“Katherine Neville” “April 4” « Search Results

Saturday, April 4, 2009

Saturday April 4, 2009

Filed under: General,Geometry — Tags: Geometry, Springer — m759 @ 8:00 am

Annual Tribute to
The Eight

Katherine Neville's 'The Eight,' edition with knight on cover, on her April 4 birthday

Other knight figures:

Click on the SpringerLink
knight for a free copy
(pdf, 1.2 mb) of
the following paper
dealing with the geometry
underlying the R.T. Curtis
knight figures above:

Context:

Literature and Chess and
Sporadic Group References

Details:

Adapted (for HTML) from the opening paragraphs of the above paper, W. Jonsson's 1970 "On the Mathieu Groups M₂₂, M₂₃, M₂₄…"–

"[A]… uniqueness proof is offered here based upon a detailed knowledge of the geometric aspects of the elementary abelian group of order 16 together with a knowledge of the geometries associated with certain subgroups of its automorphism group. This construction was motivated by a question posed by D.R. Hughes and by the discussion Edge [5] (see also Conwell [4]) gives of certain isomorphisms between classical groups, namely

PGL(4,2)~PSL(4,2)~SL(4,2)~A₈,
PSp(4,2)~Sp(4,2)~S₆,

where A₈ is the alternating group on eight symbols, S₆ the symmetric group on six symbols, Sp(4,2) and PSp(4,2) the symplectic and projective symplectic groups in four variables over the field GF(2) of two elements, [and] PGL, PSL and SL are the projective linear, projective special linear and special linear groups (see for example [7], Kapitel II).

The symplectic group PSp(4,2) is the group of collineations of the three dimensional projective space PG(3,2) over GF(2) which commute with a fixed null polarity tau…."

References

4. Conwell, George M.: The three space PG(3,2) and its group. Ann. of Math. (2) 11, 60-76 (1910).

5. Edge, W.L.: The geometry of the linear fractional group LF(4,2). Proc. London Math. Soc. (3) 4, 317-342 (1954).

7. Huppert, B.: Endliche Gruppen I. Berlin-Heidelberg-New York: Springer 1967.

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Friday, April 4, 2003

Friday April 4, 2003

Filed under: General,Geometry — Tags: 4403, Octad, Octad Generator — m759 @ 3:33 pm

The Eight

Today, the fourth day of the fourth month, plays an important part in Katherine Neville's The Eight. Let us honor this work, perhaps the greatest bad novel of the twentieth century, by reflecting on some properties of the number eight. Consider eight rectangular cells arranged in an array of four rows and two columns. Let us label these cells with coordinates, then apply a permutation.

Decimal
labeling

Binary
labeling

Algebraic
labeling

IMAGE- Knight figure for April 4
Permutation
labeling

The resulting set of arrows that indicate the movement of cells in a permutation (known as a Singer 7-cycle) outlines rather neatly, in view of the chess theme of The Eight, a knight. This makes as much sense as anything in Neville's fiction, and has the merit of being based on fact. It also, albeit rather crudely, illustrates the "Mathematics and Art" theme of this year's Mathematics Awareness Month. (See the 4:36 PM entry.)

The visual appearance of the "knight" permutation is less important than the fact that it leads to a construction (due to R. T. Curtis) of the Mathieu group M₂₄ (via the Curtis Miracle Octad Generator), which in turn leads logically to the Monster group and to related "moonshine" investigations in the theory of modular functions. See also "Pieces of Eight," by Robert L. Griess.

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Wednesday, July 12, 2023

The Sunset of Dissolution

Filed under: General — m759 @ 6:59 pm

Dwight Garner today on the late Milan Kundera:

"Kundera’s novels, especially his later ones, could be abstract and
heavy-handed. His characters, at times, were little more than chess pieces.
Their author could be pretentious. His work is filled with observations such as:
'In the sunset of dissolution, everything is illuminated by the aura of nostalgia,
even the guillotine.' But his best fiction retains its moments of sweep and power."

Illustration for Florence King's 1989 review of The Eight , a novel
by Katherine Neville that features prominently the date April 4.

See also "Dissolution" in this journal.

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Wednesday, March 17, 2021

Mind the Gaps

Filed under: General — Tags: Cube School, Interality, Mind the Gap — m759 @ 12:23 pm

Page from 'The Paradise of Childhood,' 1906 edition

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Sunday, August 23, 2020

Sprechen Sie Neutsch?

Filed under: General — Tags: Springer — m759 @ 2:06 pm

Related images —

Chess Knight
(in German, Springer)

Wednesday, April 8, 2020

A Midrash for Steiner

Filed under: General — Tags: Figaro's Passover, Isidore of Seville — m759 @ 12:12 pm

(The late Mark Steiner, not the late George Steiner.)

See Katherine Neville’s novel The Eight ,
Log24 posts tagged Crucible Raiders, and
St. Isidore, whose feast day is April 4 —

Mark Steiner’s book The Applicability of Mathematics
as a Philosophical Problem (Harvard University Press, 2002,
$36.50) is available for free at a website named for St. Isidore.)

Ereignis ereignet.

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Monday, December 2, 2019

D8: The Black Queen’s Square

Filed under: General — Tags: Richardson, The Fontana Arches — m759 @ 3:45 am

The previous post quoted some dialogue from Victor Hugo's
novel about the French Revolution, Ninety-Three.

This suggests a look at the following non-fiction book:

Compare and contrast with the novel The Eight , by Katherine Neville,
about chess and the French Revolution.

Neville's birthday, April 4, plays a major role in her novel. The dies natalis
(in the Roman Catholic sense) of the above Birth of the Chess Queen
author, on the other hand, was reportedly November 20, 2019.

Following a link in this journal from November 20 leads to remarks
that might interest the subjects of an upcoming film, "The Two Popes."

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Sunday, October 15, 2017

An Interesting Symbol

Filed under: General — m759 @ 2:00 pm

"His story is tragic and fascinating, but also
an interesting symbol for the 20th century."

— "Pawn Sacrifice" review by Jordan Hoffman,
Sept. 18, 2015

See as well William J. Lombardy's obituary in
today's online New York Times .

Other symbols —

Logo for a current New York Times series —

A 1989 New York Times illustration for Florence King's review of The Eight ,
a novel by Katherine Neville that features prominently the date April 4 —

Illustration by Rodrigo Shopis

See also recent posts now tagged Five Movements for Lombardy.

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Saturday, May 14, 2016

The Hourglass Code

Filed under: General,Geometry — Tags: Hourglass Code — m759 @ 1:28 pm

A version of the I Ching’s Hexagram 19:

I Ching Hexagram 19, 'Approach,' the box-style version

From Katherine Neville's The Eight , a book on the significance
of the date April 4 — the author's birthday —

Axe image from Katherine Neville's 'The Eight'

The Eight by Katherine Neville —

    “What does this have to do with why we’re here?”
    “I saw it in a chess book Mordecai showed me. The most ancient chess service ever discovered was found at the palace of King Minos on Crete– the place where the famous Labyrinth was built, named after this sacred axe. The chess service dates to 2000 B.C. It was made of gold and silver and jewels…. And in the center was carved a labrys.”
… “But I thought chess wasn’t even invented until six or seven hundred A.D.,” I added. “They always say it came from Persia or India. How could this Minoan chess service be so old?”
    “Mordecai’s written a lot himself on the history of chess,” said Lily…. “He thinks that chess set in Crete was designed by the same guy who built the Labyrinth– the sculptor Daedalus….”
    Now things were beginning to click into place….
    “Why was this axe carved on the chessboard?” I asked Lily, knowing the answer in my heart before she spoke. “What did Mordecai say was the connection?”….
    “That’s what it’s all about,” she said quietly. “To kill the King.”

     The sacred axe was used to kill the King. The ritual had been the same since the beginning of time. The game of chess was merely a reenactment. Why hadn’t I recognized it before?

Related material: Posts now tagged Hourglass Code.

See also the hourglass in a search for Pilgrim's Progress Illustration.

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Monday, April 4, 2016

Midnight for Paris

Filed under: General — m759 @ 12:00 am

Illustration for Florence King's 1989 review of The Eight , a novel
by Katherine Neville that features prominently the date April 4.

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Sunday, August 10, 2014

Knight Moves

Filed under: General,Geometry — Tags: Knight Move, Springer — m759 @ 7:00 pm

Some illustrations:

Chess Knight
(in German, Springer)

Saturday, April 5, 2014

A Princeton Half-Hour

Filed under: General — Tags: Lone Pine Obit — m759 @ 12:00 pm

"May you be in heaven a full half-hour
before the devil knows you're dead ."

Related material:
Yesterday's posts of 12 PM and 8 PM,
and the life of Philip Seymour Hoffman.

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Thursday, April 5, 2012

Go Ask Emma*

Filed under: General — Tags: Sherman Brothers — m759 @ 11:07 pm

From Katherine Neville's novel The Eight (see also April 4, Der Einsatz )—

"You walked out of my dreams and into my car…"

* Frost

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Sunday, January 18, 2009

Sunday January 18, 2009

Filed under: General — Tags: Jigs — m759 @ 8:00 am

Birthdays

Part I: The Pagan View

From The Fire, Katherine Neville's sequel to her novel The Eight:

"'Cat…. realized that we all need some kind of a chariot driver to pull our forces together, like those horses of Socrates, one pulling toward heaven, one toward the earth….'

… I asked, 'Is that why you said my mother's and my birthdays are important? Because April 4 and October 4 are opposite in the calendar?'

Rodo beamed a smile…. He said, 'That's how the process takes place….'"

Part II: The Christian View

"The Calendar of saints is a traditional Christian method of organizing a liturgical year by associating each day with one or more saints and referring to the day as that saint's feast day. The system arose from the very early Christian custom of annual commemoration of martyrs on the dates of their deaths, or birth into heaven, and is thus referred to in Latin as dies natalis ('day of birth')." –Wikipedia

The October 4 date above, the birthday of Cat's daughter, Xie, in The Fire, is also the liturgical Feast of St. Francis of Assisi (said by some to be also the date of his death).

The April 4 date above is Neville's birthday and that of her alter ego Cat in The Eight and The Fire. Neville states that this is also the birth date of Charlemagne. It is, as well, the dies natalis (in the "birth into heaven" sense), of Dr. Martin Luther King.

For more about April 4, see Art Wars and 4/4/07.

For more about October 4, see "Revelation Game Continued: Short Story."

Conclusion:

"et lux in tenebris lucet
et tenebrae eam
non comprehenderunt"

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Wednesday, September 10, 2003

Wednesday September 10, 2003

Filed under: General — Tags: Glasperlenspiel, Springer — m759 @ 4:04 pm

4:04:08

The title refers to my entry of last April 4,

The Eight,

and to the time of this entry.

From D. H. Lawrence and the Dialogical Principle:

“Plato’s Dialogues…are queer little novels….[I]t was the greatest pity in the world, when philosophy and fiction got split. They used to be one, right from the days of myth. Then they went and parted, like a nagging married couple, with Aristotle and Thomas Aquinas and that beastly Kant. So the novel went sloppy, and philosophy went abstract-dry. The two should come together again, in the novel.”

— pp. 154-5 in D. H. Lawrence, “The Future of the Novel,” in Study of Thomas Hardy and Other Essays. Ed. Bruce Steele. Cambridge: Cambridge University Press,1983. 149-55.

Philosophy

Fiction

“The wild, brilliant, alert head of St. Mawr seemed to look at her out of another world… the large, brilliant eyes of that horse looked at her with demonish question…. ‘Meet him half way,’ Lewis [the groom] said. But halfway across from our human world to that terrific equine twilight was not a small step.”

— pp. 30, 35 in D. H. Lawrence, “St. Mawr.” 1925. St. Mawr and Other Stories. Ed. Brian Finney. Cambridge: Cambridge University Press, 1983.

Monday, April 28, 2003

Monday April 28, 2003

Filed under: General,Geometry — Tags: 4403, Octad, Octad Generator — m759 @ 12:07 am

ART WARS:

Toward Eternity

April is Poetry Month, according to the Academy of American Poets. It is also Mathematics Awareness Month, funded by the National Security Agency; this year's theme is "Mathematics and Art."

Some previous journal entries for this month seem to be summarized by Emily Dickinson's remarks:

"Because I could not stop for Death–
He kindly stopped for me–
The Carriage held but just Ourselves–
And Immortality.

………………………
Since then–'tis Centuries–and yet
Feels shorter than the Day
I first surmised the Horses' Heads
Were toward Eternity– "

Consider the following journal entries from April 7, 2003:

Math Awareness Month

April is Math Awareness Month.
This year's theme is "mathematics and art."

An Offer He Couldn't Refuse

Today's birthday: Francis Ford Coppola is 64.

"There is a pleasantly discursive treatment
of Pontius Pilate's unanswered question
'What is truth?'."

— H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau's remarks on the "Story Theory" of truth as opposed to the "Diamond Theory" of truth in The Non-Euclidean Revolution

From a website titled simply Sinatra:

"Then came From Here to Eternity. Sinatra lobbied hard for the role, practically getting on his knees to secure the role of the street smart punk G.I. Maggio. He sensed this was a role that could revive his career, and his instincts were right. There are lots of stories about how Columbia Studio head Harry Cohn was convinced to give the role to Sinatra, the most famous of which is expanded upon in the horse's head sequence in The Godfather. Maybe no one will know the truth about that. The one truth we do know is that the feisty New Jersey actor won the Academy Award as Best Supporting Actor for his work in From Here to Eternity. It was no looking back from then on."

From a note on geometry of April 28, 1985:

The "horse's head" figure above is from a note I wrote on this date 18 years ago. The following journal entry from April 4, 2003, gives some details:

The Eight

Decimal
labeling

Binary
labeling

Algebraic
labeling

Permutation
labeling

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