An image from the opening of the Netflix series “Locke & Key” —
See also Omega in this journal.
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
An image from the opening of the Netflix series “Locke & Key” —
See also Omega in this journal.
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
(With apologies to Susanne K. Langer, née Susanne Katherina Knauth)
See too the buzzard-related Catch-22 song —
In Memoriam
"Renowned Canadian theologian Gregory Baum, 94,
author of the first draft of the Second Vatican Council's
'Nostra Aetate,' died Oct. 18 in a Montreal hospital."
— National Catholic Reporter , Oct. 20, 2017
October 18 was St. Luke's Day.
From the Log24 post "Prose" on that date —
"Mister Monkey . . . . is also Hanuman, the Hindu monkey god . . . ."
— Cathleeen Schine in an online October 17 NY Times review.
From the novel under review —
"Only the heart of the monkey god is large enough
to contain the hearts and souls of all the monkeys,
all the humans, the gods, every shining thread
that connects them."
— Francine Prose, Mister Monkey: A Novel (p. 263).
HarperCollins. Kindle Edition.
See as well all posts now tagged Prose Monkey.
See Langer (Harvard U. Press, Third Edition, Jan. 31, 1957, pp. 3-4-5).
See also Old Key : Pythagoras, harmony, and the 3-4-5 triangle.
With apologies to those readers unable to follow knight moves .
The Queen’s Gambit , by Walter Tevis,
published Feb. 16, 1983 —
“Would you care for a cocktail?” he asked pleasantly.
She looked around her at the quiet restaurant,
at the people eating lunch, at the table with desserts
near the velvet rope at the entrance to the dining room.
“A Gibson,” she said. “On the rocks.”
“A silver tide of phosphenes boiled across my field of vision
as the matrix began to unfold in my head, a 3-D chessboard,
infinite and perfectly transparent.”
“‘Rikki Don’t Lose That Number‘ is a single
released in 1974 by rock/jazz rock group Steely Dan
and the opening track of their third album Pretzel Logic .
It was the most successful single of the group’s career,
peaking at number 4 on the Billboard Hot 100 in
the summer of 1974.” — Wikipedia
Brian Harley, Mate in Two Moves , 1931—
“The key is the cocktail that begins the proceedings.”
See as well my post “Introduction to Cyberspace” (May 26, 2020).
"Step by step, Kepes follows the liberation of the plastic elements:
lines, planes, and colors, and the creation of a world of forms of our own.
The spatial conception interconnects the meaning fragments and
binds them together just as in another period perspective did when it used
a single station point for naturalistic representation."
— S. Giedion, introduction to Language of Vision by Gyorgy Kepes
See as well a post from this journal on the above date —
June 12, 2014. (That post revisits a post from today's date —
January 7 — eight years ago, in 2012.)
Related material: Dharma Fabric and Symplectic.
Lines from "Description Without Place" —
"An age is green or red. An age believes
Or it denies. An age is solitude
Or a barricade against the singular man
By the incalculably plural."
— Wallace Stevens
In memory of an artist who reportedly died in Venice, CA, on Jan. 2 —
Two quotes from the website Quotes Sayings —
"I always felt like I was right out of Dickens, looking in the window
of the Christmas feast, but not at the feast." — John Baldessari
"A TWO-DIMENSIONAL SURFACE WITHOUT ANY ARTICULATION
IS A DEAD EXPERIENCE" — John Baldessari
The "dead experience" quote is actually from Gyorgy Kepes:
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
“Just as these lines that merge to form a key
Are as chess squares . . . .” — Katherine Neville, The Eight
“The complete projective group of collineations and dualities of the
[projective] 3-space is shown to be of order [in modern notation] 8! ….
To every transformation of the 3-space there corresponds
a transformation of the [projective] 5-space. In the 5-space, there are
determined 8 sets of 7 points each, ‘heptads’ ….”
— George M. Conwell, “The 3-space PG (3, 2) and Its Group,”
The Annals of Mathematics , Second Series, Vol. 11, No. 2 (Jan., 1910),
pp. 60-76.
“It must be remarked that these 8 heptads are the key to an elegant proof….”
— Philippe Cara, “RWPRI Geometries for the Alternating Group A8,” in
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.
See as well some notes from the date of the above death:
Related material: Endgame (November 7, 1986).
The terms glitch and cross-carrier in the previous post
suggest a review —
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|
For some backstory, see Glitch, Gerard Manley Hopkins, Inscape —
particularly the post A Balliol Star.
From a 1962 young-adult novel —
"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."
Song adapted from a 1960 musical —
"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"
"The man touched the white bishop, queen and king,
and ran his finger over the jagged crest of the rook.
Then, sitting down before the chess set owner could nod
his head, he made his first move with the white pawn."
— The late Stephen Dixon, "The Chess House," in
The Paris Review , Winter-Spring 1963 (early in 1963).
"Visual forms— lines, colors, proportions, etc.—
are just as capable of articulation ,
i.e. of complex combination, as words.
But the laws that govern this sort of articulation
are altogether different from the laws of syntax
that govern language. The most radical difference
is that visual forms are not discursive .
They do not present their constituents successively,
but simultaneously, so the relations determining
a visual structure are grasped in one act of vision."
— Susanne K. Langer, Philosophy in a New Key
From The Boston Globe yesterday evening —
" Ms. Adams 'had this quiet intelligence that made you feel like
she understood you and she loved you. She was a true friend —
a true generous, generous friend. This is the kind of person
you keep in your life,' Birdseye added.
'And she had such a great sense of humor,' Birdseye said.
“She would always have the last laugh. She wasn’t always
the loudest, but she was always the funniest, and in the
smartest way.' "
"Ms. Adams, who lived in Waltham, was 55 when she died April 9 . . . ."
See as well April 9 in the post Math Death and a post from April 8,
also now tagged "Berlekamp's Game" — Horses of a Dream.
"When logic and proportion have fallen sloppy dead
And the white knight is talking backwards . . . ."
— Grace Slick in a song from yesterday's post "When the Men"
From a post last month —
"You're gonna need a bigger boat."
— Roy Scheider in "Jaws"
"We're gonna need more holy water."
— "Season of the Witch"
… and for Tom Hanks, Dan Brown, and Francine Prose —
"While Prose's adult works have touched on various subjects,
her fiction for children, which she began writing in earnest
in the mid-1990s, all has a basis in Jewish folklore."
» Read more.
Aficionados of what Dan Brown has called "symbology"
can read about the above right-chevrons symbol in
Fast Forward, a post of November 21, 2010.
The Harvard Crimson , Feb. 28, 2017 —
Cambridge City Councillors formally requested that the Cambridge
Historical Commission consider designating the Abbott Building in
Harvard Square as a historical landmark at its weekly meeting Monday.
. . . .
“There are only a few gems that give the really Square character.”
Councillor Dennis J. Carlone said. “And in the heart of the square,
it’s this building.”
See as well the cover of
The Monkey Grammarian ,
a book by Octavio Paz —
A related NPR book review yesterday —
"Like Curious George , another vaguely imperialist children's classic —
which Prose refers to frequently — the simian hero of Mister Monkey
gets into trouble in his new urban environment."
New York Times review of a new novel by Francine Prose —
"Mister Monkey . . . . is also Hanuman, the Hindu monkey god . . . ."
— Cathleeen Schine in in the above October 17 review.
A related book —
See as well The Monkey Grammarian in this journal.
From a search in this journal for "More Holy Water" —
A post of January 7, 2011, has the following:
"Infinite Jest… now stands as the principal contender
for what serious literature can aspire to
in the late twentieth and early twenty-first centuries."
— All Things Shining, a work of pop philosophy
published January 4th
"You're gonna need a bigger boat."
— Roy Scheider in "Jaws"
"We're gonna need more holy water."
— "Season of the Witch"
Notes for a monkey grammarian —
"Visual forms— lines, colors, proportions, etc.—
are just as capable of articulation ,
i.e. of complex combination, as words.
But the laws that govern this sort of articulation
are altogether different from the laws of syntax
that govern language. The most radical difference
is that visual forms are not discursive .
They do not present their constituents successively,
but simultaneously, so the relations determining
a visual structure are grasped in one act of vision."
— Susanne K. Langer, Philosophy in a New Key
See also Langer's New Key in this journal.
Related material —
"I've got a brand-new pair of roller skates …"
Related material — Salinger in the Park and
Philosophy in a New Key.
The previous post discussed a tune ending in the following
sequence of notes (symbols as in a Wikipedia article):
C#4 B4 A4 E4 G4 .
(This sequence was approximated in that post by integers
representing the relative frequencies of the notes: 5 9 8 6 7 .)
Yesterday’s simple tune may suggest to some a similar refrain:
D4 E4 C4 C3 G3 .
This is, as a helpful page at Ars Nova Software explains,
the theme from “Close Encounters of the Third Kind.”
The notes of the just intonation major scale:
The corresponding ratios from Close Encounters are…
9/8 5/4 1/1 1/2 3/4 , or, in whole numbers, 9 10 8 4 6.
These numbers also correspond, as in yesterday’s post, to the notes
B4 C#5 A4 A3 E4 .
Click the image below to try this on an online keyboard, playing keys
9 10 8 4 6 for Close Encounters.
“And you can tell everybody this is your song…”
1 2 3 4 5 9 8 6 7
220 * (1/4) = 55 = A1
220 * (2/4) = 110 = A2
220 * (3/4) = 165 = approximately E3 (164.8)
220 * (4/4) = 220 = A3
220 * (5/4) = 275 = approximately C♯4/D♭4 (277.2)
220 * (6/4) = 330 = approximately E4 (329.6)
220 * (7/4) = 385 = approximately G4 (392.0)
220 * (8/4) = 440 = A4
220 * (9/4) = 495 = approximately B4 (493.9)
Exact frequencies (such as 277.2) are from Wikipedia’s Piano key frequencies.
“It may be quite simple, but now that it’s done….“
(Continued from August 9, 2014.)
Syntactic:
Symplectic:
"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive . They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."
– Susanne K. Langer, Philosophy in a New Key
For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).
This is a symplectic correlation,* constructed using the following
visual structure:
.
* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
See also yesterday's Endgame , as well as Play and Interplay
from April 28… and, as a key, the following passage from
an earlier April 28 post—
Euclidean geometry has long been applied to physics; Galois geometry has not. The cited webpage describes the interplay of both sorts of geometry— Euclidean and Galois, continuous and discrete— within physical space— if not within the space of physics . |
In memory of S. Neil Fujita, who died last Saturday—
Fujita did the cover art for this edition.
Another book by Langer with a striking cover (artist unknown)—
Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.
"Visual forms— lines, colors, proportions, etc.— are just as capable of articulation , i.e. of complex combination, as words. But the laws that govern this sort of articulation are altogether different from the laws of syntax that govern language. The most radical difference is that visual forms are not discursive . They do not present their constituents successively, but simultaneously, so the relations determining a visual structure are grasped in one act of vision."
— Susanne K. Langer, Philosophy in a New Key
(continued from April 16)
Background:
Click on the image for an
interview with the author of
Giordano Bruno and
the Geometry of Language.
Related material:
Joyce on language —
Click on images for details.
For Mary Gaitskill,
continued from
June 21, 2008:
This minimal art
is the basis of the
chess set image
from Tuesday:
Related images:
“The key is the
cocktail that begins
the proceedings.”
— Brian Harley,
Mate in Two Moves
(A Mathematician's Apology, Cambridge at the University Press, first edition, 1940)
Brian Harley on chess problems–
"It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver's banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be."
(Mate in Two Moves, London, Bell & Sons, first edition, 1931)
… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
— Rubén Darío,
born January 18, 1867
"Mazur introduced the topic of prime numbers with a story from Don Quixote in which Quixote asked a poet to write a poem with 17 lines. Because 17 is prime, the poet couldn't find a length for the poem's stanzas and was thus stymied."
— Undated American Mathematical Society news item about a Nov. 1, 2007, event
Desconvencida,
Jueves, Enero 17, 2008
Horses of a Dream
(Log24, Sept. 12, 2003)
Knight Moves
(Log24 yesterday–
anniversary of the
Jan. 16 publication
of Don Quixote)
Windmill and Diamond
(St. Cecilia's Day 2006)
Click on the image for a larger version
and an expansion of some remarks
quoted here on Christmas 2005.
Kernel
Mathematical Reviews citation:
MR2163497 (2006g:81002) 81-03 (81P05)
Gieser, Suzanne The innermost kernel. Depth psychology and quantum physics. Wolfgang Pauli's dialogue with C. G. Jung. Springer-Verlag, Berlin, 2005. xiv+378 pp. ISBN: 3-540-20856-9
A quote from MR at Amazon.com:
"This revised translation of a Swedish Ph. D. thesis in philosophy offers far more than a discussion of Wolfgang Pauli's encounters with the psychoanalyst Carl Gustav Jung…. Here the book explains very well how Pauli attempted to extend his understanding beyond superficial esotericism and spiritism…. To understand Pauli one needs books like this one, which… seems to open a path to a fuller understanding of Pauli, who was seeking to solve a quest even deeper than quantum physics." (Arne Schirrmacher, Mathematical Reviews, Issue 2006g)
The four-group is also known as the Vierergruppe or Klein group. It appears, notably, as the translation subgroup of A, the group of 24 automorphisms of the affine plane over the 2-element field, and therefore as the kernel of the homomorphism taking A to the group of 6 automorphisms of the projective line over the 2-element field. (See Finite Geometry of the Square and Cube.)
The "chessboard" of
Nov. 7, 2006
(as revised Nov. 7, 2012)–
(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
Related material:
"At the still point,
there the dance is"
and
And the
"Meet Max Black"
Award goes to…
"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:
From the
National Design Museum:
From Log24 on the
date of Stumpf's death,
Pictorial version of
Hexagram 20,
Contemplation (View)
See also
Fearful Symmetry
and
Symmetry Framed.
Introduction to Aesthetics
“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology
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“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases,’ indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.
A chess problem also has unexpectedness, and a certain economy; it is essential that the moves should be surprising, and that every piece on the board should play its part. But the aesthetic effect is cumulative. It is essential also (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. ‘If P-B5 then Kt-R6; if …. then …. ; if …. then ….’ — the effect would be spoilt if there were not a good many different replies. All this is quite genuine mathematics, and has its merits; but it just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly*) which a real mathematician tends to despise.
* I believe that is now regarded as a merit in a problem that there should be many variations of the same type.”
(Cambridge at the University Press. First edition, 1940.)
Brian Harley in
Mate in Two Moves:
“It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver’s banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be.”
(London, Bell & Sons. First edition, 1931.)
Before and After
From Understanding the (Net) Wake:
24 A.
Joyce shows an understanding of the problems that an intertextual book like the Wake poses for the notion of authorship. |
G. H. Hardy in A Mathematician’s Apology:
“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases,’ indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.
A chess problem also has unexpectedness, and a certain economy; it is essential that the moves should be surprising, and that every piece on the board should play its part. But the aesthetic effect is cumulative. It is essential also (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. ‘If P-B5 then Kt-R6; if …. then …. ; if …. then ….’ — the effect would be spoilt if there were not a good many different replies. All this is quite genuine mathematics, and has its merits; but it just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly*) which a real mathematician tends to despise.
* I believe that is now regarded as a merit in a problem that there should be many variations of the same type.”
(Cambridge at the University Press. First edition, 1940.)
Brian Harley in Mate in Two Moves:
“It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver’s banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be.”
(London, Bell & Sons. First edition, 1931.)
Force Field of Dreams
Metaphysics and chess in today’s New York Times Magazine:
Joss Whedon, creator of a new TV series —
“I’m a very hard-line, angry atheist” and
“I want to invade people’s dreams.”
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,
Other relevant links:
“As you read, watch for patterns. Pay special attention to imagery that is geometric…”
and
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