Log24

Monday, August 14, 2017

Chess Records

Filed under: General — m759 @ 10:30 pm

In memory of a Chess Records star who died on March 18, 2017

Thursday, April 21, 2016

The Alchemist’s Chessboard

Filed under: General,Geometry — m759 @ 12:25 pm

Material related to the previous post and to Alfred Bester's
1981 followup to The Stars My Destination  titled The Deceivers

The Lapis Philosophorum :

"The lapis  was thought of as a unity and therefore often stands for the prima materia  in general."
— Aion , by C. G. Jung

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."
— The Stars My Destination , by Alfred Bester

And from Bester's The Deceivers :

Meta  Physics

"'… Think of a match.  You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released.  Friction does it.  But when Meta  excites and releases energy, it's like a stick of dynamite compared to a match.  It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah.  The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what.  The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

'That doesn't sound like much.'"

Related material :

Geometry of the I Ching

Sunday, April 8, 2018

OK Movie

Filed under: General — m759 @ 11:00 am

See also Chess War posts.

Tuesday, August 27, 2024

For Rubik Worshippers

Filed under: General — Tags: , — m759 @ 2:37 pm

Galois space of six dimensions represented in Euclidean spaces of three and of two dimensions

The above is six-dimensional as an affine  space, but only five-dimensional
as a  projective  space . . . the space PG(5, 2).

As the domain of the smallest model of the Klein correspondence and the
Klein quadric, PG (5,2) is not without mathematical importance.

See Chess Bricks and Ovid.group.

This post was suggested by the date July 6, 2024 in a Warren, PA obituary
and by that date in this  journal.

Tuesday, April 23, 2024

Golden Keys

Filed under: General — Tags: — m759 @ 7:55 pm

“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology

The image “http://www.log24.com/log/pix04A/041010-Hardy2.jpg” cannot be displayed, because it contains errors.
The image “http://www.log24.com/log/pix04A/041010-Mate2.jpg” cannot be displayed, because it contains errors.

Bogart and Lorre in 'Casablanca' with chessboard and cocktail

The key is the cocktail that begins the proceedings.”

– Brian Harley, Mate in Two Moves

"I named this script ocode and chmod 755'd it to make it executable…"

Software forum post on the OCR program Tesseract

Garfield, Dec. 4, 2008:  Mouse's Xmas bulb-lighting

From the author of
The Pearly Gates of Cyberspace:

"Like so many other heroes
 who have seen the light
 of a higher order…."

Friday, April 12, 2024

The Gambit Plan

Filed under: General — Tags: — m759 @ 11:47 pm

Citation — Lattanzio, Ryan (December 7, 2020). "After 'Queen's Gambit,'
Anya Taylor-Joy and Scott Frank Reuniting for Nabokov Adaptation"
.
IndieWire. — Wikipedia

Thanks for the warning.

See as well Scott Frank on chessboard space.

Friday, December 22, 2023

Wiki’d

Filed under: General — Tags: , — m759 @ 11:14 am

Lewis Carroll's chess  Red Queen, from Through the Looking Glass,
is "often confused with" the playing cards  Queen of Hearts, 
from Alice in Wonderland

" The King turned pale, and shut his notebook hastily.
'Consider your verdict,' he said to the jury in a low, trembling voice….

. . . . 'No, no!' said the Queen. 'Sentence first—verdict afterward.' "

— Lewis Carroll, Alice in Wonderland

The figure at right in the video of today's previous post,
Peter Berck —

"In Alice in Wonderland , the Red Queen
does everything backwards—
she demands the punishment first, and then
the trial, and then the crime comes last of all.
Today, the Red Queen is everywhere."

College of Natural Resources commencement address,
May 12, 2018, University of California, Berkeley

Berck's address was titled "The Red Queen."
It would have had diminished rhetorical effect if
correctly  titled "The Queen of Hearts."

Berck's dies natalis — "birth into heaven," in Catholic parlance —
was reportedly August 10, 2018.  A Log24 synchronology check
yields a different chess-related figure Actor/director John Huston:

Friday, September 15, 2023

For the Players

Filed under: General — Tags: — m759 @ 9:08 am
 

From "Knight to Move," by Fritz Leiber

"… You were talking about basic games. Well, the chessboard is clearly a spider’s web with crisscross strands—in Go you even put the pieces on the intersections. The object of the game is to hunt down and immobilize the enemy King, just as a spider paralyzes its victim and sometimes wraps it in its silk. But here’s the clincher: the Knight, the piece most characteristic of chess, has exactly eight crooked moves when it stands in the clear—the number of a spider’s crooked legs, and eyes too! This suggests that all chess-playing planets are Spider-infiltrated from way back. It also suggests that all the chessplayers here for the tournament are Spiders—your shock battalion to take over 61 Cygni 5.”

Colonel von Hohenwald sighed. “I was afraid you’d catch on, dear,” he said softly. “Now you’ve signed your abduction warrant at the very least. You may still be able to warn your HQ, but before they can come to your aid, this planet will be in our hands.”

He frowned. “But why did you spill this to me, Erica? If you had played dumb—”

“I spilled it to you,” she said, “because I wanted you to know that your plot’s been blown––and that my side has already taken countermeasures! We’ve made a crooked Knight’s move too. Has the significance of track games never occurred to you, Colonel? The one-dimensional track, sinuously turning, obviously symbolizes the snake. The pieces are the little bugs and animals the snake has swallowed. As for the dice, well, one of the throws is called Snake Eyes. So be assured that all the k’ta’hra players here are Snakes, ready to counter any Spider grab at 61 Cygni 5.”

The Colonel’s mouth almost gaped. 

Sunday, September 10, 2023

Games Theory

Filed under: General — Tags: , — m759 @ 11:32 pm
 

From "Knight to Move," by Fritz Leiber

"… You were talking about basic games. Well, the chessboard is clearly a spider’s web with crisscross strands—in Go you even put the pieces on the intersections. The object of the game is to hunt down and immobilize the enemy King, just as a spider paralyzes its victim and sometimes wraps it in its silk. But here’s the clincher: the Knight, the piece most characteristic of chess, has exactly eight crooked moves when it stands in the clear—the number of a spider’s crooked legs, and eyes too! This suggests that all chess-playing planets are Spider-infiltrated from way back. It also suggests that all the chessplayers here for the tournament are Spiders—your shock battalion to take over 61 Cygni 5.”

Colonel von Hohenwald sighed. “I was afraid you’d catch on, dear,” he said softly. “Now you’ve signed your abduction warrant at the very least. You may still be able to warn your HQ, but before they can come to your aid, this planet will be in our hands.”

He frowned. “But why did you spill this to me, Erica? If you had played dumb—”

“I spilled it to you,” she said, “because I wanted you to know that your plot’s been blown––and that my side has already taken countermeasures! We’ve made a crooked Knight’s move too. Has the significance of track games never occurred to you, Colonel? The one-dimensional track, sinuously turning, obviously symbolizes the snake. The pieces are the little bugs and animals the snake has swallowed. As for the dice, well, one of the throws is called Snake Eyes. So be assured that all the k’ta’hra players here are Snakes, ready to counter any Spider grab at 61 Cygni 5.”

The Colonel’s mouth almost gaped. 

Wednesday, June 28, 2023

Actual Data

Filed under: General — Tags: , — m759 @ 3:23 pm

From the above image: "/gds_rip/" —

Related geek lore:

Saturday, June 3, 2023

Gesamtkunstwerk for Wagner

Filed under: General — Tags: , , — m759 @ 9:47 am

In memory of set designer Robin Wagner, winner of three
Tony awards, who reportedly died at 89 on May 29 —

From Log24 on May 29
and the preceding day —

"When the men on the chessboard
get up and tell you where to go . . . ."

Don't take the Brown acid!

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

Sunday, May 28, 2023

Breadcrumbs for Gretel . . .

Tags:  — m759 @ 3:47 PM 

Continues .

See as well Chess Set and Efficient Packing.

Thursday, January 20, 2022

Vieux Carré

Filed under: General — Tags: , , — m759 @ 1:59 pm

Tevis on chess — 'The squares have names'

'Last Night in Soho' ad

Cullinane, Epiphany 1989, I Ching chessboard, lower right'

"Aooo! " — Warren Zevon

The Solomon Pill

Filed under: General — Tags: — m759 @ 1:26 pm

"Howard Solomon was building the pharmaceutical company
Forest Laboratories, not by manufacturing drugs but by
licensing them. In his search for deals in the United States and
Europe, he learned about citalopram, a Danish antidepressant."

Richard Sandomir, New York Times , Friday, Jan. 14, 2022

" '… he’d talk about Verdi writing "Falstaff" in his 80s,' Andrew Solomon
said. ' "Imagine that," he’d say, "in his 80s, he wrote some of the greatest
music ever written." That was the path he hoped to follow.' ”

Friday, July 2, 2021

Number, Time, and The New Mutants

Filed under: General — Tags: , , — m759 @ 10:33 pm

From Number and Time ,
by Marie-Louise von Franz,
Northwestern U. Press paperback,
December 31, 1974 —

Star Wars Chess:

Originally chess seems to have represented
an earthly mirror-image of "the stars' battles
in Heaven,"22 an outline of those battles from
which man's destiny proceeded.

22. See Joseph Needham, Science and Civilization
in China (Cambridge, 1959), III, 540ff., 303ff.;
see also IV, pt. 1, 230, 265, 327 ff.

From the recent film The New Mutants —

Anya Taylor-Joy plays in a pool: 

"Roll credits."

Saturday, June 26, 2021

Our Viennese Heritage — “Racy”?!

Filed under: General — m759 @ 10:23 pm

A review of the dramatic legacy of Arthur Schnitzler
(La Ronde Traumnovelle ) seems in order.

Wednesday, January 20, 2021

Key

Filed under: General — Tags: , — m759 @ 10:55 pm

An image from the opening of the Netflix series “Locke & Key” —

See also Omega in this journal.

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

The key is the cocktail that begins the proceedings.”

– Brian Harley, Mate in Two Moves

Sunday, January 10, 2021

“Glasgow, 1937”

Filed under: General — Tags: — m759 @ 11:04 pm

The location in the title is the opening scene of the new version
of "All Creatures Great and Small."  The year  in the title suggests
a look at (for instance) The Pentagram Papers.

A "support provided by" credit suggests some related images —

A Scotland-related post: The Blue Path and the Red Path
(Log24, Aug. 24, 2014).
Wendelboe's games included chess sets.
See as well a related purchase from further north on the same block.

Tuesday, January 5, 2021

The Shop on the Corner

Filed under: General — Tags: , , — m759 @ 10:38 am

George Steiner on chess —

"… the common bond between chess, music, and mathematics
may, finally, be the absence of language."

— George Steiner, Fields of Force: Fischer and Spassky at Reykjavik ,
Viking hardcover, June 1974.

In memory of George Steiner, of Walter Tevis, and of B&B Smoke Shop,
corner of Third Ave. and Liberty St., Warren, Pennsylvania, in the 1950s,
where I purchased . . .

At that point in my life, language interested me more than chess.
But I can identify with the protagonist of Walter Tevis's  Queen's Gambit ,
(the book, not the film) who visited a similar smoke shop in 1960 —

… There was a long rack of magazines behind her. When she
got the cigarettes, she turned 
and began looking.  Senator
Kennedy’s picture was on the 
cover of Time  and Newsweek :
he was running for Pres
ident . . . . 

. . . Walking home with the folded [chess] magazine tucked
securely against her flat belly she thought again about that
rook move Morphy hadn’t made. The magazine said
Morphy was “perhaps the most brilliant player in the
history of the game.” The rook could come to bishop seven,
and Black had better not take it with his knight because…
She stopped, halfway down the block. A dog was barking
somewhere, and across the street from her on a well-mowed
lawn two small boys were loudly playing tag. After  the
second pawn moved to king knight five, then the remaining
rook could slide over, and if the black player took
the pawn, the bishop could uncover, and if he didn’t…

      She closed her eyes. If he didn’t capture it, Morphy
could force a mate in two, starting with the bishop sacrificing
itself with a check. If he did  take it, the white pawn
moved again, and then the bishop went the other way
and there was nothing Black could do. There it was.  One
of the little boys across the street began crying. There was
nothing Black could do.  The game would be over in
twenty-nine moves at least. The way it was in the book, it
had taken Paul Morphy thirty-six moves to win. He
hadn’t seen the move with the rook. But she had. 

      Overhead the sun shone in a blank blue sky. The dog
continued barking. The child wailed. Beth walked slowly
home and replayed the game. Her mind was as lucid as a
perfect, stunning diamond.

***

Wednesday, November 18, 2020

La Chanson Fatale

Filed under: General — Tags: — m759 @ 11:31 pm

Harold Edwards, a founding co-editor of The Mathematical Intelligencer ,
reportedly  died at 84 on Tuesday, Nov. 10, 2020.

Images from this  journal on that date

"Surprise Party" revisited —

A Philippine meditation by Alex Garland quoted here on May 6, 2010

Sunday, July 7, 2019

Annie

Filed under: General — Tags: — m759 @ 10:25 pm

This journal last Wednesday —

Related material —

Wednesday, May 8, 2019

When the Men

Filed under: General — Tags: — m759 @ 6:33 pm

In Memoriam . . .

"When the men on the chessboard
get up and tell you where to go …."

"The I Ching encodes the geometry of the fabric of spacetime."

Sure it does.
 

Tuesday, June 12, 2018

Like Decorations in a Cartoon Graveyard

Filed under: General — m759 @ 11:00 pm

(Continued)

Two visions of happy neurons:

This post was suggested by a link in today's New York Times

"Simon Denny, the New Zealand artist whose work incorporates
board games, intervenes by introducing his own pieces into an attic of
the late-18th-century Haus zum Kirschgarten, already filled with
'old historical dollhouses, board games, chess games' and the like …."

Tuesday, August 29, 2017

Pakanga

Filed under: General — Tags: — m759 @ 1:37 am

Continued from August 23, 2017.  See a death on that date
reported by a funeral home in Monterey, California.

Pakanga = Wargame

Wednesday, August 23, 2017

Pakanga

Filed under: General — Tags: — m759 @ 4:44 am

("Every Picture Tells a Story," continued from August 15 )

Related material — Laughing-Academy Cartography.

Tuesday, August 15, 2017

Every Picture Tells a Story

Filed under: General,Geometry — Tags: — m759 @ 11:48 am

Hexagram 15:
Modesty

See also remarks today by David Brooks at The New York Times .

Friday, January 27, 2017

In Memory of Actor John Hurt

Filed under: General,Geometry — Tags: — m759 @ 11:00 pm

Hurt, who reportedly died today, played a purveyor
of magic wands
in the Harry Potter series and also
Control in “Tinker Tailor Soldier Spy.”

“In the original screenplay for the film adaptation
of Tinker Tailor Soldier Spy, Smiley muses that
Control had once told him that Howard Staunton
was the greatest chess master Britain had ever
produced. ‘Staunton’ later turns out to be the name
that Control used for the rental of his flat.”

— Wikipedia, Control (fictional character)

Related images —

Happy Chinese New Year.

Monday, May 9, 2011

Queen’s Gambit*

Filed under: General — m759 @ 9:00 am

From March 9 four years ago—

Chessboard (Detail)

* See this journal and the novel.

Update of 10 AM May 9—

Midrash for Gnostics —

A post linked to under "this journal" (above) has a brief discussion of theology and Wallace Stevens—

"Professor Eucalyptus in 'Ordinary Evening' XIV, for example, 'seeks/ God in the object itself '…."

I have more confidence that God is to be found in the Ping Pong balls of the New York Lottery.

This suggests a check of yesterday's NY numbers. They were… Midday 780, Evening 302.

A search for 780 in this journal yields a post quoting The Scotsman 's reporter Rhiannon Edward.

Related material:

Rhiannon's Scotsman  story of May 6—

Rapist gets 20 years after justice system finally believes his victims

Published Date: 06 May 2011
By Rhiannon Edward
 
A SCOTTISH care home worker who groomed and raped teenage girls for more than a decade has been jailed for 20 years.
 
James Boyes abused a string of underage girls at Frant Court care home in Frant, East Sussex, during the 1980s and 1990s, leaving one so traumatised she is still being treated in a secure mental hospital….

See also this  journal on May 7 —

Stranger Than Fiction

http://www.log24.com/log/pix11A/110507-StrangerThanFiction.jpg

For yesterday's NY evening 302, see the "780" post involving Rhiannon—

Glenn Ford as a playboy from Argentina —

The 4 Horsemen, Ingrid Thulin, Glenn Ford

— and "302" interpreted as "3/02," which yields…

"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"

For some background music, click here.

Thursday, January 6, 2011

Epiphany for Hal

Filed under: General — m759 @ 12:00 pm

IMAGE- 'A Beautiful Mind' on games (from index)

IMAGE- 'War Games' computer- 'How about a nice game of chess?'

See also Nabokov + chess + patterns.

Saturday, February 13, 2010

Entertainment continued

Filed under: General,Geometry — m759 @ 9:28 am

Logic is all about the entertaining of possibilities.”

– Colin McGinn, Mindsight: Image, Dream, Meaning,
   Harvard University Press, 2004

Geometry of Language,
continued from St. George's Day, 2009


Professor Arielle Saiber with chess set

Excerpt from Jasper Hopkins's 'Concise Introduction to the Philosophy of Nicholas of Cusa

Related material:

Prima Materia,
The Galois Quaternion,
and The Wake of Imagination.

See also the following from a physicist
(not of the most orthodox sort, but his remarks
  here on Heisenberg seem quite respectable)–

Ian J. Thompson, 7 Dec. 2009

Quantum mechanics describes the probabilities of actual outcomes in terms of a wave function, or at least of a quantum state of amplitudes that varies with time. The public always asks what the wave function is, or what the amplitudes are amplitudes of. Usually, we reply that the amplitudes are ‘probability amplitudes’, or that the wave function is a ‘probability wave function’, but neither answer is ontologically satisfying since probabilities are numbers, not stuff. We have already rehearsed the objections to the natural world being made out of numbers, as these are pure forms. In fact, ‘waves’, ‘amplitudes’ and ‘probabilities’ are all forms, and none of them can be substances. So, what are quantum objects made of: what stuff?

According to Heisenberg [6], the quantum probability waves are “a quantitative formulation of the concept of ‘dynamis’, possibility, or in the later Latin version, ‘potentia’, in Aristotle’s philosophy. The concept of events not determined in a peremptory manner, but that the possibility or ‘tendency’ for an event to take place has a kind of reality—a certain intermediate layer of reality, halfway between the massive reality of matter and the intellectual reality of the idea or the image—this concept plays a decisive role in Aristotle’s philosophy. In modern quantum theory this concept takes on a new form; it is formulated quantitatively as probability and subjected to mathematically expressible laws of nature.” Unfortunately Heisenberg does not develop this interpretation much beyond the sort of generality of the above statements, and the concept of ‘potentiality’ remains awkwardly isolated from much of his other thought on this subject [7]. It is unclear even what he means by ‘potentia’.

Reference

Heisenberg, W. 1961 On Modern Physics, London: Orion Press.

Notes

[6] W. Heisenberg, ‘Planck’s discovery and the philosophical problems of atomic physics’, pp. 3-20 in Heisenberg (1961).

[7] Heisenberg, for example, brings into his thought on quantum physics the Kantian phenomena/noumena distinction, as well as some of Bohr’s ideas on ‘complementarity’ in experimental arrangements.

Friday, September 4, 2009

Friday September 4, 2009

Filed under: General — Tags: , — m759 @ 2:02 pm
Closing the Circle

Continued from Monday

“This is a chapel 
 of mischance;
ill luck betide it, ’tis
the cursedest kirk
  that ever I came in!”

Philip Kennicott on
Kirk Varnedoe in
The Washington Post:

“Varnedoe’s lectures were
ultimately about faith,
about his faith in
the power of abstraction,
 and abstraction as a kind of
    anti-religious faith in itself….”

Kennicott’s remarks were
 on Sunday, May 18, 2003.
They were subtitled
“Closing the Circle
on Abstract Art.”

Also on Sunday, May 18, 2003:

 “Will the circle be unbroken?
  As if some southern congregation
  is praying we will come to understand.”


Princeton University Press
:

Empty canvas on cover of Varnedoe's 'Pictures of Nothing'

See also

Parmiggiani’s 
  Giordano Bruno

Parmiggiani's Bruno: empty canvas with sculpture of Durer's solid

Dürer’s Melencolia I

Durer, Melencolia I

and Log24 entries
of May 19-22, 2009,
ending with
    “Steiner System” —

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design

George Steiner on chess
(see yesterday morning):

“There are siren moments when quite normal creatures otherwise engaged, men such as Lenin and myself, feel like giving up everything– marriage, mortgages, careers, the Russian Revolution– in order to spend their days and nights moving little carved objects up and down a quadrate board.”

Steiner continues

“Allegoric associations of death with chess are perennial….”

Yes, they are.

April is Math Awareness Month.
This year’s theme is “mathematics and art.”

Mathematics and Art: Totentanz from Seventh Seal

Cf. both of yesterday’s entries.

Thursday, September 3, 2009

Thursday September 3, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:07 am
Autistic Enchantment

“Music and mathematics are among the pre-eminent wonders of the race. Levi-Strauss sees in the invention of melody ‘a key to the supreme mystery’ of man– a clue, could we but follow it, to the singular structure and genius of the species. The power of mathematics to devise actions for reasons as subtle, witty, manifold as any offered by sensory experience and to move forward in an endless unfolding of self-creating life is one of the strange, deep marks man leaves on the world. Chess, on the other hand, is a game in which thirty-two bits of ivory, horn, wood, metal, or (in stalags) sawdust stuck together with shoe polish, are pushed around on sixty-four alternately coloured squares. To the addict, such a description is blasphemy. The origins of chess are shrouded in mists of controversy, but unquestionably this very ancient, trivial pastime has seemed to many exceptionally intelligent human beings of many races and centuries to constitute a reality, a focus for the emotions, as substantial as, often more substantial than, reality itself. Cards can come to mean the same absolute. But their magnetism is impure. A mania for whist or poker hooks into the obvious, universal magic of money. The financial element in chess, where it exists at all, has always been small or accidental.

To a true chess player, the pushing about of thirty-two counters on 8×8 squares is an end in itself, a whole world next to which that of a mere biological or political or social life seems messy, stale, and contingent. Even the patzer, the wretched amateur who charges out with his knight pawn when the opponent’s bishop decamps to R4, feels this daemonic spell. There are siren moments when quite normal creatures otherwise engaged, men such as Lenin and myself, feel like giving up everything– marriage, mortgages, careers, the Russian Revolution– in order to spend their days and nights moving little carved objects up and down a quadrate board. At the sight of a set, even the tawdriest of plastic pocket sets, one’s fingers arch and a coldness as in a light sleep steals over one’s spine. Not for gain, not for knowledge or reknown, but in some autistic enchantment, pure as one of Bach’s inverted canons or Euler’s formula for polyhedra.”

— George Steiner in “A Death of Kings,” The New Yorker, issue dated September 7, 1968, page 133

“Examples are the stained-glass windows of knowledge.” —Nabokov

Quaternion rotations in a finite geometry
Click above images for some context.

See also:

Log24 entries of May 30, 2006, as well as “For John Cramer’s daughter Kathryn”– August 27, 2009— and related material at Wikipedia (where Kathryn is known as “Pleasantville”).

Tuesday, July 28, 2009

Tuesday July 28, 2009

Filed under: General,Geometry — m759 @ 1:06 pm
Man and
His Symbols 101

Continued from July 21

A headline from yesterday:

US-China ties will shape
21st century: Obama

A headline from 2003,
with an epiphany from
twenty years ago:

The Tables of Time

JFK and chess at Chinatown picnic table

Peace Rune
Hexagram 11,
Jan. 6, 1989

Picnic Symbol 

Picnic site symbol,
British Sea Scouts

In related news:

Obama to hold picnic-table peace talk

Wednesday, April 8, 2009

Wednesday April 8, 2009

Filed under: General — Tags: , , — m759 @ 12:12 am

Good’s Singularity

Irving John “I.J.” Good died Sunday, April 5, 2009.

The date of his death was also Palm Sunday and the day of the Academy of Country Music Awards.

Information from Wikipedia:

Good, 92, was a cryptanalyst at Bletchley Park during World War II.

“He was born as Isidore Jacob Gudak to a Jewish family in London. In his publications he was called I. J. Good. He studied mathematics at Jesus College, Cambridge, graduating in 1938. He did research work under G.H. Hardy and Besicovitch before moving to Bletchley Park in 1941 on completing his doctorate.

At Bletchley Park, he was initially in Hut 8 under the supervision of Alan Turing…”

[Related material: the death of Turing (a major fan of the Evil Queen in Snow White) and yesterday’s entry]

Wikipedia states that “I. J. Good’s vanity car license plate, hinting at his spylike wartime work, was ‘007 IJG’…. He played chess to county standard, and helped to popularise Go, an Asian boardgame, through a 1965 article in New Scientist (he had learned the rules from Turing). In 1965, he described a concept similar to today’s meaning of technological singularity, in that it included in it the advent of superhuman intelligence:

Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion,’ and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make….
— Good, I. J. (1965). ‘Speculations Concerning the First Ultraintelligent Machine‘, Advances in Computers, Vol. 6.”
“Some say the symbol
of Apple Computers,
the apple with a bite out of it,
is a nod to Alan Turing.”– from “Alan Turing and
the Apple
at Flickr, uploaded
on Epiphany 2006 by guano

Alan Turing and the Apple

http://www.log24.com/log/pix09/090408-TuringApples.jpg

Above: Composite by “guano” at Flickr

Will: Do you like apples?
Clark: Yeah.
Will: Well, I got her number.
How do you like them apples?

— “Good Will Hunting

Happy Spy Wednesday.

Friday, April 3, 2009

Friday April 3, 2009

Filed under: General,Geometry — Tags: , — m759 @ 5:24 am
Knight Moves

“Lord, I remember”
Bob Seger 


“Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday….”

Bernard Holland in The New York Times of Monday, May 20, 1996

Yesterday’s afternoon entry cited philosopher John Holbo on chess. This, together with Holland’s remark above and Monday’s entries on Zizek, suggests…

Holbo on Zizek
(pdf, 11 pages)

In this excellent analysis,
Holbo quotes Kierkegaard:

“… the knight of faith
‘has the pain of being unable to
make himself intelligible to others'”

(Kierkegaard, Fear and Trembling)

For some material that may serve to illustrate Kierkegaard’s remark, see Log24 on Twelfth Night and Epiphany this year.

“… There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight…. I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”


— Raymond Chandler, The Big Sleep

Perhaps a game for bishops?

Henry Edward Cardinal Manning

Cardinal Manning

Click on the cardinal
for a link to some remarks
related to the upcoming film
 “Angels & Demons” and to
a Paris “Sein Feld.”


Context: the five entries
ending at 9:26 AM
on March 10, 2009…
and, for Kierkegaard,
Diamonds Are Forever.

Saturday, March 21, 2009

Saturday March 21, 2009

Filed under: General,Geometry — Tags: , — m759 @ 12:25 am

Counters in Rows

"Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns)."

— George Steiner
   (See March 10, "Language Game.")
 



For example:

Model of the 21-point projective plane consisting of the 1- and 2- subsets of a 6-set

Click to enlarge.

Context:

Notes on Finite Geometry
(Section on 6-set structures)
 

Friday, January 16, 2009

Friday January 16, 2009

Filed under: General — Tags: — m759 @ 10:31 am
Academy Award

“Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday.”

Bernard Holland

“I feel very happy to be a part of Mind Champions Academy.”

— A winner at a chess awards ceremony in India on Monday

John Mortimer, who wrote the TV version of Brideshead Revisited, died today. In his memory:

Todo lo sé
 por el lucero puro
que brilla en
 la diadema de la Muerte.

Rubén Darío    

King's Moves

King’s Moves,
adapted from
a figure by
F. Lanier Graham

Related material:
Will this be  
  on the test?

Thursday, January 15, 2009

Thursday January 15, 2009

Filed under: General — Tags: — m759 @ 6:00 pm
Harvard, Magic,
and The New York Times

The New York Times Magazine for next Sunday:

The Edge of the Mystery, by Matt Bai–

“Weeks before the election of 1960, Norman Mailer, already an accomplished novelist, sat down to write his first major work of political journalism, an essay for Esquire in which he argued that only John F. Kennedy could save America… the only kind of leader who could rescue it, who could sweep in an era of what Mailer called ‘existential’ politics, was a ‘hipster’ hero– someone who welcomed risk and adventure, someone who sought out new experience, both for himself and for the country….

… Mailer essentially created a new genre for a generation of would-be literary philosophers covering politics….  By 1963, Mailer and other idealists were crushed to discover that Kennedy was in fact a fairly conventional and pragmatic politician, more Harvard Yard than Fortress of Solitude.”

The New York Times today:

Magic and Realism, by Roger Cohen–

“… what I want from the Obama administration is something more than Harvard-to-the-Beltway smarts. I want magical realism.”

Mailer and Cohen, taken together, suggest I should review two authors– Picard and Hesse– I encountered as a Harvard freshman in 1960.

Max Picard:

“In the ‘Prologue in Heaven’ in Goethe’s Faust a powerful silence is produced by the powerful word after each verse. There is an active, audible silence after every verse. The things that were moved into position by the word stand motionless in the silence, as if they were waiting to be called back into the silence and to disappear therein. The word not only brings the things out of silence; it also produces the silence in which they can disappear again.”

Goethe:

DER HERR:
Kennst du den Faust?

MEPHISTOPHELES:
Den Doktor?

DER HERR:
Meinen Knecht!

Online Etymology Dictionary:

knight
O.E. cniht “boy, youth, servant,” common W.Gmc. (cf. O.Fris. kniucht, Du. knecht, kneht “boy, youth, lad,” Ger. Knecht “servant, bondsman, vassal”), of unknown origin. Meaning “military follower of a king or other superior” is from c.1100. Began to be used in a specific military sense in Hundred Years War, and gradually rose in importance through M.E. period until it became a rank in the nobility 16c. The verb meaning “to make a knight of (someone)” is from c.1300. Knighthood is O.E. cnihthad M.H.G. “the period between childhood and manhood;” sense of “rank or dignity of a knight” is from c.1300. The chess piece so called from c.1440.

Further background on the word “Knecht”–

'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

Epigraph to Magister Ludi
(Joseph Knecht’s translation):


“… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

Tuesday, January 13, 2009

Tuesday January 13, 2009

Filed under: General — Tags: — m759 @ 1:00 pm

Something Traditional —

“German Chancellor Dr. Angela Merkel is the Charlemagne Prize laureate of 2008…. The prize will be awarded on 1 May, Ascension Day.”

The City of Aachen

Something Modern —

Previously undescribed in this journal:

A chess set
by F. Lanier Graham
of modular design:

Interlocking chess pieces by F. Lanier Graham, 1967

A NOTE BY THE DESIGNER

“The traditional chess set, with its naturalistic images of medieval armies, suggests a game between combatants who enjoy the winning of battles. This chess set, with its articulated images of abstract force, suggests a game between contestants who enjoy the process of thinking.
   
The primary principle of this design… is that the operating reality or function of each piece– both its value and how it moves– is embodied in a simple self-expressive form….

Chess pieces by F. Lanier Graham, 1967

Design Copyright F. Lanier Graham 1967


These pieces are designed to have the look and feel of little packages of power. The hardwoods (walnut and korina) are left unfinished, not only because of tactile values, but also to emphasize the simplicity of the design. The interlocking blocks are packaged to reflect the essential nature of the game– rational recreation, played with basic units whose fields of force continuously interact in subtle, complex patterns.”

— F. Lanier Graham, 1967

For those whose tastes in recreation are less rational, there is also the legendary chess set of Charlemagne described in novels by Katherine Neville. (See ART WARS.)

Related material: this journal on the First of May, 2008, the date of last year’s Charlemagne award.

Sunday, October 5, 2008

Sunday October 5, 2008

Filed under: General — Tags: — m759 @ 4:23 pm
Nash Equilibrium or:
To Make a Short Story Long

Last night's entry presented a
short story summarized by
four lottery numbers.

Today's mid-day lotteries
and associated material:

Pennsylvania, 201– i.e., 2/01:
Kindergarten Theology

Theologian James Edwin Loder:

"In a game of chess, the knight's move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a 'knight's move' in intelligence."

New York, 229– i.e., 2/29:
I Have a Dreamtime

"One must join forces with friends of like mind"

Related material:

Terence McKenna:

"Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey 'haunts time like a ghost.'"

Anonymous author:

"'Knight's move thinking' is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia."

Star Wars:
 
John Nash, as portrayed by Russell Crowe

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O'Bedlam's Song

For more on the sleep of Apollo,
see the front page of today's
New York Times Book Review.

Garrison Keillor's piece there,
"Dying of the Light," is
about the fear of death felt
by an agnostic British twit.

For relevant remarks by
a British non-twit, see
William Dunbar–

Timor Mortis conturbat me.

Friday, February 1, 2008

Friday February 1, 2008

Filed under: General,Geometry — Tags: — m759 @ 5:01 am
Kindergarten Theology

On the late James Edwin Loder,
a Presbyterian minister and
a professor of Christian education
at Princeton Theological Seminary,
co-author of The Knight’s Move (1992):

“At his memorial service his daughter Tami told the story of ‘little Jimmy,’ whose kindergarten teacher recognized a special quality of mind that set him apart. ‘Every day we read a story, and after the story is over, Jimmy gets up and wants to tell us what the story means.'” — Dana R. Wright

For a related story about
knight moves and kindergarten,
see Knight Moves: The Relativity
Theory of Kindergarten Blocks
,
and Log24, Jan. 16, 17, and 18.

See also Loder’s book
(poorly written, but of some
interest in light of the above):

The Knight's Move, by Loder and Neidhardt

Opening of The Knight’s Move —

“In a game of chess, the knight’s move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a ‘knight’s move’ in intelligence.

The significance of the title of this volume might stop there but for Kierkegaard’s use of the ‘knight’ image. The force of Kierkegaards’s usage might be described in relation to the chess metaphor by saying that not merely does Kierkegaard’s ‘knight of faith’ undertake a unique move within the rules of the human game, but faith transposes the whole idea of a ‘knight’s move’ into the mind of the Chess Master Himself. That is to say, chess is a game of multiple possibilities and interlocking strategies, so a chess master must combine the  continuity represented by the whole complex of the game with the unpredictable decision he must make every time it is his turn. A master chess player, then, does not merely follow the rules; in him the game becomes a construct of consciousness. The better the player the more fully the game comes into its own as a creation of human intelligence. Similarly, for Kierkegaard, the knight of faith is a unique figure in human experience. The knight shows how, by existing in faith as a creative act of Christ’s Spirit, human existence comes into its own as an expression of the mind of Christ. Thus, the ultimate form of a ‘knight’s move’ is a creative act raised to the nth power by Spiritus Creator, but it still partakes fully in the concrete pieces and patterns that comprise the nature of the human game and the game of nature.”

— James E. Loder and W. Jim Neidhardt (Helmers & Howard Publishing, 1992)

For a discussion, see Triplett’s
Thinking Critically as a Christian.”

Many would deny that such
a thing is possible; let them
read the works of T. S. Eliot.

Related material:

The Knight’s Move
discusses (badly) Hofstadter’s
“strange loop” concept; see
Not Mathematics but Theology
(Log24, July 12, 2007).

Saturday, January 19, 2008

Saturday January 19, 2008

Filed under: General — Tags: , — m759 @ 7:00 am
In Memory of
Bobby Fischer

Edward Rothstein has a piece on Bobby Fischer in today’s New York Times.  The Rothstein opening:

“There may be only three human activities in which miraculous accomplishment is possible before adulthood: mathematics, music and chess.”

This echoes the opening of a classic George Steiner essay (The New Yorker, Sept. 7, 1968):

“There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess.”

— “A Death of Kings,” reprinted in George Steiner: A Reader, Oxford University Press, 1984, pp. 171-178.

Despite its promising (if unoriginal) opening, the New York Times piece is mainly an attack on Fischer’s anti-Jewish stance.  Rothstein actually has little of interest to say about what he calls the “glass-bead games” of music, mathematics, and chess. For a better-written piece on chess and madness, see Charles Krauthammer’s 2005 essay in TIME. The feuilletons of Rothstein and Krauthammer do not, of course, come close to the genuinely bead-game-like writing of Steiner.

Related material on
chess and religion:
Magical Thinking
(December 7th, 2005)

Saturday, July 14, 2007

Saturday July 14, 2007

Filed under: General — m759 @ 4:07 am
A Note from the
Catholic University
of America


The August 2007 issue of Notices of the American Mathematical Society contains tributes to the admirable personal qualities and mathematical work of the late Harvard professor George Mackey.  For my own tributes, see Log24 on March 17, 2006April 29, 2006, and March 10, 2007.  For an entry critical of Mackey’s reductionism– a philosophical, not mathematical, error– see Log24 on May 23, 2007 (“Devil in the Details”).

Here is another attack on reductionism, from a discussion of the work of another first-rate mathematician, the late Gian-Carlo Rota of MIT:

“Another theme developed by Rota is that of ‘Fundierung.’ He shows that throughout our experience we encounter things that exist only as founded upon other things: a checkmate is founded upon moving certain pieces of chess, which in turn are founded upon certain pieces of wood or plastic. An insult is founded upon certain words being spoken, an act of generosity is founded upon something’s being handed over. In perception, for example, the evidence that occurs to us goes beyond the physical impact on our sensory organs even though it is founded upon it; what we see is far more than meets the eye. Rota gives striking examples to bring out this relationship of founding, which he takes as a logical relationship, containing all the force of logical necessity. His point is strongly antireductionist. Reductionism is the inclination to see as ‘real’ only the foundation, the substrate of things (the piece of wood in chess, the physical exchange in a social phenomenon, and especially the brain as founding the mind) and to deny the true existence of that which is founded. Rota’s arguments against reductionism, along with his colorful examples, are a marvelous philosophical therapy for the debilitating illness of reductionism that so pervades our culture and our educational systems, leading us to deny things we all know to be true, such as the reality of choice, of intelligence, of emotive insight, and spiritual understanding. He shows that ontological reductionism and the prejudice for axiomatic systems are both escapes from reality, attempts to substitute something automatic, manageable, and packaged, something coercive, in place of the human situation, which we all acknowledge by the way we live, even as we deny it in our theories.”

Robert Sokolowski, foreword to Rota’s Indiscrete Thoughts

Father Robert Sokolowski

Father Robert Sokolowski

Fr. Robert Sokolowski, Ph.D., is Professor of Philosophy at The Catholic University of America in Washington, D.C. Ordained a Roman Catholic priest in 1962, he is internationally recognized and honored for his work in philosophy, particularly phenomenology. In 1994, Catholic University sponsored a conference on his work and published several papers and other essays under the title, The Truthful and the Good, Essays In Honor of Robert Sokolowski.

Thomas Aquinas College newsletter

The tributes to Mackey are contained in the first of two feature articles in the August 2007 AMS Notices.  The second feature article is a review of a new book by Douglas Hofstadter.  For some remarks related to that article, see Thursday’s Log24 entry “Not Mathematics but Theology.”

Wednesday, June 6, 2007

Wednesday June 6, 2007

Filed under: General,Geometry — m759 @ 11:07 am
It is now 3:07 AM
June 7 in New Zealand.
Today at Cullinane College:

Examination Day

IMAGE- Rogue Winter with spear, Jupiter in background, on cover of 'The Deceivers,' a novel by Alfred Bester.

(For the college curriculum,
see the New Zealand
Qualifications Authority.)

If Cullinane College were Hogwarts–

Last-minute exam info:

The Lapis Philosophorum

"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
Aion, by C. G. Jung

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."
The Stars My Destination, by Alfred Bester

And from Bester's The Deceivers:

Meta Physics

"'… Think of a match.  You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released.  Friction does it.  But when Meta excites and releases energy, it's like a stick of dynamite compared to a match.  It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah.  The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what.  The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

'That doesn't sound like much.'

'So the rajah said. …'"

Related material:

Geometry of the I Ching
 

Friday, April 20, 2007

Friday April 20, 2007

Filed under: General — m759 @ 11:07 am
Icons

Part I

The Library of Congress
Today in History, April 20:

“American sculptor Daniel Chester French was born in Exeter, New Hampshire on April 20, 1850. His colossal seated figure of Abraham Lincoln presides over the Lincoln Memorial.

Reared in Cambridge and Concord, Massachusetts, he was embraced by members of the Transcendentalist community including Ralph Waldo Emerson. Author and fellow Concord resident Louisa May Alcott encouraged young French to pursue a career as an artist. Louisa’s sister, artist May Alcott, was his early teacher.

French studied in Boston and New York prior to receiving his first commission for the 1875 statue The Minute Man. Standing near the North Bridge in Concord, in the Minute Man National Historical Park, this work commemorates events at the North Bridge, the site of ‘the shot heard ’round the world.’ An American icon, images derivative of The Minute Man statue appeared on defense bonds, stamps, and posters during World War II.”

Part II:

Entertainment Weekly,

November 7, 2003

Keanu Reeves, Entertainment Weekly, Nov. 7, 2003

Part III:

Log24 on the anniversary of
Lincoln’s assassination —

Saturday, April 14, 2007  4:30 AM

The Sun Also Sets, or…

This Way to
the Egress

Continued from April 12:

“I have only come here 
seeking knowledge,
 Things they would not   
       teach me of in college….”
 
— Synchronicity
lyrics

Quoted in Log24,
Time’s Labyrinth continued:

“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?”

— Katherine Neville,
The Eight,

Ballantine reprint, 1990,


“Know the one about
the Demiurge and the
Abridgment of Hope?”

— Robert Stone,
A Flag for Sunrise,
Knopf, 1981,
the final page

Part IV:

Log24 entry of

November 7, 2003

Nixon's the One button

— and a
student play from
Virginia Tech:

Play by Virginia Tech student

Part V:


Symmetry
for Beavis and Butt-Head

and
The Rhetoric of Scientism:

It’s a very ancient saying,
But a true and honest thought,
That if you become a teacher,
By your pupils you’ll be taught.

— Oscar Hammerstein,
“Getting to Know You”

Saturday, March 10, 2007

Saturday March 10, 2007

Filed under: General,Geometry — m759 @ 9:00 am

The Logic of Dreams

From A Beautiful Mind–

“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”

Ideas:

The image “http://www.log24.com/log/pix07/070309-NYlottery.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070309-PAlottery.jpg” cannot be displayed, because it contains errors.

These numbers may, in the mad way so well portrayed by Sylvia Nasar in the above book, be regarded as telling a story… a story that should, of course, not be taken too seriously.

Friday’s New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11.  Clicking on these dates will lead the reader to Log24 entries featuring, among others, T. S. Eliot and Stephen King– two authors not unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:

Chessboard (Detail)

This illustration refers to chess rather than to geometry, and to the mind of an addict rather than to that of a slave, but chess and geometry, like addiction and slavery, are not unrelated.


Friday’s Pennsylvania numbers, midday 429 and evening 038, suggest that the story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“–  “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)

Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).

More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.

Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:

The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Wednesday, March 7, 2007

Wednesday March 7, 2007

Filed under: General,Geometry — m759 @ 8:24 am
In the Labyrinth
of Time:


8:24:48
AM EST


Related material–


Symbols:

The image “http://www.log24.com/log/pix07/070307-Symbols.gif” cannot be displayed, because it contains errors.

and

The False Artaxerxes:
Borges and the
Dream of Chess

This entry was inspired by
Xanga footprints yesterday
from Virginia:

 
1. Virginia
Weblog
ART WARS:
Time and the Grid
3/6/2007
9:48 AM
2. Virginia
Weblog
Sequel
3/6/2007
11:38 AM
3. Virginia
Weblog
Games and Truth
3/6/2007
1:25 PM
4. Virginia
/item.aspx?user=m759&ta…
The Transcendent Signified
3/6/2007
5:15 PM
5. Virginia
/item.aspx?user=m759&ta…
Zen and Language Games
3/6/2007
5:16 PM
6. Virginia
/item.aspx?user=m759&ta…
Balanchine’s Birthday
3/6/2007
6:12 PM
7. Virginia
/item.aspx?user=m759&ta…
The Agony and the Ya-Ya
3/6/2007
6:12 PM
8. Virginia
/item.aspx?user=m759&ta…
Directions Out
3/6/2007
6:13 PM
9. Virginia
/item.aspx?user=m759&ta…
The Four Last Things
3/6/2007
6:13 PM

Thursday, January 4, 2007

Thursday January 4, 2007

Filed under: General — Tags: — m759 @ 12:00 pm

Readings for wise men
on the date of
T. S. Eliot's death:

"A cold coming we had of it…."

"… a Church is to be judged by its intellectual fruits, by its influence on the sensibility of the most sensitive and on the intellect of the most intelligent, and it must be made real to the eye by monuments of artistic merit."

— T. S. Eliot, For Lancelot Andrewes: Essays on Style and Order, published by Faber & Gwyer, London,  in 1928.

The visual "monuments of artistic merit" I prefer are not those of a Church– except, perhaps, the Church of Modernism.  Literary monuments are another matter.  I recommend:

The Death of Adam,

The Novels of Charles Williams, and

Let Sleeping Beauties Lie.
 

Related material
on style and order:

 

Eliot's essay on Andrewes begins,
"The Right Reverend Father in God,
Lancelot Bishop of Winchester,
died on September 25, 1626."

For evidence of Andrewes's
saintliness (hence, that
of Eliot) we may examine
various events of the
25th of September.

("On September 25th most of
the Anglican Communion
commemorates the day on which
Lancelot Andrewes died."
)

In Log24,
these events are…

Sept. 25, 2002

"Las Mañanitas"

Sept. 25, 2003

The image “http://www.log24.com/log/pix07/030925-Bubbles2.jpg” cannot be displayed, because it contains errors.

Aloha.

Sept. 25, 2004

Sept. 25, 2005

The image “http://www.log24.com/log/pix05B/050925-db3.gif” cannot be displayed, because it contains errors.

Sept. 25, 2006

The image “http://www.log24.com/log/pix07/060925-Medal2.jpg” cannot be displayed, because it contains errors.
(Yau and Perelman)

It seems that I am
somewhat out of step with
  the Anglican Communion…
though perhaps, in a sense,
in step with Eliot.

Note his words in
"Journey of the Magi":

Birth or Death?
There was a Birth, certainly,
We had evidence and no doubt.
I had seen birth and death,
But had thought they were different;
this Birth was
Hard and bitter agony for us,
like Death, our death.

See also entries for
Dec. 27, 2006 (the day of
Itche Goldberg's death) —

Photo op for Gerald Ford

— "Least Popular
Christmas Present
Revisited
" —

and for the same date
three years earlier

"If you don't play
some people's game, they say
that you have 'lost your marbles,'
not recognizing that,

while Chinese checkers
is indeed a fine pastime,
a person may also play dominoes,
chess, strip poker, tiddlywinks,
drop-the-soap or Russian roulette
with his brain.

One brain game that is widely,
if poorly, played is a gimmick
called 'rational thought.'"

Tom Robbins
 

Sunday, September 10, 2006

Sunday September 10, 2006

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 am

And the
"
Meet Max Black"
Award goes to…

The image “http://www.log24.com/log/pix06A/060910-Obits.jpg” cannot be displayed, because it contains errors.

"For the Aeron and other designs,
Mr. Stumpf won this year’s
National Design Award
in Product Design
,
which is to be presented
posthumously on Oct. 18
by the Cooper-Hewitt
National Design Museum
in Manhattan."

— Today's New York Times

Stumpf died on August 30,
the date of the Log24 entry
"The Seventh Symbol."

Related material:

From
Geometry of the I Ching,
a chessboard:

I Ching chessboard (original 1989 arrangement)

From the
 National Design Museum:

The image “http://www.log24.com/log/pix06A/060910-DesignAwards.gif” cannot be displayed, because it contains errors.

 From Log24 on the
date of Stumpf's death,

The Seventh Symbol:

The image “http://www.log24.com/log/pix06A/060910-Box121.jpg” cannot be displayed, because it contains errors.

Pictorial version of
Hexagram 20,
Contemplation (View)

See also
Fearful Symmetry
and
Symmetry Framed.

Monday, July 3, 2006

Monday July 3, 2006

Filed under: General — m759 @ 11:07 pm

Culture War

The New York Times, August 6, 2003,
on its executive editor Bill Keller:

“‘It is past time for our magnificent coverage of culture and lifestyles, so essential to our present allure and to our future growth, to get the kind of attention we routinely bestow on hard news,’ Mr. Keller wrote in an e-mail message to the staff.”

The New York Times, June 25, 2006,
on art in Mexico:

“At the Hilario Galguera gallery, newly opened in a fortresslike, century-old building, was Damien Hirst’s gory new series ‘The Death of God– Towards a Better Understanding of Life Without God Aboard the Ship of Fools.’  He conceived the work at his part-time home in the Mexican surf town Troncones.”

Raymond Chandler in The Big Sleep:

   “I went over to a floor lamp and pulled the switch, went back to put off the ceiling light, and went across the room again to the chessboard on a card table under the lamp. There was a problem laid out on the board, a six-mover.  I couldn’t solve it, like a lot of my problems.  I reached down and moved a knight, then pulled my hat and coat off and threw them somewhere.  All this time the soft giggling went on from the bed, that sound that made me think of rats behind a wainscoting in an old house.

…………

    I looked down at the chessboard.  The move with the knight was wrong.  I put it back where I had moved it from.  Knights had no meaning in this game.  It wasn’t a game for knights.”

Wednesday, December 7, 2005

Wednesday December 7, 2005

Filed under: General — m759 @ 1:00 pm
Magical Thinking
 
(continued)

1:00:19 EST

The Lion, the Witch
and the Wardrobe

premieres tonight at
 the Royal Albert Hall.

Log24 Dec. 2:

Hexagram 19 in the
Cullinane series:

The image “http://www.log24.com/log/pix05B/051202-Hex19.jpg” cannot be displayed, because it contains errors.

Log24 Dec. 3:

The image “http://www.log24.com/log/pix05B/051202-Axe.jpg” cannot be displayed, because it contains errors.

Katherine Neville, The Eight

    “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?


“But what does it all mean?” asked Susan when they were somewhat calmer.

“It means,” said Aslan, “that though the Witch knew the Deep Magic, there is a magic deeper still which she did not know. Her knowledge goes back only to the dawn of Time. But if she could have looked a little further back, into the stillness and the darkness before Time dawned, she would have read there a different incantation. She would have known that when a willing victim who had committed no treachery was killed in a traitor’s stead, the Table would crack and Death itself would start working backward.”

 

Wednesday, November 30, 2005

Wednesday November 30, 2005

Filed under: General,Geometry — Tags: — m759 @ 8:20 pm

Hobgoblin?

Brian Davies is a professor of mathematics at King’s College London.  In the December Notices of the American Mathematical Society, he claims that arithmetic may, for all we know, be inconsistent:

“Gödel taught us that it is not possible to prove that Peano arithmetic is consistent, but everyone has taken it for granted that in fact it is indeed consistent.
    Platonistically-inclined mathematicians would deny the possibility that Peano arithmetic could be flawed.  From Kronecker onwards many consider that they have a direct insight into the natural numbers, which guarantees their existence. If the natural numbers exist and Peano’s axioms describe properties that they possess then, since the axioms can be instantiated, they must be consistent.”

“It is not possible to prove that Peano arithmetic is consistent”…?!

Where did Gödel say this?  Gödel proved, in fact, according to a well-known mathematician at Princeton, that (letting PA stand for Peano Arithmetic),

“If PA is consistent, the formula expressing ‘PA is consistent’ is unprovable in PA.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Remarkably, even after he has stated correctly Gödel’s result, Nelson, like Davies, concludes that

“The consistency of PA cannot be concretely demonstrated.”

I prefer the argument that the existence of a model ensures the consistency of a theory.

For instance, the Toronto philosopher William Seager writes that

“Our judgement as to the consistency of some system is not dependent upon that system’s being able to prove its own consistency (i.e. generate a formula that states, e.g. ‘0=1’ is not provable). For if that was the sole basis, how could we trust it? If the system was inconsistent, it could generate this formula as well (see Smullyan, Gödel’s Incompleteness Theorems, (Oxford, 1992, p. 109)). Furthermore, [George] Boolos allows that we do know that certain systems, such as Peano Arithmetic, are consistent even though they cannot prove their own consistency. Presumably, we know this because we can see that a certain model satisfies the axioms of the system at issue, hence that they are true in that model and so must be consistent.”

Yesterday’s Algorithm:
    Penrose and the Gödel Argument

The relationship between consistency and the existence of a model is brought home by the following weblog entry that neatly summarizes a fallacious argument offered in the AMS Notices by Davies:

The following is an interesting example that I came across in the article “Whither Mathematics?” by Brian Davies in the December issue of Notices of the American Mathematical Society.

Consider the following list A1 of axioms.

(1) There is a natural number 0.
(2) Every natural number a has a successor, denoted by S(a).
(3) There is no natural number whose successor is 0.
(4) Distinct natural numbers have distinct successors: a = b if and only if S(a) = S(b).
(5) If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all the natural numbers.

Now consider the following list A2 of axioms.

(1) G is a set of elements and these elements obey the group axioms.
(2) G is finite but not isomorphic to any known list of finite simple groups.
(3) G is simple, in other words, if N is a subset of G satisfying certain properties then N=G.

We can roughly compare A2 with A1. The second axiom in A2 can be thought of as analogous to the third axiom of A1. Also the third axiom of A2 is analogous to the fifth axiom of A1, insofar as it refers to an unspecified set with cetain properties and concludes that it is equal to G.

Now, as is generally believed by most group theorists, the system A2 is internally inconsistent and the proof its inconsistency runs for more than 10000 pages.

So who is to deny that the system A1 is also probably internally inconsistent! Particularly since Godel proved that you can not prove it is consistent (staying inside the system). May be the shortest proof of its inconsistency is one hundred million pages long!

— Posted by Krishna,
   11/29/2005 11:46:00 PM,
   at his weblog,
  “Quasi-Coherent Ruminations”

An important difference between A1 (the set of axioms of Peano arithmetic) and A2 (a set of axioms that describe a new, unknown, finite simple group) is that A1 is known to have a model (the nonnegative integers) and A2 is not known to have a model.

Therefore, according to Seager’s argument, A1 is consistent and A2 may or may not be consistent.

The degree to which Seager’s argument invokes Platonic realism is debatable.  Less debatable is the quasireligious faith in nominalism proclaimed by Davies and Nelson.  Nelson’s own account of a religious experience in 1976 at Toronto is instructive.

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

— Edward Nelson,
   Mathematics and Faith (pdf)

Nelson’s “Mathematics and Faith” was written for the Jubilee for Men and Women from the World of Learning held at the Vatican, 23-24 May 2000.  It concludes with an invocation of St. Paul:

During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his Pellegrino di Roma.  “For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Belief in the consistency of arithmetic may or may not be foolish, and therefore an Emersonian hobgoblin of little minds, but bullshit is bullshit, whether in London, in Princeton, in Toronto, or in Rome.

Saturday, October 15, 2005

Saturday October 15, 2005

Filed under: General — m759 @ 10:28 am

Canon

A brief note to place Edward Bennett Marks, who died either on Saturday, October 8, 2005 (Washington Post), or on Monday, October 10, 2005 (New York Times), in my personal canon of saints.  Today’s New York Times says that Marks spent his career “aiding refugees as an executive of American and international agencies, both official and volunteer.”  This alone was commendable, but not miraculous.  The miraculous is contained in three words from the Log24 entry of October 10, the date of death of Orson Welles, of Yul Brynner, and perhaps of Marks: “All come home.”

For a rather different perspective on St. Yul Brynner, see “Shall We Dance?”–  a profile by Calvin Tomkins in this week’s New Yorker (issue dated 2005 10/17, posted 10/10) of an artist raised in Bangkok.  It is perhaps not irrelevant that the chess enthusiast Marcel Duchamp plays a prominent role in this piece.

The image “http://www.log24.com/log/pix05B/051015-Duchamp2.gif” cannot be displayed, because it contains errors.
 
Marcel Duchamp
 
Some other remarks on chess and art:

From Introduction to Aesthetics
(Log24, October 10, 2004) —

G. H. Hardy on chess problems:

“It is essential… (unless the problem is too simple to be really amusing) that the key-move should be followed by a good many variations, each requiring its own individual answer.”

According to the New York Times, Marks died on Oct. 10 (see related entry).

According to the Washington Post, Marks died on Oct. 8 (see related entry).

For some remarks on art by St. Edward, see UN Chronicle, Issue 4, 1998.

Friday, April 15, 2005

Friday April 15, 2005

Filed under: General — Tags: — m759 @ 7:11 am
Leonardo Day

The image “http://www.log24.com/log/pix05/050415-Google.gif” cannot be displayed, because it contains errors.

In memory of Leonardo and of Chen Yifei (previous entry), a link to the Sino-Judaic Institute’s review of Chen’s film “Escape to Shanghai” —

The image “http://www.log24.com/log/pix05/050415-PointsEast.gif” cannot be displayed, because it contains errors.
Click on the above for details.

Related material
from Log24.net:


Saturday, December 27, 2003  10:21 PM

Toy

“If little else, the brain is an educational toy.  While it may be a frustrating plaything — one whose finer points recede just when you think you are mastering them — it is nonetheless perpetually fascinating, frequently surprising, occasionally rewarding, and it comes already assembled; you don’t have to put it together on Christmas morning.

The problem with possessing such an engaging toy is that other people want to play with it, too.  Sometimes they’d rather play with yours than theirs.  Or they object if you play with yours in a different manner from the way they play with theirs.  The result is, a few games out of a toy department of possibilities are universally and endlessly repeated.  If you don’t play some people’s game, they say that you have ‘lost your marbles,’ not recognizing that,

while Chinese checkers is indeed a fine pastime, a person may also play dominoes, chess, strip poker, tiddlywinks, drop-the-soap or Russian roulette with his brain.

One brain game that is widely, if poorly, played is a gimmick called ‘rational thought.’ “

— Tom Robbins, Even Cowgirls Get the Blues

Sol LeWitt
June 12, 1969
:

“I took the number twenty-four and there’s twenty-four ways of expressing the numbers one, two, three, four.  And I assigned one kind of line to one, one to two, one to three, and one to four.  One was a vertical line, two was a horizontal line, three was diagonal left to right, and four was diagonal right to left.  These are the basic kind of directions that lines can take…. the absolute ways that lines can be drawn.   And I drew these things as parallel lines very close to one another in boxes.  And then there was a system of changing them so that within twenty-four pages there were different arrangements of actually sixteen squares, four sets of four.  Everything was based on four.  So this was kind of a… more of a… less of a rational… I mean, it gets into the whole idea of methodology.”

Yes, it does.
See Art Wars, Poetry’s Bones, and Time Fold.


Friday, December 26, 2003  7:59 PM

ART WARS, St. Stephen’s Day:

The Magdalene Code

Got The Da Vinci Code for Xmas.

From page 262:

When Langdon had first seen The Little Mermaid, he had actually gasped aloud when he noticed that the painting in Ariel’s underwater home was none other than seventeenth-century artist Georges de la Tour’s The Penitent Magdalene — a famous homage to the banished Mary Magdalene — fitting decor considering the movie turned out to be a ninety-minute collage of blatant symbolic references to the lost sanctity of Isis, Eve, Pisces the fish goddess, and, repeatedly, Mary Magdalene.

Related Log24 material —

December 21, 2002:

A Maiden’s Prayer

The Da Vinci Code, pages 445-446:

“The blade and chalice?” Marie asked.  “What exactly do they look like?”

Langdon sensed she was toying with him, but he played along, quickly describing the symbols.

A look of vague recollection crossed her face.  “Ah, yes, of course.  The blade represents all that is masculine.  I believe it is drawn like this, no?”  Using her index finger, she traced a shape on her palm.

“Yes,” Langdon said.  Marie had drawn the less common “closed” form of the blade, although Langdon had seen the symbol portrayed both ways.

“And the inverse,” she said, drawing again upon her palm, “is the chalice, which represents the feminine.”

“Correct,” Langdon said….

… Marie turned on the lights and pointed….

“There you are, Mr. Langdon.  The blade and chalice.”….

“But that’s the Star of Dav–“

Langdon stopped short, mute with amazement as it dawned on him.

The blade and chalice.

Fused as one.

The Star of David… the perfect union of male and female… Solomon’s Seal… marking the Holy of Holies, where the male and female deities — Yahweh and Shekinah — were thought to dwell.

Related Log24 material —

May 25, 2003:
Star Wars.
 


Concluding remark of April 15, 2005:
For a more serious approach to portraits of
redheads, see Chen Yifei’s work.

The image “http://www.log24.com/log/pix05/050415-TheDuet-ChenYifei.jpg” cannot be displayed, because it contains errors.

Wednesday, October 13, 2004

Wednesday October 13, 2004

Filed under: General — m759 @ 2:56 pm

Show Business
according to Fritz Leiber

(Leiber's "Changewar" is my
favorite mythology.)

The image “http://www.log24.com/log/pix04A/Changewar.jpg” cannot be displayed, because it contains errors.

From the Changewar story
"No Great Magic" (1963) Part V:

Even little things are
turning out to be great things
and becoming intensely interesting.
Have you ever thought about
the properties of numbers?

— The Maiden

"I've had this idea– it's just a sort of fancy, remember– that if you wanted to time-travel and, well, do things, you could hardly pick a more practical machine than a dressing-room and a sort of stage and half-theater attached, with actors to man it…."

For the remainder of this section
of Leiber's story, see

Show Business.

Related material:
The previous entry,
The Eight, and
Now We See Wherein
Lies the Pleasure
.

Wednesday, January 14, 2004

Wednesday January 14, 2004

Filed under: General — Tags: , — m759 @ 2:00 am

Games

On this date —

Alfred Tarski was born
in 1902 in Warsaw, and

Kurt Friedrich Gödel died
in 1978 in Princeton.

From last year’s entry on this date:

What is Truth?

“What is called ‘losing’ in chess
may constitute winning
in another game.”

— Ludwig Wittgenstein,
Remarks on the
Foundations of Mathematics
(revised edition, MIT Press, 1978)

Friday, January 9, 2004

Friday January 9, 2004

Filed under: General — m759 @ 2:01 am

HURRY UP PLEASE
IT’S TIME

— T. S. Eliot,
The Waste Land, II
A Game of Chess

“Make the white Queen run so fast 
 she hasn’t got time to make you wise, 
 ’cause it’s time, it’s time
    in time with your time
                              and its news
 is captured
                  for the Queen to use.”

—   from “Your Move,” or
    “I’ve Seen All Good People,”
     by Yes (Jon Anderson and
     Chris Squire), played in the
     soundtrack of a “Big Fish”
     movie trailer tonight in the
     obituary of Brian Gibson at
     the New York Times site.

     For related material, see
     The Black Queen and 
     History of a Symbol.

Jan. 9 obituary of Brian Gibson

“In 2002 he was executive producer of the film ‘Frida,’ about the artist Frida Kahlo….”

Captured for the Queen

Joan Aiken


Photo by Alex Gotfryd,
circa 1972
 

Jan. 9 obituary of Joan Aiken

“Joan Aiken was born in Rye, England, a daughter of the American poet Conrad Aiken….”

Dust jacket of a novel — 

“Malcolm Lowry’s Under the Volcano must be, for anyone who loves the English language, a sheer joy.”

Conrad Aiken

“He was never inclined to small talk.”

Jan. 9 obituary of Steven Edward Dorfman, writer of questions (i.e., answers) for the game show “Jeopardy!”

“What’s the Hellfire Club?”

— Joan Aiken, beginning of the final chapter of The Shadow Guests

Note that Dorfman, Gibson, and Aiken
all died on Sunday, Jan. 4, 2004.
For some related material, see

Sunday in the Park with Death.

Saturday, December 27, 2003

Saturday December 27, 2003

Filed under: General — m759 @ 10:21 pm

Toy

“If little else, the brain is an educational toy.  While it may be a frustrating plaything — one whose finer points recede just when you think you are mastering them — it is nonetheless perpetually fascinating, frequently surprising, occasionally rewarding, and it comes already assembled; you don’t have to put it together on Christmas morning.

The problem with possessing such an engaging toy is that other people want to play with it, too.  Sometimes they’d rather play with yours than theirs.  Or they object if you play with yours in a different manner from the way they play with theirs.  The result is, a few games out of a toy department of possibilities are universally and endlessly repeated.  If you don’t play some people’s game, they say that you have ‘lost your marbles,’ not recognizing that,

while Chinese checkers is indeed a fine pastime, a person may also play dominoes, chess, strip poker, tiddlywinks, drop-the-soap or Russian roulette with his brain.

One brain game that is widely, if poorly, played is a gimmick called ‘rational thought.’ “

— Tom Robbins, Even Cowgirls Get the Blues

Sol LeWitt
June 12, 1969
:

“I took the number twenty-four and there’s twenty-four ways of expressing the numbers one, two, three, four.  And I assigned one kind of line to one, one to two, one to three, and one to four.  One was a vertical line, two was a horizontal line, three was diagonal left to right, and four was diagonal right to left.  These are the basic kind of directions that lines can take…. the absolute ways that lines can be drawn.   And I drew these things as parallel lines very close to one another in boxes.  And then there was a system of changing them so that within twenty-four pages there were different arrangements of actually sixteen squares, four sets of four.  Everything was based on four.  So this was kind of a… more of a… less of a rational… I mean, it gets into the whole idea of methodology.”

Yes, it does.
See Art Wars, Poetry’s Bones, and Time Fold.

Thursday, November 13, 2003

Thursday November 13, 2003

Filed under: General — m759 @ 7:30 pm

The Tables of Time

Implied by previous two entries:

“This Jack, joke, poor potsherd, patch, matchwood, immortal diamond,

                Is immortal diamond.”
 

— Gerard Manley Hopkins,

That Nature is a Heraclitean Fire

and of the Comfort of the Resurrection

New York Times, Nov. 13, 2003:

Peace Rune
Hexagram 11,
Jan. 6, 1989

Picnic Symbol 

Picnic site symbol,
British Sea Scouts

See, too, Art Wars and Time Fold.

Monday, April 28, 2003

Monday April 28, 2003

Filed under: General,Geometry — Tags: , , — 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

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


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.

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.

Friday, April 4, 2003

Friday April 4, 2003

Filed under: General,Geometry — Tags: , , — 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.
 

Tuesday, January 14, 2003

Tuesday January 14, 2003

Filed under: General — Tags: — m759 @ 5:55 pm

Remarks on Day 14 of
the Year of Our Lord 2003

On this date —

Alfred Tarski was born in 1902 in Warsaw, and

Kurt Friedrich Gödel died in 1978 in Princeton.

What is Truth?

“What is called ‘losing’ in chess may constitute winning in another game.”

Cited in “A Note on Wittgenstein’s ‘Notorious Paragraph’ about the Gödel Theorem,” by Juliet Floyd (Boston University) and Hilary Putnam (Harvard University), Journal of Philosophy (November 2000), 45 (11): 624-632.

See also

Juliet Floyd’s “Prose versus proof : Wittgenstein on Gödel, Tarski and truth,” Philosophia Mathematica  3, vol. 9 (2001): 901-928,

and

Juliet Floyd’s “The Rule of the Mathematical: Wittgenstein’s Later Discussions.” PhD Dissertation, Harvard University, 1990. Abstract in Dissertation Abstracts International (June 1991), 51 (12A): 4146-A:

“My thesis aims to defend Wittgenstein from the charges of benighted arrogance traditionally levelled against him.”

Romeo: O, she doth teach
the torches to burn bright!
 “Romeo and Juliet,” Act One, Scene V

  Ludwig Wittgenstein, Remarks on the Foundations of Mathematics (revised edition, Cambridge, Mass.: MIT Press, 1978)

Wednesday, January 8, 2003

Wednesday January 8, 2003

Filed under: General — Tags: — m759 @ 4:17 pm

In the Labyrinth of Memory

Taking a cue from Danny in the labyrinth of Kubrick's film "The Shining," today I retraced my steps.

My Jan. 6 entry, "Dead Poet in the City of Angels," links to a set of five December 21, 2002, entries.  In the last of these, "Irish Lament," is a link to a site appropriate for Maud Gonne's birthday — a discussion of Yeats's "Among School Children."

Those who recall a young woman named Patricia Collinge (Radcliffe '64) might agree that her image is aptly described by Yeats:

Hollow of cheek as though it drank the wind
And took a mess of shadows for its meat

This meditation leads in turn to a Sept. 20, 2002, entry, "Music for Patricias," and a tune familiar to James Joyce, "Finnegan's Wake," the lyrics of which lead back to images in my entries of Dec. 20, 2002, "Last-Minute Shopping," and of Dec. 28, 2002, "Solace from Hell's Kitchen."  The latter entry is in memory of George Roy Hill, director of "The Sting," who died Dec. 27, 2002.

The Dec. 28 image from "The Sting" leads us back to more recent events — in particular, to the death of a cinematographer who won an Oscar for picturing Newman and Redford in another film — Conrad L. Hall, who died Saturday, Jan. 4, 2003. 

For a 3-minute documentary on Hall's career, click here.

Hall won Oscars for "Butch Cassidy and the Sundance Kid" and "American Beauty," and may win a posthumous Oscar for "Road to Perdition," last year's Irish-American mob saga:

"Tom Hanks plays Angel of Death Michael Sullivan. An orphan 'adopted' by crime boss John Rooney (Paul Newman), Sullivan worships Rooney above his own family. Rooney gave Sullivan a home when he had none. Rooney is the father Sullivan never knew. Too bad Rooney is the

Rock Island
branch of Capone's mob."

In keeping with this Irish connection, here is a set of images.

American Beauty
© Suzanne Harle 1997

Conrad L. Hall

 

A Game of Chess

I need a photo-opportunity.
I want a shot at redemption.
Don't want to end up a cartoon
In a cartoon graveyard.
— Paul Simon

"Like a chess player, he knows that to win a tournament, it is sometimes wise to offer a draw in a game even when you think you can win it."

Roger Ebert on Robert Duvall's character in "A Civil Action"

Director Steven Zaillian will take part in a tribute to Conrad L. Hall at the Palm Springs International Film Festival awards ceremony on Jan 11.  Hall was the cinematographer for Zaillian's films "A Civil Action" and "Searching for Bobby Fischer." 

"A Civil Action" was cast by the Boston firm Collinge/Pickman Casting, named in part for that same Patricia Collinge ("hollow of cheek") mentioned above.

See also "Conrad Hall looks back and forward to a Work in Progress."  ("Work in Progress" was for a time the title of Joyce's Finnegans Wake.)

What is the moral of all this remembrance?

An 8-page (paper) journal note I compiled on November 14, 1995 (feast day of St. Lawrence O'Toole, patron saint of Dublin, allegedly born in 1132) supplies an answer in the Catholic tradition that might have satisfied Joyce (to whom 1132 was a rather significant number): 

How can you tell there's an Irishman present
at a cockfight?
     He enters a duck.
How can you tell a Pole is present?
     He bets on the duck.
How can you tell an Italian is present?
     The duck wins.

Every picture tells a story.

Hall wins Oscar for "American Beauty"

 

Sunday, September 22, 2002

Sunday September 22, 2002

Filed under: General,Geometry — Tags: , , , , — m759 @ 8:02 pm

Force Field of Dreams

Metaphysics and chess in today’s New York Times Magazine:

  • From “Must-See Metaphysics,” by Emily Nussbaum:

    Joss Whedon, creator of a new TV series —

    “I’m a very hard-line, angry atheist” and
    “I want to invade people’s dreams.”

  • From “Check This,” by Wm. Ferguson:

    Garry Kasparov on chess —

    “When the computer sees forced lines,
    it plays like God.”

Putting these quotations together, one is tempted to imagine God having a little game of chess with Whedon, along the lines suggested by C. S. Lewis:

As Lewis tells it the time had come for his “Adversary [as he was wont to speak of the God he had so earnestly sought to avoid] to make His final moves.” (C. S. Lewis, Surprised by Joy, Harcourt, Brace, and World, Inc., 1955, p. 216) Lewis called them “moves” because his life seemed like a chess match in which his pieces were spread all over the board in the most disadvantageous positions. The board was set for a checkmate….

For those who would like to imagine such a game (God vs. Whedon), the following may be helpful.

George Steiner has observed that

The common bond between chess, music, and mathematics may, finally, be the absence of language.

This quotation is apparently from

Fields of Force:
Fischer and Spassky at Reykjavik
. by George Steiner, Viking hardcover, June 1974.

George Steiner as quoted in a review of his book Grammars of Creation:

“I put forward the intuition, provisional and qualified, that the ‘language-animal’ we have been since ancient Greece so designated us, is undergoing mutation.”

The phrase “language-animal” is telling.  A Google search reveals that it is by no means a common phrase, and that Steiner may have taken it from Heidegger.  From another review, by Roger Kimball:

In ”Grammars of Creation,” for example, he tells us that ”the classical and Judaic ideal of man as ‘language animal,’ as uniquely defined by the dignity of speech . . . came to an end in the antilanguage of the death camps.”

This use of the Holocaust not only gives the appearance of establishing one’s credentials as a person of great moral gravity; it also stymies criticism. Who wants to risk the charge of insensitivity by objecting that the Holocaust had nothing to do with the ”ideal of man as ‘language animal’ ”?

Steiner has about as clear an idea of the difference between “classical” and “Judaic” ideals of man as did Michael Dukakis. (See my notes of September 9, 2002.)

Clearly what music, mathematics, and chess have in common is that they are activities based on pure form, not on language. Steiner is correct to that extent. The Greeks had, of course, an extremely strong sense of form, and, indeed, the foremost philosopher of the West, Plato, based his teachings on the notion of Forms. Jews, on the other hand, have based their culture mainly on stories… that is, on language rather than on form. The phrase “language-animal” sounds much more Jewish than Greek. Steiner is himself rather adept at the manipulation of language (and of people by means of language), but, while admiring form-based disciplines, is not particularly adept at them.

I would argue that developing a strong sense of form — of the sort required to, as Lewis would have it, play chess with God — does not require any “mutation,” but merely learning two very powerful non-Jewish approaches to thought and life: the Forms of Plato and the “archetypes” of Jung as exemplified by the 64 hexagrams of the 3,000-year-old Chinese classic, the I Ching.

For a picture of how these 64 Forms, or Hexagrams, might function as a chessboard,

click here.

Other relevant links:

“As you read, watch for patterns. Pay special attention to imagery that is geometric…”

and


from Shakhmatnaia goriachka

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