern and postmodern, renaissance, baroque, primitivism, imperialism and so on. Splice that up with Research Papers, Vacation, Midterms. All that order– simply divine.’ Blue’s syllabus also includes a murder or two. Her book’s last pages are a final exam. You will be relieved to learn it is mostly multiple choice, and there is no time limit.”

Multiple choice:
The examination below, taken from a page by a scholar at a Jesuit university, is on the Borges story “The Garden of Forking Paths”– a classic of multiple choice.

No time limit:
See the first question.

Examination on
“The Garden of Forking Paths“

“What is the meaning of the idea expressed by Yu Tsun that ‘everything happens to a man precisely, precisely now. Centuries of centuries and only in the present do things happen’? What is the significance of the emphasis on the present moment, the here and now? Is this related to the carpe diem (‘seize the day’) idea? How? How is the present effectively connected to the past and the future? How is the present associated simultaneously to choices, actions, and consequences? How is the present moment relevant to the idea of the ‘forking paths’? What is the symbolic meaning of forking paths when understood as a crossroads? What is a person confronted with when standing at a crossroads? What are the implications of a choice of road? May this be connected to the myth of Oedipus and its concerns with human choices and supposed predestination? What is suggested by the idea that ‘in all fictional works, each time a man is confronted with several alternatives, he chooses one and eliminates the others; in the fiction of Ts’ui Pen, he chooses– simultaneously– all of them. He creates, in this way, diverse futures, diverse times which themselves also proliferate and fork’? What does it mean to make all choices at once? What view of life do such beliefs embody?”

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.

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

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.”

“… 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.
 

Snippets:
A Reply to John Updike

See Updike on digitized snippets.

The following four snippets were pirated from the end of MathPages Quotations, compiled by Kevin Brown.

They are of synchronistic interest in view of the previous two Log24 entries, which referred (implicitly) to a Poe story and (explicitly) to Pascal.

"That is another of your odd notions,"
said the Prefect, who had the fashion
of calling everything 'odd' that was
beyond his comprehension, and thus
lived amid an absolute legion of 'oddities.'
                             Edgar Allan Poe

I knew when seven justices could not
take up a quarrel, but when the parties
were met themselves, one of them
thought but of an If,  as, 'If you said so,
then I said so'; and they shook hands
and swore brothers. Your If is the only
peacemaker; much virtue in If.
                             Shakespeare

I have made this letter longer than usual
because I lack the  time to make it shorter.
                             Blaise Pascal

S'io credessi che mia risposta fosse
a persona che mai tornasse al mondo,
questa fiamma staria senza piu scosse.
Ma per cio che giammai di questo fondo
non torno vivo alcun, s'i'odo il vero,
senza tema d'infamia ti rispondo.
                             Dante, 1302

For translations of the Dante (including one by Dorothy Sayers), see everything2.com.

An anonymous author there notes that Dante describes a flame in which is encased a damned soul. The flame vibrates as the soul speaks:

If I thought that I were making
Answer to one that might return to view
The world, this flame should evermore
    cease shaking.

But since from this abyss, if I hear true,
None ever came alive, I have no fear
Of infamy, but give thee answer due.

-- Dante, Inferno, Canto 27, lines 61-66,
    translated by Dorothy Sayers

Updike says,

“Yes, there is a ton of information on the web but much of it is grievously inaccurate, unedited, unattributed and juvenile. The electronic marvels that abound around us serve, I have the impression, to inflame what is most informally and non-critically human about us. Our computer screens stare back at us with a kind of giant, instant aw-shucks, disarming in its modesty.”

Note Updike’s use of “inflame.”

For an aw-shucks version of “what is most informally and non-critically human about us,” as well as a theological flame, see both the previous entry and the above report from Hell.

Note that the web serves also to correct material that is inaccurate, unedited, unattributed, and juvenile. For examples, see Mathematics and Narrative. The combination of today’s entry for Pascal’s birthday with that web page serves both to light one candle and to curse the darkness.

” ‘I know what it is you last saw,’ she said; ‘for that is also in my mind. Do not be afraid! But do not think that only by singing amid the trees, nor even by the slender arrows of elvenbows, is this land of Lothlórien maintained and defended against the Enemy. I say to you, Frodo, that even as I speak to you, I perceive the Dark Lord and know his mind, or all his mind that concerns the Elves. And he gropes ever to see me and my thought. But still the door is closed!’
      She lifted up her white arms, and spread out her hands towards the East in a gesture of rejection and denial. Eärendil, the Evening Star, most beloved of the Elves, shone clear above. So bright was it that the figure of the Elven-lady cast a dim shadow on the ground. Its ray glanced upon a ring about her finger; it glittered like polished gold overlaid with silver light, and a white stone in it twinkled as if the Even-star had come to rest upon her hand. Frodo gazed at the ring with awe; for suddenly it seemed to him that he understood.
      ‘Yes,’ she said, divining his thought, ‘it is not permitted to speak of it, and Elrond could not do so. But it cannot be hidden from the Ring-Bearer, and one who has seen the Eye. Verily it is in the land of Lórien upon the finger of Galadriel that one of the Three remains. This is Nenya, the Ring of Adamant, and I am its keeper.’ ”

— J. R. R. Tolkien, The Lord of the Rings

From James A. Michener‘s The Source:

“Trouble started in a quarter that neither Uriel nor Zadok could have foreseen.  For many generations the wiser men of Zadok’s clan had worshipped El-Shaddai with the understanding that whereas Canaanites and Egyptians could see their gods directly, El-Shaddai was invisible and inhabited no specific place.  Unequivocally the Hebrew patriarchs had preached this concept and the sager men of the clans accepted it, but to the average Hebrew who was not a philosopher the theory of a god who lived nowhere, who did not even exist in corporeal form, was not easy to comprehend.  Such people were willing to agree with Zadok that their god did not live on this mountain– the one directly ahead– but they suspected that he did live on some mountain nearby, and when they said this they pictured an elderly man with a white beard who lived in a proper tent and whom they might one day see and touch.  If questioned, they would have said that they expected El-Shaddai to look much like their father Zadok, but with a longer beard, a stronger voice, and more penetrating eyes.

Now, as these simpler-minded Hebrews settled down outside the walls of Makor, they began to see Canaanite processions leave the main gate and climb the mountain to the north, seeking the high place where Baal lived, and they witnessed the joy which men experienced when visiting their god, and the Hebrews began in subtle ways and easy steps to evolve the idea that Baal, who obviously lived in a mountain, and El-Shaddai, who was reported to do so, must have much in common.  Furtively at first, and then openly, they began to climb the footpath to the place of Baal, where they found a monolith rising from the highest point of rock.  Here was a tangible thing they could comprehend, and after much searching along the face of the mountain, a group of Hebrew men found a straight rock of size equal to the one accorded Baal, and with much effort they dragged it one starless night to the mountain top, where they installed it not far from the home of Baal….”

Rabbi Chitrik died on
Valentine’s Day, 2006,
having had a heart attack
on Feb. 8, 2006–

Grammy Night.

The above monolith is perhaps more
closely related to El-Shaddai than to
Madonna, Grammy Night, and Baal.
It reflects my own interests
(Mathematics and Narrative)
and those of Martin Buber
(Jews on Fiction):
 

“Among Buber’s early philosophical influences were Kant’s Prolegomena, which he read at the age of fourteen, and Nietzsche’s Zarathustra.  Whereas Kant had a calming influence on the young mind troubled by the aporia of infinite versus finite time, Nietzsche’s doctrine of ‘the eternal recurrence of the same’ constituted a powerful negative seduction.  By the time Buber graduated from Gymnasium he felt he had overcome this seduction, but Nietzsche’s prophetic tone and aphoristic style are evident in Buber’s subsequent writings.”

— Plato.stanford.edu

Martin Buber

Rabbi Chitrik

Jews on Fiction

See Tony Kushner and E.L. Doctorow in today’s New York Times, Rebecca Goldstein’s talk from last summer’s Mykonos conference on mathematics and narrative, and Martin Buber on the Bible.

Mathematics and Narrative

Rebecca Goldstein, Mathematics and the Character of Tragedy:

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

Veritably.

Wikipedia on the tesseract:

Robert A. Heinlein in Glory Road:

Johnny Cash: “And behold, a white horse.”

On The Last Battle, a book in the Narnia series by C. S. Lewis:

Lewis said in “The Weight of Glory”—
 

On enchantments that need to be broken:

See the description of the Eater of Souls in Glory Road and of Scientism in

• Mathematics and Narrative,

• The Rhetoric of Scientism,

• and the C. S. Lewis classic,
  That Hideous Strength.

Narrative and Latin Squares

From The Independent, 15 August 2005:

“Millions of people now enjoy Sudoku puzzles. Forget the pseudo-Japanese baloney: sudoku grids are a version of the Latin Square created by the great Swiss mathematician Leonhard Euler in the late 18th century.”

The Independent was discussing the conference on “Mathematics and Narrative” at Mykonos in July.

From the Wikipedia article on Latin squares:

“The popular Sudoku puzzles are a special case of Latin squares; any solution to a Sudoku puzzle is a Latin square. Sudoku imposes the additional restriction that 3×3 subgroups must also contain the digits 1–9 (in the standard version).

The Diamond 16 Puzzle illustrates a generalized concept of Latin-square orthogonality: that of “orthogonal squares” (Diamond Theory, 1976) or “orthogonal matrices”– orthogonal, that is, in a combinatorial, not a linear-algebra sense (A. E. Brouwer, 1991).”

This last paragraph, added to Wikipedia on Aug. 14,  may or may not survive the critics there.

From crankbuster, July 18:

“Do not underestimate Evil Cullinane’s plan for World Domination!  http://www.log24.com now shows that he has crossed over to the dark side, making sacrifices to the Ancient Hindu Goddess ‘Kalli’ to ward off our attacks!  ‘Kalli’-nane will soon appear as the top result on every Google search.

July 20 illustration of
crankbuster’s remarks

Soon, all young mathematicians will be hypnotised by his dark diamonds of falsehood.  At least, that’s his plan.  But wait, who’s that brilliant mathematician who shines the light right through Cullinane’s fraud and exposes him to the whole world?!  Crankbuster saves the day! (applause)”

From Log24, July 18:

Birthday Links

Today’s birthdays:
Gene Wilder and Adrienne Barbeau.

For Gene:
A discussion of Frankenstein as
The Modern Prometheus at
Mathematics and Narrative.

For Adrienne:
Chinese Arithmetic.

“Poetry is a satisfying of
the desire for resemblance….
If resemblance is described as
a partial similarity between
two dissimilar things,
it complements and reinforces
that which the two dissimilar things
have in common.
It makes it brilliant.”

— Wallace Stevens,
    “Three Academic Pieces” in
    The Necessary Angel (1951)

Two dissimilar things:

1.  A talk to be given at a conference on “Mathematics and Narrative” in Mykonos in July:

Mark Turner,
“The Role of Narrative Imagining in Blended Mathematical Concepts” —

Abstract:
“The Way We Think (Gilles Fauconnier and Mark Turner; Basic Books, 2002) presents a theory of conceptual integration, or “blending,” as a basic mental operation. See http://blending.stanford.edu. This talk will explore some ways in which narrative imagining plays a role in blended mathematical concepts.”

2.  An application of the “conceptual blending” of  Fauconnier and Turner to some journal entries of 2004:  Cognitive Blending and the Two Cultures.