"with Mearingstone in Fore ground"
"…the Somerville group has grown…."
Sunday, April 15, 2012
Fun and Games
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Irish Geometry
— Finnegans Wake , Book II,
Episode 2, page 293
Background—
- The Great Hunger,
- the facetious NY Times ‘s
‘Hunger Games’ Parenting, - and (Feb. 13 and 14, 2012)—
Why Now? and Notable Transitions.
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Saturday, April 14, 2012
Scottish Algebra
Two papers suggested by Google searches tonight—
|
[PDF] PAPERS HELD OVER FROM THEME ISSUE ON ALGEBRA AND …
ajse.kfupm.edu.sa/articles/271A_08p.pdf
File Format: PDF/Adobe Acrobat – View as HTML by RT Curtis – 2001 – Related articles This paper is based on a talk given at the Scottish Algebra Day 1998 in Edinburgh. …… |
Curtis discusses the exceptional outer automorphism of S6
as arising from group actions of PGL(2,5).
See also Cameron and Galois on PGL(2,5)—
[PDF] ON GROUPS OF DEGREE n AND n-1, AND HIGHLY-SYMMETRIC …
|
Illustration from Cameron (1973)—
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Friday, April 13, 2012
Meditation for Friday the 13th
From Friday, May 13, 2005—
“All the saints have powers.”
See also Friday, April 13, 2007 and Friday, February 13, 2009.
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Constructive
The two previous posts have referred to the HBO series "Big Love."
For a more constructive production related to a Latter-Day Saint,
see the video of the 1989 song "Sacred Emotion."
The visually impaired may be forgiven for thinking
the voice in the video is that of Michael Jackson.
"Our love is like a sacred emotion." — Donny Osmond
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Putting the Prime in “Primate”
See Prime Cut and Lavender Blue, Dilly Dilly
as well as Sissy Spacek on "Big Love."
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Askew Crews
| A Large & Startling Figure: The Harry Crews Online Bibliography www.harrycrews.org/Features/News/index.html Page updated: March 29, 2012, 08:16 PM Copyright © 1998 – 2010 |
The "large and startling" phrase is from Flannery O'Connor—
|
From Georgia College, Milledgeville, GA— … in Flannery O'Connor's essay "The Fiction Writer and His Country"… she explains why she writes the way she does: "When you can assume that your audience holds the same beliefs you do, you can relax a little and use more normal means of talking to it; when you have to assume that it does not, then you have to make your vision apparent by shock— to the hard of hearing you shout, and for the almost-blind you draw large and startling figures" (Mystery and Manners , p. 34). |
For a large and startling figure played by Askew, see a scene from "Big Love."
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The Primate and the Bee
"Man is, in Lévi-Strauss's view, a mythopoetic primate
(it's a difficult phrase but we don't have a better one)…."
Pope Benedict XVI at the 2012 Easter Vigil on April 7 —
"The great hymn of the Exsultet, which the deacon sings at the beginning of the Easter liturgy, points us quite gently towards a further aspect. It reminds us that this object, the candle, has its origin in the work of bees. So the whole of creation plays its part. In the candle, creation becomes a bearer of light.
But in the mind of the Fathers, the candle also in some sense contains a silent reference to the Church. The cooperation of the living community of believers in the Church in some way resembles the activity of bees. It builds up the community of light."
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Thursday, April 12, 2012
Mythopoetic*
"Is Space Digital?"
— Cover story, Scientific American magazine, February 2012
"The idea that space may be digital
is a fringe idea of a fringe idea
of a speculative subfield of a subfield."
— Physicist Sabine Hossenfelder
at her weblog on Feb. 5, 2012
"A quantization of space/time
is a holy grail for many theorists…."
— Peter Woit in a comment at his physics weblog today
See also
* See yesterday's Steiner's Systems.
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Wednesday, April 11, 2012
Steiner’s Systems
Background— George Steiner in this journal
and elsewhere—
"An intensity of outward attention —
interest, curiosity, healthy obsession —
was Steiner’s version of God’s grace."
— Lee Siegel in The New York Times ,
March 12, 2009
(See also Aesthetics of Matter in this journal on that date.)
Steiner in 1969 defined man as "a language animal."
Here is Steiner in 1974 on another definition—
Related material—
Also related — Kantor in 1981 on "exquisite finite geometries," and The Galois Tesseract.
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Tuesday, April 10, 2012
Death on Good Friday
|
Edward Reed Whittemore Jr. was born |
In memoriam:
PART I —
PART II —
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Carpenter Song…
Where Entertainment is God
(Continued from April 4 and April 8)
"Hot dog… I'm a winner either way."
— Mary Chapin Carpenter
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The Christening
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Dehors*
"A New York Jew imitates D. H. Lawrence at his peril."
“Our focus is on creating very high quality, highly artistically produced programs that bring together worlds that usually don’t talk to each other,” said Dr. Greene, a physics and math professor at Columbia and well-known popularizer of science. “We’ve tried to inject the drama of science into these highly produced programs, so people leave the event saying, ‘Wow, I didn’t know that’s what science is like.’ ”
As for D. H. Lawrence, see this journal on September 10, 2003.
* For the title, see last night's Turing Gate.
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Turing Gate
In memory of Christine Brooke-Rose,
an image from the date of her death—
See also A Little Story and Before Dehors.
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Monday, April 9, 2012
Eightfold Cube Revisited
A search today (Élie Cartan's birthday) for material related to triality*
yielded references to something that has been called a Bhargava cube .
Two pages from a 2006 paper by Bhargava—
Bhargava's reference [4] above for "the story of the cube" is to…
Higher Composition Laws I:
A New View on Gauss Composition,
and Quadratic Generalizations
Manjul Bhargava
The Annals of Mathematics
Second Series, Vol. 159, No. 1 (Jan., 2004), pp. 217-250
Published by: Annals of Mathematics
Article Stable URL: http://www.jstor.org/stable/3597249
A brief account in the context of embedding problems (click to enlarge)—
For more ways of slicing a cube,
see The Eightfold Cube —
* Note (1) some remarks by Tony Smith
related to the above Dynkin diagram
and (2) another colorful variation on the diagram.
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Easter Act
"And when he had apprehended him,
he put him in prison, and delivered him
to four quaternions of soldiers to keep him;
intending after Easter to bring him forth to the people."
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Sunday, April 8, 2012
Steiner System
See George Steiner on Autistic Enchantment, as well as…
(Click images for further details.)
This year, Autism Awareness Day was April 2.
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The Two Towers
Click to enlarge.
See also March 9, 2007 and the film Queen to Play (NY-LA release: 2011, April 1).
The U.S. premiere of Queen to Play was on April 25, 2009 at the Tribeca Festival.
"Now, I'll open up a line of credit for you.
You'll be wantin' a few toys."
— A Robert De Niro character quoted in
Lines (St. Andrew's Day, 2011)
Update of 10:10 AM EDT April 8 (Easter Day)—
See an "old Brooklyn haunt" in The Easter Phantom.
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Saturday, April 7, 2012
Appeasing Epstein
… On Holy Saturday
"'If only they could send us something grown-up… a sign or something.'
And a sign does come from the outside. That night, unknown to the children,
a plane is shot down and its pilot parachutes dead to earth and is caught
in the rocks on the mountain. It requires no more than the darkness of night
together with the shadows of the forest vibrating in the signal fire to distort
the tangled corpse with its expanding silk 'chute into a demon that must
be appeased."
— Claire Rosenfield, 1961 essay about Lord of the Flies
A Flies-related death from April 1—
Edmund L. Epstein, Scholar Who Saved ‘Lord of the Flies,’ Dies at 80
See also Holy Saturday, 2004.
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Foreground
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Background
From Joyce's 1912 Trieste lecture on Blake:
"Michelangelo's influence is felt in all of Blake's work, and especially in some passages of prose collected in the fragments, in which he always insists on the importance of the pure, clean line that evokes and creates the figure on the background of the uncreated void."
For a related thought from Michelangelo, see Marmo Solo .
For pure, clean lines, see Galois Geometry.
As for "the uncreated void," see the Ernst Gombrich link in Marmo Solo for "an almost medieval allegory of how man confronts the void."
For some related religious remarks suited to the Harrowing of Hell on this Holy Saturday, see August 16, 2003.
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The Void
(Continued from March 10, 2012)
An inaccuracy in a passage linked to yesterday—
“The created universe, the whole of things, is,
in words from Joyce’s Ulysses , ‘predicated on the void.'”
The “predicated” phrase seems to be absent from Ulysses .
Joyce does, however, have the following (from ricorso.net)—
| “William Blake” (March 1912) – cont.: ‘Armed with this two-edged sword, the art of Michaelangelo and the revelations of Swedenborg, Blake killed the dragon of experience and natural wisdom, and, by minimising space and time and denying the existence of memory and the senses, he tried to paint his works on the void of the divine bosom. [See note, infra.]To him, each moment shorter than a pulse-beat was equivalent in its duration to six thousand years, because in such an infinitely short instant the work of the poet is conceived and born. To him, all space larger than a red globule of human blood was visionary, created by the hammer of Los, while in a space smaller than a globule of blood we approach eternity, of which our vegetable world is but a shadow. Not with the eye, then, but beyond the eye, the soul and the supreme move must look, because the eye, which was born in the night while the soul was sleeping in rays of light, will also die in the night. […] The mental process by which Blake arrives at the threshold of the infinite is a similar process. Flying from the infinitely small to the infinitely large, from a drop of blood to the universe of stars, his soul is consumed by the rapidity of flight, and finds itself renewed and winged and immortal on the edge of th dark ocean of God. And althought he based his art on such idealist premises, convinced that eternity was in love with the products of time, this sons of God with the sons of [MS ends here].’ (Critical Writings, 1959, 1966 Edn., pp.221-22; quoted [in part] in Richard Ellmann, James Joyce, 1965 Edn., p.330.) [For full text, see RICORSO Library, “Major Authors”, via index, or direct.] Note – for “void” [supra] , cf. Stephen in “Scylla & Charybdis”: ‘Fatherhood […] is a mystical estate, an apostolic succession, from only begetter to only begotten. On that mystery and not on the madonna which the cunning Italian intellect flung to the mob of Europe the church is founded and founded irremovably because founded, like the world, macro- and microcosm, upon the void.’ (Ulysses, Penguin Edn. 1967, p.207; [my itals.].) |
Some academics may prefer a more leftist version of
“predicated on the void”—
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Knowing Brooklyn
For St. Dismas, a Holy Saturday story—
"Mr. Rosensaft told another story to illustrate his friend's mix of grit and wit. Mr. Steinberg was negotiating one day with the French culture minister to recover paintings stolen from Jews during the Holocaust. The minister huffed that Mr. Steinberg knew nothing about art.
'You're right,' Mr. Steinberg said. 'I don't know anything about art. I'm from Brooklyn. I know about stolen goods.'"
— New York Times this morning
See also yesterday afternoon's Good Friday post
and the passage on Aquinas that it links to.
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Friday, April 6, 2012
For Good Friday
From St. Dismas, a link: http://www.scribd.com/doc/62700189/9/nine *
And in this journal… "Nine is a Vine."
* Aquinas, Ethics, and Philosophy of Religion:
Metaphysics and Practice , by Thomas Hibbs,
Indiana University Press, Bloomington and Indianapolis, 2007
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Reine Form
„Ein formal stimmiges Produkt braucht keine Verzierung,
es soll durch die reine Form erhöht werden.“
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Spectral Theory
“And we may see the meadow in December,
icy white and crystalline” — Johnny Mercer
“At another end of the sexual confusion spectrum….”
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Thursday, April 5, 2012
Go Ask Emma*
From Katherine Neville's novel The Eight (see also April 4, Der Einsatz )—
"You walked out of my dreams and into my car…"
* Frost
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In the Details
An image from 62 years ago:
Click image for details.
For the religious significance of "62," see Strong Emergence Illustrated.
See also a related search.
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Leap Day of Faith
Presidential candidate Mitt Romney on Monday, April 2, 2012—
"I think there is in this country a war on religion.
I think there is a desire to establish a religion
in America known as secularism."
Nancy Haught of The Oregonian on Leap Day, Feb. 29, 2012—
|
William Hamilton, the retired theologian who declared in the 1960s that God was dead, died Tuesday [Feb. 28, 2012] in his downtown Portland apartment at 87. Hamilton said he'd been haunted by questions about God since he was a teenager. Years later, when his conclusion was published in the April 8, 1966, edition of Time Magazine, he found himself in a hornet's nest. Time christened the new movement "radical theology" and Hamilton, one of its key figures, received death threats and inspired angry letters to the editor in newspapers that carried the story. He encountered hostility at Colgate Rochester Crozer Divinity School, where he had been teaching theology, and lost his endowed chair in 1967. Hamilton moved on to teach religion at New College in Sarasota, Fla. |
(See also this journal on Leap Day.)
From New College: The Honors College of Florida—
|
Oct. 11, 1960: New College is founded as a private college 1961: Trustees obtain options to purchase the former Charles Ringling estate on Sarasota Bay and 12 acres of airport land facing U.S. 41 held by private interests. The two pieces form the heart of the campus Nov. 18, 1962: the campus is dedicated. Earth from Harvard is mixed with soil from New College as a symbol of the shared lofty ideals of the two institutions. |
See also, in this journal, "Greatest Show on Earth" and The Harvard Crimson—
| The Harvard Crimson, Online Edition |
Sunday, Oct. 8, 2006 |
|
POMP AND
Friday, Oct. 6:
The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden. |
OPINION At Last, a By THE CRIMSON STAFF The Trouble By SAHIL K. MAHTANI |
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Wednesday, April 4, 2012
Carpenter Song
I said, "Look out, boys, I've got a license to fly"
And that Caddy pulled over and let us by
Followup story to this morning's Easter Prayer Breakfast—
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Der Einsatz
|
”Confusion is nothing new.” |
(This may serve as today’s tribute to Katherine Neville.)
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Death Proof
In memory of
Bill Jenkins, 81, Drag Racing
Driver and Innovator —
Pulled out of San Pedro late one night…
Jenkins died on Thursday, March 29, 2012.
See also this morning's SPECTRE and
http://www.spectreperformance.com/#GARAGE.
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SPECTRE
Meanwhile, back in June 2004—
The Marilyn Monroe Rose and JFK …
… meet The Crimson Spectre —
(Suggested by this morning's
New York Times obituaries—
"A spectre is haunting…"— Karl Marx)
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Tuesday, April 3, 2012
Community*
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Catholic View
"When shall we three meet again?"
Left to right— John von Neumann, Richard Feynman, Stanislaw Ulam
The source of the above book's title, "Analogies between Analogies,"
was misattributed in a weblog post linked to here on March 4th, 2012.
It occurs in a quote due not to Stanislaw Ulam but to Stefan Banach—
Ulam was Jewish. Banach was not.
From a webpage on Banach—
"On 3 April 1892, he was baptized in the Roman Catholic
Parish of St. Nicholas in Krakow."
See also…
- a post of Sunday, April 2, 2006,
- yesterday's Pennsylvania lottery, and
- post 585 in this journal.
(At Los Alamos, Ulam developed the Monte Carlo method.)
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Monday, April 2, 2012
Intelligence Test
This journal on June 18, 2008—
The Wechsler Cubes story continues with a paper from December 2009…
"Learning effects were assessed for the block design (BD) task,
on the basis of variation in 2 stimulus parameters:
perceptual cohesiveness (PC) and set size uncertainty (U)." —
(Click image for some background.)
The real intelligence test is, of course, the one Wechsler flunked—
investigating the properties of designs made with sixteen
of his cubes instead of nine.
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Nine Stories
See a search for the title in this journal.
See also Stories about Nine.
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A Saint for Patrick —
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Sunday, April 1, 2012
The Palpatine Dimension
A physics quote relayed at Peter Woit's weblog today—
"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."
Some related material from this weblog—
(See Big Apple and Columbia Film Theory)
The Meno Embedding:
Some related material from the Web—
See also uses of the word triality in mathematics. For instance…
A discussion of triality by Edward Witten—
Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6 thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.
— "Conformal Field Theory in Four and Six Dimensions"
and a discussion by Peter J. Cameron—
There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG( 3,2).
Both admit 2-transitive groups.
— "The Klein Quadric and Triality"
Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality link from above
and Cameron's Klein Correspondence and Triality.)
Cameron applies his triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning—
|
From MIT Commencement Day, 2011— A symbol related to Apollo, to nine, and to "nothing"— A minimalist favicon—
This miniature 3×3 square— |
Happy April 1.
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Saturday, March 31, 2012
The Kick
"The inception of critical thought, of a philosophic anthropology, is contained in the archaic Greek definition of man as a 'language-animal'…."
— George Steiner, Real Presences , U. of Chicago Press, 1991, p. 89 (See also Steiner on Language.)
"To some, Inception is a film about the creative process, specifically filmmaking, with Cobb as the director, Saito the producer, Ariadne the screenwriter, Eames the actor, and so on. To others the entire movie is a dream in that the film supports Carl Jungs' dream analysis; with all of the supporting characters acting as classical archetypes to Cobb's multiple personalities (which would also justify the lack of development in the supporting characters). The fact that Inception , in the few months since its initial release, has already given rise to so much discussion and critical thought is much more revelatory than whether or not Cobb is still dreaming."
— Russell Espinosa at FilmFracture.com, Jan. 1, 2011
See also Piaf's "Rien de Rien " in a Log24 post from Jan. 19, 2012.
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Friday, March 30, 2012
Steiner on Language
March 28 review in the Times Literary Supplement of
George Steiner's new book The Poetry of Thought—
"If this new book opens with the concession that
language has neither the performative power of music
nor the elegant precision of mathematics,
it is language, for Steiner, that defines the human.
The survey accordingly begins from the ancient Greek
view of man as the 'language-animal.'"
A check of this phrase yields, in a 1969 Steiner essay,
"The Language Animal," a Greek form of the phrase—
In short, the least inadequate definition we can arrive at
of the genus homo , the definition that fully distinguishes
him from all neighbouring life-forms, is this:
man is a zoon phonanta , a language-animal.
— p. 10 in Encounter , August 1969 (essay on pp. 7-23)
After introducing "language-animal" as a translation of "zoon phonanta " in 1969,
Steiner in later writing went on to attribute this phrase to the ancient Greeks.
"The inception of critical thought, of a philosophic anthropology,
is contained in the archaic Greek definition of man as a
'language-animal'…."
— George Steiner, Real Presences , U. of Chicago Press, 1991, p. 89
"… the 'language-animal' we have been since ancient Greece
so designated us…. "
— George Steiner, Grammars of Creation , Yale U. Press, 2002, p. 265
Despite this, there seems to be no evidence for use of this phrase
by the ancient Greeks.
A Google search today for zoon phonanta (ζῷον φωνᾶντα)—
There are also no results from searches for the similar phrases
"ζωον φωναντα," "ζωον φωνᾶντα," and "ζῷον φωναντα."
Brain Boost*
See "Dark Fields" in this journal
and Peter J. Cameron's weblog today.
* Phrase from "Forbidden Planet" (1956).
See previous post.
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Meanwhile… (continued)
In memory of actor Warren Stevens—
“… Which makes it a gilt-edged priority that one of us
gets into that Krell lab and takes that brain boost.”
— American adaptation of Shakespeare's Tempest , 1956
Some other dialogue—
"Where is the cat?" he asked at last.
"Where is the box?"
"Here."
"Where's here?"
"Here is now."
"We used to think so," I said,
"but really we should use larger boxes."
— "Schrödinger's Cat,"
by Ursula K. Le Guin (1974)
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Thursday, March 29, 2012
Meanwhile…
| A Large & Startling Figure: The Harry Crews Online Bibliography www.harrycrews.org/Features/News/index.html Page updated: March 29, 2012, 08:16 PM Copyright © 1998 – 2010 |
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Appalachian Spring
"Earl Eugene Scruggs was born on Jan. 6, 1924,
in Flint Hill, near Shelby, N.C.,
to George Elam Scruggs, a farmer and bookkeeper,
and the former Georgia Lula Ruppe,
who played the pump organ in church.
He attended high school in Boiling Springs, N.C."
— Today's online New York Times—
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Wednesday, March 28, 2012
Review
… of background for yesterday's Log24 posts—
"Now that philosophy has become a scientific pursuit…."
leads to the following article from St. Patrick's Day—
See also this journal on St. Patrick's Day—
Doodle Dandy and The Purloined Diamond (scroll down).
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Tuesday, March 27, 2012
Requiem for a Cat
| From “Schrödinger’s Cat,” by Ursula K. Le Guin (Buffalo Gals and Other Animal Presences ) …. There was silence then: deep silence. We both gazed, I afoot, Rover kneeling, at the box. No sound. Nothing happened. Nothing would happen. Nothing would ever happen, until we lifted the lid of the box. “Like Pandora,” I said in a weak whisper. I could not quite recall Pandora’s legend. She had let all the plagues and evils out of the box, of course, but there had been something else, too. After all the devils were let loose, something quite different, quite unexpected, had been left. What had it been? Hope? A dead cat? I could not remember. Impatience welled up in me. I turned on Rover, glaring. He returned the look with expressive brown eyes. You can’t tell me dogs haven’t got souls. “Just exactly what are you trying to prove?” I demanded. “That the cat will be dead, or not dead,” he murmured submissively. “Certainty. All I want is certainty. To know for sure that God does play dice with the world.” I looked at him for a while with fascinated incredulity. “Whether he does, or doesn’t,” I said, “do you think he’s going to leave you a note in the box?” I went to the box, and with a rather dramatic gesture, flung the lid back. Rover staggered up from his knees, gasping, to look. The cat was, of course, not there. Rover neither barked, nor fainted, nor cursed, nor wept. He really took it very well. “Where is the cat?” he asked at last. “Where is the box?” “Here.” “Where’s here?” “Here is now.” “We used to think so,” I said, “but really we should use larger boxes.” He gazed about in mute bewilderment, and did not flinch even when the roof of the house was lifted off just like the lid of the box, letting in the unconscionable, inordinate light of the stars. He had just time to breathe, “Oh, wow!” I have identified the note that keeps sounding. I checked it on the mandolin before the glue melted. It is the note A, the one that drove the composer Schumann mad. It is a beautiful, clear tone, much clearer now that the stars are visible. I shall miss the cat. I wonder if he found what it was we lost? |
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The Word
(In memory of art critic Hilton Kramer,
who died this morning)
See also “crucial” in this journal.
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Literary Field
An image suggested by Google's observance today
of Mies van der Rohe's 126th birthday—
Related material:
See also yesterday's Chapter and Verse by Stanley Fish,
and today's Arts & Letters Daily .
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Finnegans Kaleidoscope
In appreciation of their essays in last
Sunday’s New York Times Book Review ,
a link for David Albert and Philip Kitcher—
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Monday, March 26, 2012
Smackdown!
(The title is a nod to Peter Woit's recent post "Nothingness Smackdown.")
"To wrestle new mediums to the mat of specificity has been a preoccupation of mine since the inception of October , the magazine I founded in 1976 with Annette Michelson, the first issue of which carried my essay 'Video and Narcissism' which attempts to tie the essence of video to the spectacular nature of mirrors."
— Rosalind Krauss, 2008, introduction to Perpetual Inventory (MIT Press, 2010)
Related material— The video art and mirror art of Josefine Lyche.
See also Krauss's essay on video in Perpetual Inventory— "Video: The Aesthetics of Narcissism" (first published as "Video and Narcissism," October , no. 1 (Spring 1976))—
"In The Language of the Self , Lacan begins by characterizing the space of the therapeutic transaction as an extraordinary void created by the silence of the analyst. Into this void the patient projects the monologue of his own recitation, which Lacan calls 'the monumental construct of his narcissism.'"
— and related remarks on October and the void quoted here March 10 in "Boo Boo Boo."
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Sunday, March 25, 2012
Compare and Contrast
Background:
The Origin and Development of Erwin Panofsky's Theories of Art ,
Michael Ann Holly, doctoral thesis, Cornell University, 1981 (pdf, 10 MB)
Panofsky, Cassirer, and Perspective as Symbolic Form ,
Allister Neher, doctoral thesis, Concordia University, 2000
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Saturday, March 24, 2012
The David Waltz…
"At the still point…" — T. S. Eliot
In memory of David L. Waltz, artificial-intelligence pioneer,
who died Thursday, March 22, 2012—
- The Log24 post of March 22 on the square-triangle theorem
- The March 18 post, Square-Triangle Diamond
- Remarks from the BBC on linguistic embedding
that begin as follows—
"If we draw a large triangle and embed smaller triangles in it,
how does it look?"—
and include discussion of a South American "tribe called Piranha" [sic ] - The result of a Cartoon Bank search suggested by no. 3 above—
(Click image for some related material.)
- A suggestion from the Cartoon Bank—
-
The following from the First of May, 2010—
Some context–
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71 - The phrase "embedding the stone" —
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Friday, March 23, 2012
Embedding the Stone
"Imbedding the God character in a holy book's very detailed narrative
and building an entire culture around this narrative
seems by itself to confer a kind of existence on Him."
— John Allen Paulos in the philosophy column "The Stone,"
New York Times online, Oct. 24, 2010
A related post from Log24 later that year—
Sunday, November 28, 2010
|
"Next come the crown of thorns and Jesus' agonized crawl across the stage,
bearing the weight of his own crucifix. And at last, after making
yet another entrance, Mr. Nolan strikes the pose immortalized
in centuries of art, clad in a demure loincloth, arms held out to his sides,
one leg artfully bent in front of the other, head hanging down
in tortured exhaustion. Gently spotlighted, he rises from the stage
as if by magic, while a giant cross, pulsing with hot gold lights,
descends from above to meet him. Mr. Lloyd Webber's churning guitar rock
hits a climactic note, and the audience erupts in excited applause."
— Charles Isherwood, review of "Jesus Christ Superstar" in today's New York Times
Other remarks on embedding —
Part I
Review of a new book on linguistics, embedding, and a South American tribe—
"Imagine a linguist from Mars lands on Earth to survey the planet's languages…."
— Chronicle of Higher Education , March 20, 2012
Part II
The Embedding , by Ian Watson (Review of a 1973 novel from Shakespeare's birthday, 2006)
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Thursday, March 22, 2012
Square-Triangle Theorem continued
Last night's post described a book by Alexander Soifer
on questions closely related to— and possibly
suggested by— a Miscellanea item and a letter to
the editor in the American Mathematical Monthly ,
June-July issues of 1984 and 1985.
Further search yields a series of three papers by
Michael Beeson on the same questions. These papers are
more mathematically presentable than Soifer's book.
Triangle Tiling I —
http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf
March 2, 2012
Triangle Tiling II —
http://www.michaelbeeson.com/research/papers/TriangleTiling2.pdf
February 18, 2012
Triangle Tiling III —
http://www.michaelbeeson.com/research/papers/TriangleTiling3.pdf
March 11, 2012
These three recent preprints replace some 2010 drafts not now available.
Here are the abstracts of those drafts—
"Tiling triangle ABC with congruent triangles similar to ABC"
(March 13, 2010),
"Tiling a triangle with congruent triangles"
(July 1, 2010).
Beeson, like Soifer, omits any reference to the "Triangles are square" item
of 1984 and the followup letter of 1985 in the Monthly .
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Wednesday, March 21, 2012
Square-Triangle Theorem
(Continued from March 18, 2012)
Found in a search this evening—
How Does One Cut a Triangle? by Alexander Soifer
(Second edition, Springer, 2009. First edition published
by Soifer's Center for Excellence in Mathematical Education,
Colorado Springs, CO, in 1990.)
This book, of xxx + 174 pages, covers questions closely related
to the "square-triangle" result I published in a letter to the
editor of the June-July 1985 American Mathematical Monthly
(Vol. 92, No. 6, p. 443). See Square-Triangle Theorem.
Soifer's four pages of references include neither that letter
nor the Monthly item, "Miscellaneum 129: Triangles are square"
of a year earlier that prompted the letter.
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Digital Theology
See also remarks on Digital Space and Digital Time in this journal.
Such remarks can, of course, easily verge on crackpot territory.
For some related pure mathematics, see Symmetry of Walsh Functions.
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Tuesday, March 20, 2012
Field (continued)
In memory of director Ulu Grosbard (continued from yesterday)
From http://scripturetext.com/matthew/13-44.htm —
Again the kingdom of heaven is like unto treasure hid in a field
the which when a man hath found he hideth and for joy thereof
goeth and selleth all that he hath and buyeth that field
ΚΑΤΑ ΜΑΤΘΑΙΟΝ 13:44 Greek NT: Byzantine/Majority Text (2000)
παλιν ομοια εστιν η βασιλεια των ουρανων θησαυρω κεκρυμμενω εν τω αγρω
LEXICON —
παλιν adverb
palin pal'-in: (adverbially) anew, i.e. (of place) back, (of time) once more, or (conjunctionally) furthermore or on the other hand — again.
ομοια adjective – nominative singular feminine
homoios hom'-oy-os: similar (in appearance or character) — like, + manner.
εστιν verb – present indicative – third person singular
esti es-tee': he (she or it) is; also (with neuter plural) they are
η definite article – nominative singular feminine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.
βασιλεια noun – nominative singular feminine
basileia bas-il-i'-ah: royalty, i.e. (abstractly) rule, or (concretely) a realm — kingdom, + reign.
των definite article – genitive plural masculine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.
ουρανων noun – genitive plural masculine
ouranos oo-ran-os': the sky; by extension, heaven (as the abode of God); by implication, happiness, power, eternity; specially, the Gospel (Christianity) — air, heaven(-ly), sky.
θησαυρω noun – dative singular masculine
thesauros thay-sow-ros': a deposit, i.e. wealth — treasure.
κεκρυμμενω verb – perfect passive participle – dative singular masculine
krupto kroop'-to: to conceal (properly, by covering) — hide (self), keep secret, secret(-ly).
εν preposition
en en: in, at, (up-)on, by, etc.
τω definite article – dative singular masculine
ho ho: the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.
αγρω noun – dative singular masculine
agros ag-ros': a field (as a drive for cattle); genitive case, the country; specially, a farm, i.e. hamlet — country, farm, piece of ground, land.
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Monday, March 19, 2012
Field
— Illustration by Neill Cameron for his father, combinatorialist Peter J. Cameron
Illustration by Nao of the Japanese (and Chinese) character for "field"—
Related material—
Finitegeometry.org favicon from February 24, 2012—
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Sunday, March 18, 2012
Square-Triangle Diamond
The diamond shape of yesterday's noon post
is not wholly without mathematical interest …
"Every triangle is an n -replica" is true
if and only if n is a square.
The 16 subdiamonds of the above figure clearly
may be mapped by an affine transformation
to 16 subsquares of a square array.
(See the diamond lattice in Weyl's Symmetry .)
Similarly for any square n , not just 16.
There is a group of 322,560 natural transformations
that permute the centers of the 16 subsquares
in a 16-part square array. The same group may be
viewed as permuting the centers of the 16 subtriangles
in a 16-part triangular array.
(Updated March 29, 2012, to correct wording and add Weyl link.)
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Saturday, March 17, 2012
The Purloined Diamond
The diamond from the Chi-rho page
of the Book of Kells —
The diamond at the center of Euclid's
Proposition I, according to James Joyce
(i.e., the Diamond in the Mandorla) —
“He pointed at the football
on his desk. ‘There it is.’”
– Glory Road
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Friday, March 16, 2012
For the Clueless
"And she provided him besides with a ball of thread,
bidding him to fasten the end of it to the entrance
of the Labyrinth, and unwind it as he went in, that
it might serve him as a clue to find his way out again."
— "Theseus and Ariadne," by Charles Morris
From "Ariadne's Clue," a post of March 1 last year—
The Watson here is not Emma, but Victor—
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Thursday, March 15, 2012
The Head of Caesar
Remarks on Citizen Kane from The New York Times—
"… a kind of metaphysical detective story…. At the end we realize that the fragments are not governed by any secret unity: the detested Charles Foster Kane is a simulacrum, a chaos of appearances.” Borges concluded by quoting Chesterton, "there is nothing more frightening than a labyrinth that has no center." *
* The actual quote is from a Father Brown mystery, "The Head of Caesar," "'What we all dread most,' said the priest in a low voice, 'is a maze with no centre….'"
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Yonda
The Grind House of My Father
—New York Times headline for the latest
Will Ferrell film, Casa de Mi Padre
Related material—
- The Log24 post of March 13, "Geometry and Death"
- A post of March 13 nine years earlier, "Death Knell"
- The update to that post from nine years ago tomorrow
- The Majestic
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Wednesday, March 14, 2012
Sequels
"Greg Smith is resigning today as a Goldman Sachs executive director
and head of the firm’s United States equity derivatives business
in Europe, the Middle East and Africa." —NY Times today
Boo.
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Tuesday, March 13, 2012
Geometry and Death
Continued from other posts.
Related material from Washington Jewish Week—
"Abramson did not always get his way; he didn't have to win, but never took his eye off the ball— the Museum had to emerge the better. He did not take loses personally but pragmatically. A design for the Museum building done by an architect from his firm was charitably speaking 'mediocre.' It was replaced by a brilliant building designed by James Ingo Freed who rightfully regarded it as the master work of his distinguished career. Abramson became Freed's champion. He pushed the design team for a happy ending, saying that he knew the American people and they needed an uplifting ending since the subject of the Holocaust was so very depressing."
— and from the Holocaust Memorial Museum—
Update of 5:01 AM March 13—
See also yesterday's post The Line and
the section "The Pythagorean/ Platonic tradition"
at David Wade's website Pattern in Islamic Art.
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Monday, March 12, 2012
The Line
From a film review—
"The first half of the film has the predominant
tone and style of a comic farce. In the second
half, the film becomes darker as it delves deeper
into its central issues of human suffering,
sacrifice and faith. The film also frequently blurs
the line between the sane and the insane."
Related material— The Line: A Lenten Meditation.
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Sunday, March 11, 2012
Twinkle, Twinkle*
From one year ago today, a link—
*Title courtesy of William Peter Blatty.
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Boo continued…
Click image for some context. See also yesterday's Boo Boo Boo.
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Saturday, March 10, 2012
Boo Boo Boo*
Academics today—
-
- What Stanley H. Kaplan taught us about the S.A.T.
- VERBUM SAT in this journal
- In the Beginning Was the Void†—
Home Page of Steven Z. Levine
(A.B., A.M., Ph.D., all at Harvard University, 1968-1974)—
Note that Levine states forthrightly that he won Third Prize for Bad Writing
from the international journal Philosophy and Literature in 1998.
* Stanley H. Kaplan, mnemonic for “square root of two.”
† On the void — See this morning’s post and “Is Nothing Sacred?“
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Incoming!
"In 1957, as an incoming freshman,
I was traded by Harvard to Yale.
Harvard got a guy who could row
and Yale got a Jewish boy with good SATs."
— The late Peter Bergman
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Thursday, March 8, 2012
Light
For Women's Day—
- Reviews of GCB from Dallas and Toronto
- Sweater, a post of 2:02 PM EST Monday
(1:02 PM Monday, Dallas time) - Schedule for a Monday afternoon event in Dallas
- NY Times front page Monday evening, featuring
remarks by "The Stone" philosopher Colin McGinn - A 10 PM Monday link to a Harvard Crimson review
of a book by McGinn
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Heralds of Light
On Harvard's Memorial Church in 2007—
|
"John Harvard left no male heir to carry on the Harvard family name. Instead, the naming of the College in his honor was the undying legacy that his friends decided to grant to him. In so doing, they were saying to every succeeding generation that this was the kind of man whom they wanted others to emulate, whose spirit of courage, self-sacrifice and generosity embodied the very best of what they hoped Harvard College should become. On November 4, 2007, the gift of a tablet was presented to Harvard Memorial Church by the dean of Southwark Cathedral, London, the Rev. Colin Slee, and Emmanuel College, to commemorate the 400th anniversary of John Harvard's baptism. This, along with a combined brief exhibit called 'Heralds of Light,' which consisted in part of showing John Harvard's baptismal page from the Southwark records and his Emmanuel College signature— brought over for the occasion from England by Southwark and Emmanuel representatives—was about all the attention that Harvard University could muster to remember the 400th birthday of its namesake." — Arseny James Melnick (A.M., Harvard University, 1977), |
Related material from the entertainment world—
Phoenix Senior: "As the plaque reads, this is John Harvard,
founder of Harvard University in 1638. It's also called
the Statue of Three Lies. What are the three lies?"
Also on November 4, 2007—
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Wednesday, March 7, 2012
Tuesday, March 6, 2012
Doodle Dandy
For Princess Leia, from donshewey.com—
REVISITING ‘THE LADY FROM DUBUQUE’
| Origin of the title: Harold Ross, founding editor of The New Yorker, was once asked to describe the average reader of the magazine. He said, “One thing I know, the magazine is not going to be written for the little old lady from Dubuque.” Naming his character after Ross’s imaginary small-town creature was typically whimsical of Albee. The play’s title character is extremely worldly and other-worldly at the same time. “If The New Yorker is written for anyone, it’s written for her,” Albee said. |
Related material: Butterfly in this journal.
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A Strange Thing
In memory of songwriter Robert Sherman—
See also The Uploading.
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Monday, March 5, 2012
For a Yale 10
See a Harvard Crimson review of a book
by philosopher Colin McGinn.
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Sweater
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For the Nine Muses
From "The Talented," a post of April 26, 2011—
And for Josefine Lyche—
Unity in Multiplicity —
Pink in Wikipedia
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Establishment of the Talented
For Women's History Month —
See this post's title in Log24 and the following from Pinkdex ,
the online catalog of the MIT Science Fiction Society (MITSFS)—
"The Pinkdex is so named because it was originally
maintained by another member of MITSFS, many years ago—
Marilyn 'Fuzzy Pink' Niven [said to be so called for her sweaters],
whose husband, Larry Niven, has written
or co-authored many of the books in the MITSFS library."
See also MIT Commencement in this journal.
Postscript for the less technically oriented reader—
This post was suggested by yesterday's "Look, Buster,"
and by the middle name of William Rowan Hamilton.
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Sunday, March 4, 2012
The Haunted Galaxy
(Continued from Big Art , 1 PM EST yesterday)
In related news…
Ralph McQuarrie, who designed the Star Wars trilogy, died yesterday.
See also Haunting Time.
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Look, Buster…
(Continued from previous posts)
Detail from a Washington Post page today (below)…
In related news…
The Hallowed Crucible
"After all the pretty contrast of life and death
Proves that these opposite things partake of one,
At least that was the theory…."
— Wallace Stevens, "Connoisseur of Chaos"
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Saturday, March 3, 2012
Big Art
For Women's History Month—
The Beam of Pink Light
From a post linked to on Lyxe's upload date, Feb. 6, 2012—
“… with primitives the beginnings of art, science, and religion
coalesce in the undifferentiated chaos of the magical mentality….”
— Carl G. Jung, “On the Relation of Analytical Psychology to Poetry,”
Collected Works, Vol. 15, The Spirit in Man, Art, and Literature,
Princeton University Press, 1966, excerpted in
Twentieth Century Theories of Art, edited by James M. Thompson.
See also the NY Lottery for St. Luke's Day, 2011, publication date
of the new edition of Philip K. Dick's VALIS quoted above.
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Decomposition
A search tonight for material related to the four-color
decomposition theorem yielded the Wikipedia article
Functional decomposition.
The article, of more philosophical than mathematical
interest, is largely due to one David Fass at Rutgers.
(See the article's revision history for mid-August 2007.)
Fass's interest in function decomposition may or may not
be related to the above-mentioned theorem, which
originated in the investigation of functions into the
four-element Galois field from a 4×4 square domain.
Some related material involving Fass and 4×4 squares—
A 2003 paper he wrote with Jacob Feldman—
"Design is how it works." — Steve Jobs
An assignment for Jobs in the afterlife—
Discuss the Fass-Feldman approach to "categorization under
complexity" in the context of the Wikipedia article's
philosophical remarks on "reductionist tradition."
The Fass-Feldman paper was assigned in an MIT course
for a class on Walpurgisnacht 2003.
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Friday, March 2, 2012
Douat Facsimile
Title of a treatise by Dominique Douat—
"Méthode pour faire une infinité de desseins différens avec des carreaux mi-partis de deux couleurs par une ligne diagonale : ou observations du Père Dominique Doüat Religieux Carmes de la Province de Toulouse sur un mémoire inséré dans l'Histoire de l'Académie Royale des Sciences de Paris l'année 1704, présenté par le Révérend Père Sébastien Truchet religieux du même ordre, Académicien honoraire " (Paris, 1722)
"The earliest (and perhaps the rarest) treatise on the theory of design"
— E. H. Gombrich, 1979, in The Sense of Order
A facsimile version (excerpts, 108 pp., Feb. 5, 2010) of this treatise is available from
http://jacques-andre.fr/ed/ in a 23.1 MB pdf.
Sample page—
For a treatise on the finite geometry underlying such designs (based on a monograph I wrote in 1976, before I had heard of Douat or his predecessor Truchet), see Diamond Theory.
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Thursday, March 1, 2012
Block That Metaphor:
The Cube Model and Peano Arithmetic
The eightfold cube model of the Fano plane may or may not have influenced a new paper (with the date Feb. 10, 2011, in its URL) on an attempted consistency proof of Peano arithmetic—
The Consistency of Arithmetic, by Storrs McCall
"Is Peano arithmetic (PA) consistent? This paper contains a proof that it is. …
Axiomatic proofs we may categorize as 'syntactic', meaning that they concern only symbols and the derivation of one string of symbols from another, according to set rules. 'Semantic' proofs, on the other hand, differ from syntactic proofs in being based not only on symbols but on a non-symbolic, non-linguistic component, a domain of objects. If the sole paradigm of 'proof ' in mathematics is 'axiomatic proof ', in which to prove a formula means to deduce it from axioms using specified rules of inference, then Gödel indeed appears to have had the last word on the question of PA-consistency. But in addition to axiomatic proofs there is another kind of proof. In this paper I give a proof of PA's consistency based on a formal semantics for PA. To my knowledge, no semantic consistency proof of Peano arithmetic has yet been constructed.
The difference between 'semantic' and 'syntactic' theories is described by van Fraassen in his book The Scientific Image :
"The syntactic picture of a theory identifies it with a body of theorems, stated in one particular language chosen for the expression of that theory. This should be contrasted with the alternative of presenting a theory in the first instance by identifying a class of structures as its models. In this second, semantic, approach the language used to express the theory is neither basic nor unique; the same class of structures could well be described in radically different ways, each with its own limitations. The models occupy centre stage." (1980, p. 44)
Van Fraassen gives the example on p. 42 of a consistency proof in formal geometry that is based on a non-linguistic model. Suppose we wish to prove the consistency of the following geometric axioms:
A1. For any two lines, there is at most one point that lies on both.
A2. For any two points, there is exactly one line that lies on both.
A3. On every line there lie at least two points.
The following diagram shows the axioms to be consistent:
Figure 1
The consistency proof is not a 'syntactic' one, in which the consistency of A1-A3 is derived as a theorem of a deductive system, but is based on a non-linguistic structure. It is a semantic as opposed to a syntactic proof. The proof constructed in this paper, like van Fraassen's, is based on a non-linguistic component, not a diagram in this case but a physical domain of three-dimensional cube-shaped blocks. ….
… The semantics presented in this paper I call 'block semantics', for reasons that will become clear…. Block semantics is based on domains consisting of cube-shaped objects of the same size, e.g. children's wooden building blocks. These can be arranged either in a linear array or in a rectangular array, i.e. either in a row with no space between the blocks, or in a rectangle composed of rows and columns. A linear array can consist of a single block, and the order of individual blocks in a linear or rectangular array is irrelevant. Given three blocks A, B and C, the linear arrays ABC and BCA are indistinguishable. Two linear arrays can be joined together or concatenated into a single linear array, and a rectangle can be re-arranged or transformed into a linear array by successive concatenation of its rows. The result is called the 'linear transformation' of the rectangle. An essential characteristic of block semantics is that every domain of every block model is finite. In this respect it differs from Tarski’s semantics for first-order logic, which permits infinite domains. But although every block model is finite, there is no upper limit to the number of such models, nor to the size of their domains.
It should be emphasized that block models are physical models, the elements of which can be physically manipulated. Their manipulation differs in obvious and fundamental ways from the manipulation of symbols in formal axiomatic systems and in mathematics. For example the transformations described above, in which two linear arrays are joined together to form one array, or a rectangle of blocks is re-assembled into a linear array, are physical transformations not symbolic transformations. …"
— Storrs McCall, Department of Philosophy, McGill University
See also…
- Finite Geometry and Physical Space,
- McCall in the book search of this morning's Salvation for Gopnik, and
- the post Declarations of Jan. 29, 2012.
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Big Reveal
(Continued from 1:06 AM EST.)
Wikipedia on the late Andrew Breitbart—
"He ran his own news aggregation site, Breitbart.com,
and five other websites: Breitbart.tv, Big Hollywood,
Big Government, Big Journalism, and Big Peace."
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Salvation for Gopnik
Yesterday afternoon's post Universals Revisited linked
(indirectly) to an article in the current New Yorker on
the Book of Revelation —
"The Big Reveal: Why Does the Bible End That Way?"
The connection in that post between universals and Revelation
may have eluded readers unfamiliar with a novel by
Charles Williams, The Place of the Lion (London, Gollancz, 1931).
The article's author, Adam Gopnik, appears in the following
Google Book Search, which may or may not help such readers.
Should Gopnik desire further information on Williams and salvation,
he may consult Steps Toward Salvation: An Examination of Coinherence
and Substitution in the Seven Novels of Charles Williams ,
by Dennis L. Weeks (American University Studies: Series 4, English
Language and Literature. Vol. 125), XV + 117 pp., Peter Lang Publishing, 1991.
The ninth item in the above search refers to a boxed set
of the seven novels themselves—
.
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Wednesday, February 29, 2012
Universals Revisited
"Some philosophical pieces are like symphonies,
others like quartets."
— Gustav Bergmann, "Frege's Hidden Nominalism,"
The Philosophical Review ,
Vol. 67, No. 4 (Oct., 1958), pp. 437-459
See also Annals of Religion.
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Metamorphoses of an Author
"… I'm never sure why I like Auster books.
They have that appealing shiny-ness,
that makes me go 'oooh'
then put my hands out to touch it
even though I know I shouldn't,
much like someone giving you
a plate of mercury to play with. "
— Review at goodreads.com
See also Auster as a T-1000 Terminator
in yesterday's post Page.
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Tuesday, February 28, 2012
Page
A followup to this morning's post Stolen Glory—
Columbia's Butler Library "plays a role in
Paul Auster's 2009 novel Invisible ,
where the novel's main protagonist, Adam Walker,
takes a job as a 'page' in the library's stacks." —Wikipedia
Part I (from Feb. 24)—
Part II— (Click to enlarge)
For the page's source, see Butler Library.
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Stolen Glory
From University Diaries yesterday—
"A writer for The Atlantic applauds Santorum's attack on universities
as secular, amoral indoctrination machines.
What can UD say to this?…."
Below is a screenshot of the new home page for
Columbia University Department of Mathematics.
The impressive building in the photo is not the math department.
The building is actually Columbia's Butler Library.
"Along the front and sides of the library are inscribed the names of
Homer, Herodotus, Sophocles, Plato, Aristotle, Desmosthenes,
Cicero, Virgil, Horace, Tacitus, Saint Augustine, Aquinas, Dante,
Cervantes, Shakespeare, Milton, Voltaire, and Goethe." —Wikipedia
The inscribed names outline a defense of liberal education
perhaps more robust than the Feb. 26 effort of Andrew Delbanco,
which University Diaries calls "tepid." (See the previous Log24 post.)
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Monday, February 27, 2012
Reflection
"But even if the religious note is dissonant to some of us,
it seems hard to come up with a better formulation
of what a college should strive to be: an aid to reflection…."
— Andrew Delbanco, Chronicle of Higher Education , Feb. 26, 2012
Another aid to reflection—
The logo of an institution that advertised today in the Chronicle
next to Delbanco's article—
Click logo for context. The institution's original name
was Hesperian College.
For some background, see Evening Star in this journal.
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Annals of Religion
"Allegorical pictures of contemporary events
have a way of weaving in and out
between the symbolic and the semi-psychotic."
— Adam Gopnik in The New Yorker , issue dated March 5, 2012
See also Venue and Weaveworld .
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Sunday, February 26, 2012
Margaret’s Haiku
Margaret Soltan this morning posted a haiku about a fox in her garden.
Related material— The Ninth Gate* versus The Ninth Configuration.
* For some backstory, see pop physics.
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Sermon for Nabokov
"In linear algebra, the basis of a vector space
is an alphabet in which all vectors
can be expressed uniquely. The thing to remember
is that there are many such alphabets."
— "A Vector Alphabet of Interstellar Travel,"
by Yoon Ha Lee
See also Starflight in this journal.
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Garden of Good and Evil
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Saturday, February 25, 2012
The Rock
(Continued. See previous post and Red and Gray in this journal.)
“Give faith a fighting chance.” —Country song
From a post of June 3, 2007—
Related illustration relevant to theology—
For some background, see Cube Trinity in this journal.
For greater depth, see Levering’s Scripture and Metaphysics:
Aquinas and the Renewal of Trinitarian Theology ,
Blackwell, 2004, page 150.
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Cuber (continued)
Click images for further details.
See also Crimson Tide, Rubik, and Cuber.
For another monochromatic enigma without
guaranteed equality of results, see
Finite Geometry of the Square and Cube.
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Friday, February 24, 2012
Thursday, February 23, 2012
Minimalist Whirl
See St. Bridget's Cross
on the Web and in this journal.
Related material—
(Click images to enlarge.)
From Tablet magazine on St. Bridget's Day, 2012—
From Tablet magazine today—
Of greater secular interest—
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Wednesday, February 22, 2012
For Ash Wednesday
"And the light shone in darkness and
Against the Word the unstilled world still whirled
About the centre of the silent Word."
— T. S. Eliot, "Ash Wednesday"
This suggested a search for commentary on
Conrad Aiken's phrase "where whirled and well."
Of the nine (Google) search results, one is not from
my own journal entries—
[PDF] TIME! TIME! TIME!
https://circle.ubc.ca/bitstream/id/131009/UBC_1968_A8%20C33.pdf
File Format: PDF/Adobe Acrobat
by G Cameron – 1968 – Related articles
well where whirled and well where whirled and well—
-3. The stress on words such as "wing" is expanded for use
in Aiken's musical paragraph as follows: …
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Tuesday, February 21, 2012
Cuckoos’ Nest
See …
- St. Dunstan in this journal,
- Location for a film based on The Midwich Cuckoos ,
- Andrew Amesbury's weblog today, and
- St. Dunstan's Garden
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For Mardi Gras
See Dennis Overbye in today's New York Times
and Imago Creationis in this journal.
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