The Chicago Tribune today —
H. Wilbert Norton, college president
and Christian missionary, dies
Norton reportedly died at 102 on Feb. 20, 2017.
This evening's previous post linked the death dates of two
academics to two Log24 posts that both contained the
following image —
For some backstory, see the Log24 posts from the date
of Norton's reported death, February 20.
"Human perception is a saga of created reality."
— Don DeLillo, Point Omega
See "Important Product" in this journal and the previous post.
Continued from last night
From the American Mathematical Society, a news item
dated Thursday, March 9, 2017 —
Remarks by Schwartz quoted here on March 7—
A post suggested by remarks of J. D. Salinger in
The New Yorker of November 19, 1955 —
|
Wikipedia: Taiji (philosophy) Etymology The word 太極 comes from I Ching : "易有太極，是生兩儀，兩儀生四象，四象生八卦，八卦定吉凶，吉凶生大業。" Taiji (太極) is a compound of tai 太 "great; grand; supreme; extreme; very; too" (a superlative variant of da 大 "big; large; great; very") and ji 極 "pole; roof ridge; highest/utmost point; extreme; earth's pole; reach the end; attain; exhaust". In analogy with the figurative meanings of English pole, Chinese ji 極 "ridgepole" can mean "geographical pole; direction" (e.g., siji 四極 "four corners of the earth; world's end"), "magnetic pole" (Beiji 北極 "North Pole" or yinji 陰極 "negative pole; cathode"), or "celestial pole" (baji 八極 "farthest points of the universe; remotest place"). Combining the two words, 太極 means "the source, the beginning of the world". Common English translations of the cosmological Taiji are the "Supreme Ultimate" (Le Blanc 1985, Zhang and Ryden 2002) or "Great Ultimate" (Chen 1989, Robinet 2008); but other versions are the "Supreme Pole" (Needham and Ronan 1978), "Great Absolute", or "Supreme Polarity" (Adler 1999). |
See also Polarity in this journal.
* A phrase adapted, via Salinger,
from a poem by Sappho—
Ἴψοι δὴ τὸ μέλαθρον,
Υ᾽μήναον
ἀέρρετε τέκτονεσ ἄνδρεσ,
Υ᾽μήναον
γάμβροσ ἔρχεται ἶσοσ Ά᾽ρευϊ,
[Υ᾽μήναον]
ανδροσ μεγάλο πόλυ μείζων
[Υ᾽μήναον]
"The Bitter End’s signature stage backdrop —
a bare 150-year-old brick wall — helped distinguish it from
other popular bohemian hangouts like the Village Gate
and the Village Vanguard. It appeared on the cover of
Peter, Paul and Mary’s first album."
— The New York Times this evening on a Sunday death
“Looking carefully at Golay’s code is like staring into the sun.”
See also Schwartz in "The Omega Matrix," a post of 5 PM ET Sunday:
This journal on that date —
The Los Angeles Times this morning reported that poet
David Antin died at 84 last Tuesday, October 11.
From this journal on that date —
Quivering Antennae
This journal on that date —
Πολυμερῶς καὶ πολυτρόπως πάλαι ὁ Θεὸς λαλήσας . . . .
( Long Day's Journey into Nighttown continues. )
From yesterday's 2 PM post —
From "Inception" —
Paraphrase of remarks by "Inception" director Christopher Nolan
at Princeton on June 1, 2015 —
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
"First and last, he was a skeptic …."
— Home page of Martin-Gardner.org
See also, in this journal, Alpha and Omega.
Related material from the last full day of Gardner's life —
See as well Symplectic in this journal.
The previous post dealt with one of the 64 symbols
(in a redesigned format) of the ancient Chinese classic
The I Ching .
For those who prefer to be guided by programmed
responses to alphabetical symbols …
A lyric by Ira Gershwin —
A cinematic "T" —
See also "T for Texas" in this journal and
George Clooney's recent attempt to commercialize
both the space program and the letter Omega:
From a post of May 13, 2015 —
In memory of ballet designer
Yolanda Sonnabend, who
reportedly died at 80 on Nov. 9,
see posts on Apollo, Ballet Blanc,
maps of New Haven, etc., etc., etc.
The title pun is from a letter about Google's new parent
company, named "Alphabet" by its founders.
Related material: Alpha and Omega in this journal.
A music video that opens with remarks by Lawrence Ferlinghetti
at the Last Waltz concert (Thanksgiving Day, Nov. 25, 1976):
"Our Father, whose art's in heaven…" —
For other religious remarks from the above upload date,
Sept. 9, 2011, see Holy Field GF(3).
Click the above "ripple" image for a Grateful Dead haiku
quoted here on Sunday, July 5, 2015.
For another meditation from the second upload date above,
March 19, 2012, see some thoughts on the word "field."
* For the title, see an excerpt from Point Omega .
Do you know where your watch is?
From a post of May 13, 2015 —
From the recent film "Interstellar" —
See the previous post, "Space," as well as…
SymOmega in this journal and a suggested motto
for The University of Western Australia.
For a former president of Notre Dame
who reportedly died at 11:30 PM last night —
"Sometimes a wind comes before the rain
and sends birds sailing past the window,
spirit birds that ride the night,
stranger than dreams."
— The end of DeLillo's Point Omega
"Sometimes a wind comes before the rain
and sends birds sailing past the window,
spirit birds that ride the night,
stranger than dreams."
— The end of DeLillo's Point Omega
|
From "Origins of the Logical Theory of Probability: von Kries, Wittgenstein, Waismann," by Michael Heidelberger — "Von Kries calls a range of objective possibilities of a hypothesis or event (under given laws) its Spielraum (literally: play space), which can mean ‘room to move’, ‘leeway’, ‘latitude of choice’, ‘degree of freedom’ or ‘free play’ and ‘clearance’ – or even ‘scope’. John Maynard Keynes translated it as ‘field’, but the term ‘range’ has generally been adopted in English. Von Kries now holds that if numerical probability were to make any sense at all it must be through this concept of the Spielraum . Von Kries’s theory is therefore called a ‘Spielraum theory’ or ‘range theory of probability’." — International Studies in the Philosophy of Science , Volume 15, Issue 2, 2001, pp. 177-188 |
See also the tag Points Omega.
(Scroll down to January 11-12, 2015.)
Related material:
"Now, for example, in how far are
the six sides of a symmetric die
'equally possible' upon throwing?"
— From "The Natural-Range Conception
of Probability," by Dr. Jacob Rosenthal,
page 73 in Time, Chance, and
Reduction: Philosophical Aspects of
Statistical Mechanics , ed. by
Gerhard Ernst and Andreas Hüttemann,
Cambridge U. Press, 2010, pp. 71-90
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— “An Ordinary Evening in New Haven” VI
From the series of posts tagged "Defining Form" —
The 4-point affine plane A and
the 7-point projective plane PA —
The circle-in-triangle of Yale's Figure 30b (PA ) may,
if one likes, be seen as having an occult meaning.
For the mathematical meaning of the circle in PA
see a search for "line at infinity."
A different, cubic, model of PA is perhaps more perspicuous.
A professor at Harvard has written about
"the urge to seize and display something
real beyond artifice."
He reportedly died on January 3, 2015.
An image from this journal on that date:
Another Gitterkrieg image:
The 24-set Ω of R. T. Curtis
Click on the images for related material.
From a recent Gitterkrieg post:
"The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being…." — Wallace Stevens
See also the cover of the February 2015
Notices of the American Mathematical Society .
"Omega is as real as we need it to be."
— Burt Lancaster in The Osterman Weekend
Alexander Grothendieck, Récoltes et Semailles , 18.5.9.5. e, p. 1181 :
Pour mettre la joie à son comble, j’ajoute que le dénommé Saavedra
semble avoir disparu de la circulation sans plus laisser aucune trace….
Du coup, l’histoire prend des allures de sombre intrigue policière.
Man of La Mancha :
"Who knows where madness lies?"
An author quoted here at 10 PM ET Monday, Nov. 24, 2014 :
And then there is author Dan McGirt :
|
It sounded fun, so I signed up — and soon learned writing a story set in someone else’s fictional world presents certain … challenges. It was an enjoyable experience, yet very different than being able to write and run with whatever crazy idea pops into my head. Trying to capture the feel of a game that is more based on action and blowing stuff up than on deep character moments (not that I would know much about that … ) was also a challenge. I experimented with things like using comic book sound effects, lean descriptions (do I really need to describe a fireball spell in detail?) and other tricks to keep things moving. I also got to add to Magicka lore. Often the answer to my questions about some bit of in-world history or “fact” was “Make something up.” So I did! (Often getting a response of … “Odin’s onions, no! You can’t do that!”) So I was thrilled and excited to contribute in a small way to the development of Midgård. The result is Magicka: The Ninth Element , in which four young Wizards are sent on a quest to pursue the mysterious Purple Wizard who has stolen a powerful artifact from the Order of Magick. Which powerful artifact? No one is quite sure (for reasons explained in the story). What does it do? Again, unclear. But it can’t be good. Thus our heroes Davlo, Grimnir, Fafnir and Tuonetar set out on their quest — and promptly go off the map. (I’m not even kidding. The Midgård map in the front of the book will of little use to you. But it’s pretty!) Will they survive the dangers of the Unmapped Lands? Will they catch the Purple Wizard in time? Will they save the world? Read the book to find out! |
"We tried to create new realities overnight,
careful sets of words that resemble advertising slogans
in memorability and repeatability."
… Our Most Important Product …
"Omega is as real as we need it to be."
— Burt Lancaster in Sam Peckinpah's last film
Wallace Stevens in "An Ordinary Evening in New Haven"
(1950) on "The Ruler of Reality" —
"Again, 'He has thought it out, he thinks it out,
As he has been and is and, with the Queen
Of Fact, lies at his ease beside the sea.'"
One such scene, from 1953 —
Another perspective, from "The Osterman Weekend" (1983) —
To Feb. 11, 2012:
“News and Traffic. Sports and Weather. These were his acid terms
for the life he’d left behind, more than two years of living with
the tight minds that made the war. It was all background noise,
he said, waving a hand. He liked to wave a hand in dismissal.”
— DeLillo, Don (2010-02-02), Point Omega
Send in the Clowns. (Click to enlarge.)
The above flashback was suggested by Lev Grossman’s verb “trafficked”
in yesterday’s posts, and by the song lyric “show us the way to
the next little girl.”
Illustration from a discussion of a symplectic structure
in a 4×4 array quoted here on January 17, 2014 —
See symplectic structure in this journal.
* The final words of Point Omega , a 2010 novel by Don DeLillo.
See also Omega Matrix in this journal.
“… which is our actual experience” — Joan Didion
— Ludwig Wittgenstein, Philosophical Investigations
“This is a divorce case that was before us on an earlier occasion.”
Wild:
From the director of The Wild Bunch —
Brady:
From The New York Times —
"There is such a thing as a tesseract." — Madeleine L'Engle
An approach via the Omega Matrix:
See, too, Rosenhain and Göpel as The Shadow Guests .
Dialogue from “The Osterman Weekend”—
01:57:22 “Why did he make us try to believe Omega existed?”
01:57:25 ….
01:57:26 “The existence of Omega has not been disproved.
01:57:28 Don’t you understand that?
01:57:31 Omega is as real as we need it to be.”
See also Omega elsewhere in this journal.
Update of 9:15 PM ET —
"Bobbies on bicycles two by two…" — Roger Miller, 1965
A mathematics weblog in Australia today—
Clearly, the full symmetric group contains elements
with no regular cycles, but what about other groups?
Siemons and Zalesskii showed that for any group G
between PSL(n,q) and PGL(n,q) other than for
(n,q)=(2,2) or (2,3), then in any action of G, every
element of G has a regular cycle, except G=PSL(4,2)
acting on 8 points. The exceptions are due to
isomorphisms with the symmetric or alternating groups.
… Continues.
"24 Hour Psycho" at the Museum of Modern Art in the novel
Point Omega is illustrated in a New York Times review—
Related material — Today's 1 PM post and…
See also yesterday's 1 PM post.
Heraclitus, Fragment 60 (Diels number):
|
The way up and the way down is one and the same. ὁδὸς ἄνω κάτω μία καὶ ὡυτή hodòs áno káto mía kaì houté |
See also Blade and Chalice and, for a less Faustian
approach, Universe of Discourse.
Further context: Not Theology.
(Continued from June 2, 2013)
John Bamberg continues his previous post on this subject.
The death yesterday of British cinematographer
Gilbert Taylor suggests an image from last evening's
Log24 search Point Omega —
.
The die in the above image (shown here Dec. 28, 2012)
displays the numbers 3-6-5 in counterclockwise order.
A similar die in an earlier post served as a metaphor for
a time-jump to 365 days in the past.
For some religious remarks by Umberto Eco that may
serve as a small memorial to Taylor, see this journal
a year before the day he died— August 23, 2012.
A passage from Wallace Stevens—
The spirit and space,
The empty spirit
In vacant space.
A frame from the film American Psycho (2000), starring Christian Bale—
The rest of the film is not recommended.
Related material—
"24 Hour Psycho" at the Museum of Modern Art in the novel Point Omega .
Illustration from a New York Times review—
See the Klein correspondence at SymOmega today and in this journal.
"The casual passerby may wonder about the name SymOmega.
This comes from the notation Sym(Ω) referring to the symmetric group
of all permutations of a set Ω, which is something all of us have
both written and read many times over."
The Oslo Version and The Lyche Omega
Those who prefer more traditional art
may consult The Portal Project.
"Of course, DeLillo being DeLillo,
it’s the deeper implications of the piece —
what it reveals about the nature of
film, perception and time — that detain him."
— Geoff Dyer, review of Point Omega
Related material:
A phrase of critic Robert Hughes,
"slow art," in this journal.
A search for that phrase yields the following
figure from a post on DeLillo of Oct. 12, 2011:
The above 3×3 grid is embedded in a
somewhat more sophisticated example
of conceptual art from April 1, 2013:
Update of April 12, 2013
The above key uses labels from the frontispiece
to Baker's 1922 Principles of Geometry, Vol. I ,
that shows a three-triangle version of Desargues's theorem.
A different figure, from a site at National Tsing Hua University,
shows the three triangles of Baker's figure more clearly:
For the first two words of the title,
see the previous post.
For the third word, see a review of the recent film "Hitchcock"
about the director and Janet Leigh during the filming of "Psycho"—
Hopkins' Hitchcock more or less eats out of Janet's hand
when she feeds him candy corn during a drive together
(the reference is to the candy Norman Bates is devouring
when he's interviewed by Martin Balsam's detective).
A story that demands the blended talents of Hitchcock and of
Mel Brooks to do it justice:
See also a 2010 New York Times review of
DeLillo's novel Point Omega . The review is titled,
without any other reference to L'Engle's classic tale
of the same name, "A Wrinkle in Time."
Related material: The Crosswicks Curse.
A sequel to the quotation here March 8 (Pinter Play)
of Joan Aiken's novel The Shadow Guests—
Supposing that one's shadow guests are
Rosenhain and Göpel (see March 18)…
Hans Freudenthal at Encyclopedia.com on Charles Hermite:
"In 1855 Hermite took advantage of Göpel’s and Rosenhain’s work
when he created his transformation theory (see below)."
"One of his invariant theory subjects was the fifth-degree equation,
to which he later applied elliptic functions.
Armed with the theory of invariants, Hermite returned to
Abelian functions. Meanwhile, the badly needed theta functions
of two arguments had been found, and Hermite could apply what
he had learned about quadratic forms to understanding the
transformation of the system of the four periods. Later, Hermite’s
1855 results became basic for the transformation theory of Abelian
functions as well as for Camille Jordan’s theory of 'Abelian' groups.
They also led to Herrnite’s own theory of the fifth-degree equation
and of the modular equations of elliptic functions. It was Hermite’s
merit to use ω rather than Jacobi’s q = eπi ω as an argument and to
prepare the present form of the theory of modular functions.
He again dealt with the number theory applications of his theory,
particularly with class number relations or quadratic forms.
His solution of the fifth-degree equation by elliptic functions
(analogous to that of third-degree equations by trigonometric functions)
was the basic problem of this period."
See also Hermite in The Catholic Encyclopedia.
The title was suggested by an ad for a film that opens
at 10 PM EST today: "Hansel & Gretel: Witch Hunters."
Related material: Grimm Day 2012, as well as
Amy Adams in Raiders of the Lost Tesseract
and in a Film School Rejects page today.
See also some Norwegian art in
Trish Mayo's Photostream today and in
Omega Point (Log24, Oct. 15, 2012)—
Monday, October 15, 2012
|
|
From Don DeLillo's novel Point Omega — I knew what he was, or what he was supposed to be, a defense intellectual, without the usual credentials, and when I used the term it made him tense his jaw with a proud longing for the early weeks and months, before he began to understand that he was occupying an empty seat. "There were times when no map existed to match the reality we were trying to create." "What reality?" "This is something we do with every eyeblink. Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation. Lying is necessary. The state has to lie. There is no lie in war or in preparation for war that can't be defended. We went beyond this. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional. The reality stands, it walks, it squats. Except when it doesn't." He didn't smoke but his voice had a sandlike texture, maybe just raspy with age, sometimes slipping inward, becoming nearly inaudible. We sat for some time. He was slouched in the middle of the sofa, looking off toward some point in a high corner of the room. He had scotch and water in a coffee mug secured to his midsection. Finally he said, "Haiku." I nodded thoughtfully, idiotically, a slow series of gestures meant to indicate that I understood completely. "Haiku means nothing beyond what it is. A pond in summer, a leaf in the wind. It's human consciousness located in nature. It's the answer to everything in a set number of lines, a prescribed syllable count. I wanted a haiku war," he said. "I wanted a war in three lines. This was not a matter of force levels or logistics. What I wanted was a set of ideas linked to transient things. This is the soul of haiku. Bare everything to plain sight. See what's there. Things in war are transient. See what's there and then be prepared to watch it disappear." |
What's there—
This view of a die's faces 3, 6, and 5, in counter-
clockwise order (see previous post) suggests a way
of labeling the eight corners of a die (or cube):
123, 135, 142, 154, 246, 263, 365, 456.
Here opposite faces of the die sum to 7, and the
three faces meeting at each corner are listed
in counter-clockwise order. (This corresponds
to a labeling of one of MacMahon's* 30 colored cubes.)
A similar vertex-labeling may be used in describing
the automorphisms of the order-8 quaternion group.
For a more literary approach to quaternions, see
Pynchon's novel Against the Day .
* From Peter J. Cameron's weblog:
"The big name associated with this is Major MacMahon,
an associate of Hardy, Littlewood and Ramanujan,
of whom Robert Kanigel said,
His expertise lay in combinatorics, a sort of
glorified dice-throwing, and in it he had made
contributions original enough to be named
a Fellow of the Royal Society.
Glorified dice-throwing, indeed…"
In Like Flynn
From the Wall Street Journal site Friday evening—
| ESSAY September 21, 2012, 9:10 p.m. ET
Are We Really Getting Smarter? Americans’ IQ scores have risen steadily over the past century.
|
No, thank you. I prefer the ninth configuration as is—
Why? See Josefine Lyche’s art installation “Grids, you say?“
Her reference there to “High White Noon” is perhaps
related to the use of that phrase in this journal.
The phrase is from a 2010 novel by Don DeLillo.
See “Point Omega,” as well as Lyche’s “Omega Point,”
in this journal.
The Wall Street Journal author above, James R. Flynn (born in 1934),
“is famous for his discovery of the Flynn effect, the continued
year-after-year increase of IQ scores in all parts of the world.”
—Wikipedia
His son Eugene Victor Flynn is a mathematician, co-author
of the following chapter on the Kummer surface— 
For use of the Kummer surface in Buddhist metaphysics, see last night’s
post “Occupy Space (continued)” and the letters of Nanavira Thera from the
late 1950s at nanavira.blogspot.com.
These letters, together with Lyche’s use of the phrase “high white noon,”
suggest a further quotation—
You know that it would be untrue
You know that I would be a liar
If I was to say to you
Girl, we couldn’t get much higher
See also the Kummer surface at the web page Configurations and Squares.
(Continued from 6:08 AM EDT yesterday and the day before)
"Richard Elster was seventy-three, I was less than half his age. He’d invited me to join him here, old house, under-furnished, somewhere south of nowhere in the Sonoran Desert or maybe it was the Mojave Desert or another desert altogether.* Not a long visit, he’d said."
— Don DeLillo, Point Omega
Maybe it was the desert near Twentynine Palms.
"Sometimes a wind comes before the rain
and sends birds sailing past the window,
spirit birds that ride the night,
stranger than dreams."
— Ending of Point Omega
* Update of Sept. 2, 2012— A different passage yields a more precise location.
"Translation in the direction
conceptual -> concrete and symbolic
is much easier than
translation in the reverse direction…."
— The late William P. Thurston
(See also "Atlas to the Text," Harvard Crimson , March 8, 2011).
Related cinematic imagery
Conceptual (thanks to Don DeLillo and The New York Times )—
Concrete and symbolic (thanks to Amy Adams and Emily Blunt, as well as
Frederick Seidel in the September 3, 2012, New Yorker )—
"Biddies still cleaned the student rooms."
we are just like a couple of tots…
— Sinatra
Born 1973 in Bergen. Lives and works in Oslo.
Education
2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen
University of Bergen—
|
It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’: What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d). The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary. It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.
— Cameron McEwen, "The Digital Wittgenstein," |
* See that phrase in this journal.
“… 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
From "The Onto-theological Origin of Play:
Heraclitus and Plato," by Yücel Dursun, in
Lingua ac Communitas Vol 17 (October 2007)—
"Heraclitus’s Aion and His Transformations
The saying is as follows:
αἰὼν παῖς ἐστι παίζων, πεττεύων·
παιδὸς ἡ βασιληίη
(Aion is a child playing draughts;
the kingship is the child’s)
(Krell 1972: 64).*
* KRELL, David Farrell.
“Towards an Ontology of Play:
Eugen Fink’s Notion of Spiel,”
Research in Phenomemology ,
2, 1972: 63-93.
This is the translation of the fragment in Greek by Krell.
There are many versions of the translation of the fragment….."
See also Child's Play and Froebel's Magic Box.
Update of May 5— For some background
from the date May 4 seven years ago, see
The Fano Plane Revisualized.
For some background on the word "aion,"
see that word in this journal.
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."
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.
NOW ENJOY BRILLIANT COLLEGE COURSES
IN YOUR HOME OR CAR!
The sun was burning down….
There was a trembling in the air as the unnamed colors
and landforms took on definition, a clarity of outline and extent….
This is where we sat through his hushed hour, a torchlit sky,
the closeness of hills barely visible at high white noon.
— DeLillo, Don, Point Omega
Midi là-haut, Midi sans mouvement
En soi se pense et convient à soi-même…
Tête complète et parfait diadème,
Je suis en toi le secret changement.
— Valéry, Paul, "Le Cimetière Marin"
… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
— Darío, Rubén, "Los Tres Reyes Magos"
"News and Traffic. Sports and Weather. These were his acid terms
for the life he’d left behind, more than two years of living with
the tight minds that made the war. It was all background noise,
he said, waving a hand. He liked to wave a hand in dismissal."
— DeLillo, Don (2010-02-02), Point Omega
Send in the Clowns. (Click to enlarge.)
See Notes for a Haiku.
Related material—
A novel published on Groundhog Day, 2010—
— as well as Conceptual Art, Josefine Lyche's
"Grids, You Say?" and The Speed of Thought.
Grid from a post linked to in yesterday's 24 Hour DeLillo—
For an example of this grid as slow art , consider the following—
"One can show that the binary tetrahedral group
is isomorphic to the special linear group SL(2,3)—
the group of all 2×2 matrices over the finite field F3
with unit determinant." —Wikipedia
As John Baez has noted, these two groups have the same structure as the geometric 24-cell.
For the connection of the grid to the groups and the 24-cell, see Visualizing GL(2,p).
Related material—
The 3×3 grid has been called a symbol of Apollo (Greek god of reason and of the sun).
"This is where we sat through his hushed hour,
a torchlit sky, the closeness of hills barely visible
at high white noon." — Don DeLillo, Point Omega
Review of DeLillo's novel Point Omega—
"One difference between art and entertainment has to do with the speed of perception. Art deliberately slows and complicates reading, hearing, and/or viewing so that you’re challenged to re-think and re-feel form and experience. Entertainment deliberately accelerates and simplifies them so that you don’t have to think about or feel very much of anything at all except, perhaps, the adrenalin rush before dazzling spectacle. Although, of course, there can be myriad gradations between the former and latter, in their starkest articulation we’re talking about the distance between, say, David Foster Wallace’s Infinite Jest and Dan Brown’s The Lost Symbol…."
— Lance Olsen, March 1, 2010, in The Quarterly Conversation
Robert Hughes on fast and slow art—
"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."
– Speech of June 1, 2004
Log24 on art speeds—
A Study in Art Education (June 15, 2007)
Twenty-four (March 13, 2011)
From Winning—
"In the desert you can remember your name,
'Cause there ain't no one for to give you no pain."
— America
COLLEGE OF THE DESERT
Minutes — Organization Meeting
11:00 a.m., Saturday, July 1, 1961—
15. Preparation of College Seal:
By unanimous consent preparation of a College
Seal to contain the following features was
authorized: A likeness of the Library building
set in a matrix of date palms, backed by
a mountain skyline and rising sun; before
the Library an open book, the Greek symbol
Alpha on one page and Omega on the other;
the Latin Lux et Veritas, College of the
Desert, and 1958 to be imprinted within or
around the periphery of the seal.
From the website http://geofhagopian.net/ of
Geoff Hagopian, Professor of Mathematics,
College of the Desert—
Note that this version of the seal contains
an Aleph and Omega instead of Alpha and Omega.
From another Hagopian website, another seal.
In memory of "Mr. Piano" Roger Williams, who died today—
Related material— A quote from The Oxford Murders ,
a novel by Guillermo Martinez—
"Anyone can follow the path once it’s been marked out.
But there is of course an earlier moment of illumination,
what you called the knight’s move. Only a few people,
sometimes only one person in many centuries,
manage to see the correct first step in the darkness.”
“A good try,” said Seldom.
From Rebecca Goldstein's Talks and Appearances page—
• "36 (Bad) Arguments for the Existence of God,"
Annual Meeting of the Freedom from Religion Foundation,
Marriot, Hartford, CT, Oct 7 [2011], 7 PM
From Wallace Stevens—
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— “An Ordinary Evening in New Haven” VI
For those who prefer greater depth on Yom Kippur, yesterday's cinematic link suggests…
"Yo sé de un laberinto griego que es una línea única, recta."
—Borges, "La Muerte y la Brújula " ("Death and the Compass")
See also Alpha and Omega (Sept. 18, 2011) and some context from 1931.
For Fischer's fellow database enthusiast Codd, see Cross-Referenced (April 24, 2003).
For Birtel's fellow pseudoscience enthusiast Frank Tipler, see the artist's comment linked to in Romancing the Omega (April 19, 2011)—
"Omega Point" is a term used by mathematical physicist Frank Tipler for what he maintains is the ultimate fate of the universe required by the laws of physics."
Related material—
Yesterday, 3:33 PM, in this journal— "Time for you to see the field"— and…
Faulkner's The Sound and the Fury , opening paragraph of part two, "June Second, 1910"—
"When the shadow of the sash appeared on the curtains it was between seven and eight oclock and then I was in time again, hearing the watch. It was Grandfather's and when Father gave it to me he said I give you the mausoleum of all hope and desire; it's rather excruciating-ly apt that you will use it to gain the reducto absurdum of all human experience which can fit your individual needs no better than it fitted his or his father's. I give it to you not that you may remember time, but that you might forget it now and then for a moment and not spend all your breath trying to conquer it. Because no battle is ever won he said. They are not even fought. The field only reveals to man his own folly, and despair, and victory is an illusion of philosophers and fools."
See also Willard Van Orman Quine in this journal on August 15, 2009—
"A tale told by an idiot"— and such a tale—
For Norway's Niels Henrik Abel (1802-1829)
on his birthday, August Fifth
(6 PM Aug. 4, Eastern Time, is 12 AM Aug. 5 in Oslo.)
Plato's Diamond
The above version by Peter Pesic is from Chapter I of his book Abel's Proof , titled "The Scandal of the Irrational." Plato's diamond also occurs in a much later mathematical story that might be called "The Scandal of the Noncontinuous." The story—
Paradigms"These passages suggest that the Form is a character or set of characters common to a number of things, i.e. the feature in reality which corresponds to a general word. But Plato also uses language which suggests not only that the forms exist separately (χωριστά ) from all the particulars, but also that each form is a peculiarly accurate or good particular of its own kind, i.e. the standard particular of the kind in question or the model (παράδειγμα ) [i.e. paradigm ] to which other particulars approximate…. … Both in the Republic and in the Sophist there is a strong suggestion that correct thinking is following out the connexions between Forms. The model is mathematical thinking, e.g. the proof given in the Meno that the square on the diagonal is double the original square in area." – William and Martha Kneale, The Development of Logic , Oxford University Press paperback, 1985 Plato's paradigm in the Meno—
Changed paradigm in the diamond theorem (2×2 case) —
Aspects of the paradigm change— Monochrome figures to Areas to Continuous transformations to Euclidean geometry to Euclidean quantities to The 24 patterns resulting from the paradigm change—
Each pattern has some ordinary or color-interchange symmetry. This is the 2×2 case of a more general result. The patterns become more interesting in the 4×4 case. For their relationship to finite geometry and finite fields, see the diamond theorem. |
Related material: Plato's Diamond by Oslo artist Josefine Lyche.
“Plato’s Ghost evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”
— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics (by Jeremy Gray, September 2008)
"Remember me to her."
— Closing words of the Algis Budrys novel Rogue Moon .
Background— Some posts in this journal related to Abel or to random thoughts from his birthday.
The title was suggested by this evening's 4-digit NY lottery number.
"… the rhetoric might be a bit over the top."
According to Amazon.com, 2198 (i.e., 2/1/98) was the publication
date of Geometry of Vector Sheaves , Volume I, by Anastasios Mallios.
Related material—
The question of S.S. Chern quoted here June 10: —
"What is Geometry?"— and the remark by Stevens that
accompanied the quotation—
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI
The work of Mallios in pure mathematics cited above seems
quite respectable (unlike his later remarks on physics).
His Vector Sheaves appears to be trying to explore new territory;
hence the relevance of Stevens's "Alpha." See also the phrase
"A-Invariance" in an undated preprint by Mallios*.
For the evening 3-digit number, 533, see a Stevens poem—
This meditation by Stevens is related to the female form of Mallios's Christian name.
As for the afternoon numbers, see "62" in The Beauty Test (May 23, 2007), Geometry and Death, and "9181" as the date 9/1/81.
* Later published in International Journal of Theoretical Physics , Vol. 47, No. 7, cover date 2008-07-01
Some background for yesterday’s posts:
Midrash for Gnostics and related notes,
as well as yesterday’s New York Lottery.
…. “We seek
The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is….”
— Wallace Stevens (1879-1955),
“An Ordinary Evening in New Haven” IX
“Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals.”
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI
“A hierophant is a person who brings religious congregants into the presence of that which is deemed holy . The word comes from Ancient Greece, where it was constructed from the combination of ta hiera , ‘the holy,’ and phainein , ‘to show.’ In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles.”
Weyl as Alpha, Chern as Omega—
Postscript for Ellen Page, star of “Smart People”
and of “X-Men: The Last Stand“— a different page 679.
Your assignment, should you choose to accept it—
Interpret today’s NY lottery numbers— Midday 815, Evening 888.
My own bias is toward 815 as 8/15 and 888 as a trinity,
but there may be less obvious and more interesting approaches.
A Meditation on the NY Lottery of May 29
Yesterday's NY Lottery— Midday 981, Evening 275.
As noted in yesterday morning's linked-to post,
The Shining of May 29…
"By groping toward the light we are made to realize
how deep the darkness is around us."
— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118
One interpretation of the mystic numbers revealed by the Lottery yesterday—
981 as the final page* of David Foster Wallace's famed novel Infinite Jest …
275 as a page in Wallace's non-fiction book about infinity Everything and More …
Gregory Chaitin points out that this is nonsense …
As noted elsewhere in this journal, I have a different concept of "math's absolute
Prince of Darkness"— and, indeed, of a "quest for Omega." (See posts of May 2010.)
Yesterday's numbers indicate a different struggle between darkness and light—
Light —
Darkness —
* From infinitesummer.org/archives/168 — "A note about editions:
As it turns out, all (physical) editions of Infinite Jest have 981 pages:
the one from 1996, the one from 2004, the paperback, the hardcover, etc.
A big thank you to the men and women in the publishing industry who
were kind and/or lazy enough to keep things consistent."
"a sort of… Dr. Strangelove" —Review of Point Omega
Context— From March 13— The Counter and Twenty-Four.
"Poetry never left me stranded, and as an atheist most of my life, I presumed its mojo was a highbrow, intellectual version of what religion did for those more gullible believers in my midst— dumb bunnies to a one, the faithful seemed to me, till I became one.
In the Texas oil town where I grew up, fierceness won fights, but I was thin-skinned— an unfashionably bookish kid whose brain wattage was sapped by a consuming inner life others didn’t seem to bear the burden of. I just seemed to have more frames per second than other kids."
— "Facing Altars: Poetry and Prayer," by Mary Karr
"The original movie had been slowed to a running time of twenty-four hours.
What he was watching seemed pure film, pure time.
The broad horror of the old gothic movie was subsumed in time."
— Point Omega , by Don DeLillo
From Galleri MGM in Oslo —
Josefine Lyche "Why do we remember the past, but not the future?" "If you want a vision of the future, imagine a boot stamping on a human face – forever." Galleri MGM is pleased to present the second solo exhibition by Josefine Lyche (b.1973). Lyche presents a body of work consisting of sculptures and a wall painting, as well as a series of new paperwork, all using geometrical abstractions and light as a medium. Her work dissolves boundaries between fiction and documentation, depicting how fantasies and dreams collide with and yet help determine the shape of reality. Theme and variations is a term most commonly used in the music genre as a musical form in which the fundamental musical idea, or theme, is repeated in altered form or accompanied in a different manner. The exhibition explores geometric shapes and solids and revisits work of artists like Robert Morris and Ellsworth Kelly, giving it a disco treatment of glitter, neon and gloss. The mathematical, science-fiction and new age references incorporated in the works comments on the ambivalent foretelling of utopian hope and dystopian vision of a near, yet unknown future. The transmission between past and future is shown in the sculpture "The Omega Point" a portal that leads in or out of time and space. … |
A connection to today's earlier post, Sunday School— The Oslo Version, from Friday, May 21, 2010.
Lyche's "Omega Point" portal, together with her last name, suggested three posts from the following Saturday morning— which later proved to be the date of Martin Gardner's death—
Art Space, Through the Lyche Gate and The Lyche Gate Asterisk.
For some further religious remarks, see November 9th, 2010— A Theory of Pure Design.
"These passages suggest that the Form is a character or set of characters
common to a number of things, i.e. the feature in reality which corresponds
to a general word. But Plato also uses language which suggests not only
that the forms exist separately (χωριστά ) from all the particulars, but also
that each form is a peculiarly accurate or good particular of its own kind,
i.e. the standard particular of the kind in question or the model (παράδειγμα )
[i.e. paradigm ] to which other particulars approximate….
… Both in the Republic and in the Sophist there is a strong suggestion
that correct thinking is following out the connexions between Forms.
The model is mathematical thinking, e.g. the proof given in the Meno
that the square on the diagonal is double the original square in area."
— William and Martha Kneale, The Development of Logic,
Oxford University Press paperback, 1985
Plato's paradigm in the Meno —
Changed paradigm in the diamond theorem (2×2 case) —
Aspects of the paradigm change* —
Monochrome figures to
colored figures
Areas to
transformations
Continuous transformations to
non-continuous transformations
Euclidean geometry to
finite geometry
Euclidean quantities to
finite fields
Some pedagogues may find handling all of these
conceptual changes simultaneously somewhat difficult.
* "Paradigm shift " is a phrase that, as John Baez has rightly pointed out,
should be used with caution. The related phrase here was suggested by Plato's
term παράδειγμα above, along with the commentators' specific reference to
the Meno figure that serves as a model. (For "model" in a different sense,
see Burkard Polster.) But note that Baez's own beloved category theory
has been called a paradigm shift.
From this evening's online New York Times—
Flock Around ‘The Clock’
By RANDY KENNEDY Benjamin Norman for The New York Times “The Clock,” a video work by Christian Marclay, uses thousands of film and television clips of timepieces to create, minute by minute, a 24-hour montage that unfolds in real time. “The Clock,” a 24-hour video work by Christian Marclay, draws crowds at the Paula Cooper Gallery in Chelsea. Critic’s NotebookThe Musical Rhythms in Images Out of Time By BEN RATLIFFTime is a kind of music, music is a kind of time, and Christian Marclay seems to understand this implicitly. |
See also Don DeLillo's Point Omega , a novel published on Groundhog Day, 2010.
Commentary on Revelation 6:8—
And I looked, and behold a pale horse:
and his name that sat on him was Death,
and Hell followed with him.
| Vincent's Word Studies
Pale (χλωρὸς) Only in Revelation, except Mark 6:39. Properly, greenish-yellow, like young grass or unripe wheat. Homer applies it to honey, and Sophocles to the sand. Generally, pale, pallid. Used of a mist, of sea-water, of a pale or bilious complexion. Thucydides uses it of the appearance of persons stricken with the plague (ii., 49). In Homer it is used of the paleness of the face from fear, and so as directly descriptive of fear ("Iliad," x., 376; xv., 4). Of olive wood ("Odyssey," ix., 320, 379) of which the bark is gray. Gladstone says that in Homer it indicates rather the absence than the presence of definite color. In the New Testament, always rendered green, except here. See Mark 6:39; Revelation 8:7; Revelation 9:4. Hell Properly, Hades. The realm of the dead personified. See on Matthew 16:18. |
Related material:
Death toll climbs to 394 in Indonesian tsunami
See also, in this journal, Pale Rider and Hereafter.
In the Details
This afternoon's post, Point Omega continued, concerned the New York Lottery numbers for yesterday evening and midday today.
A footnote to that post—
Today's evening New York Lottery number was 664.
In the spirit of the theological content of this afternoon's post—
Today's evening NY number 664 may or may not refer to the year of the Synod of Whitby.
That Synod was about reconciling the customs of Rome with the customs of Iona.
A somewhat relevant link from the Language Game post referred to in this afternoon's post was on the word "selving." This link, now broken, referred to a paper hosted by, as it happens, Iona College. The following is a link to a cached copy of that paper—
"The Story of the Self: The Self of the Story," by James E. Giles (Religion and Intellectual Life, Fall 1986— Volume 4, Number 1, pages 105-112)
"What exactly was Point Omega?"
This is Robert Wright in Nonzero: The Logic of Human Destiny.
Wright is discussing not the novel Point Omega by Don DeLillo,
but rather a (related) concept of the Jesuit philosopher Pierre Teilhard de Chardin.
My own idiosyncratic version of a personal "point omega"—
The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."
For some other sorts of points, see the drawings
on the wall and Geometry Simplified—
The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.
For related darkness at noon, see Derrida on différance
as a version of Plato's khôra—
The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institution— Deconstruction in a Nutshell—
For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.
“Examples are the stained-glass
windows of knowledge.” — Nabokov
Related material:
Today's sermon mentioned the phrase "Omega number."
Other sorts of Omega numbers— 24 and 759— occur
in connection with the set named Ω by R. T. Curtis in 1976—
— R. T. Curtis, "A New Combinatorial Approach to M24,"
Math. Proc. Camb. Phil. Soc. (1976), 79, 25-42
"Throughout history mystics and philosophers have sought a compact key to universal wisdom…."
— Charles H. Bennett, "On Random and Hard-to-Describe Numbers," 1979.
Bennett was writing about Gregory Chaitin's concept of an "Omega number."
(See Thursday's "Omega at Eight" and Friday's "The Girl Who Fixed the Omega.")
Here is a different Omega number — Alt 234.
Related material:
"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…."
– Don DeLillo, Point Omega
Capitalized, the letter omega figures in the theology of two Jesuits, Teilhard de Chardin and Gerard Manley Hopkins. For the former, see a review of DeLillo. For the latter, see James Finn Cotter's Inscape and "Hopkins and Augustine."
The lower-case omega is found in the standard symbolic representation of the Galois field GF(4)—
A representation of GF(4) that goes beyond the standard representation—
Here the four diagonally-divided two-color squares represent the four elements of GF(4).
The graphic properties of these design elements are closely related to the algebraic properties of GF(4).
This is demonstrated by a decomposition theorem used in the proof of the diamond theorem.
To what extent these theorems are part of "a saga of created reality" may be debated.
I prefer the Platonist's "discovered, not created" side of the debate.
or, Darkness and Brightness at Noon
"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional."
— Don DeLillo, Point Omega
GF(4) = {0, 1, ω, ω2}
— Symbolic representation of a Galois field
"One two three four,
who are we for?"
— Cheerleaders' chant
The Plane of Time
From tomorrow's NY Times Book Review, Geoff Dyer's review of DeLillo's new novel Point Omega is now online—
"The book begins and ends with Douglas Gordon’s film project '24 Hour Psycho' (installed at the Museum of Modern Art in Manhattan in 2006), in which the 109-minute Hitchcock original is slowed so that it takes a full day and night to twitch by. DeLillo conveys with haunting lucidity the uncanny beauty of 'the actor’s eyes in slow transit across his bony sockets,' 'Janet Leigh in the detailed process of not knowing what is about to happen to her.' Of course, DeLillo being DeLillo, it’s the deeper implications of the piece— what it reveals about the nature of film, perception and time— that detain him. As an unidentified spectator, DeLillo is mesmerized by the 'radically altered plane of time': 'The less there was to see, the harder he looked, the more he saw.'
This prologue and epilogue make up a phenomenological essay on one of the rare artworks of recent times to merit the prefix 'conceptual.'"
Related material:
Steering a Space-Plane
(February 2, 2003)
Holly Day
(February 3, 2010)
Attitude Adjustment
(February 3, 2010)
Cover illustration by Stephen Savage,
NY Times Book Review,
Feb. 2 (Candlemas), 2003
“We live the time that a match flickers.”
– Robert Louis Stevenson, Aes Triplex
From "Time's Breakdown," September 17, 2003—
|
“… even if we can break down time into component Walsh functions, what would it achieve?” – The Professor, in “Passing in Silence,” by Oliver Humpage “Being is not a steady state but an occulting one: we are all of us a succession of stillness blurring into motion on the wheel of action, and it is in those spaces of black between the pictures that we find the heart of mystery in which we are never allowed to rest. The flickering of a film interrupts the intolerable continuity of apparent world; subliminally it gives us those in-between spaces of black that we crave.” – Gösta Kraken, Perception Perceived: an Unfinished Memoir (p. 9 in Fremder, a novel by Russell Hoban) |
This flashback was suggested by
DeLillo is a major novelist, but the work of Hoban seems more relevant to the phrase "frame by frame."
Perichoresis, or Coinherence
Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI —
Gibbon, discussing the theology of the Trinity, defines perichoresis as
“… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….
59 … The
or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”
“Whoever fights monsters should see to it that in the process he does not become a monster. And when you look long into an abyss, the abyss also looks into you.”
Perichoresis does NOT mean “dancing around” ….
From a mailing list message:
If [a correspondent] will but open a lexicon, she will see that perichoresis (with a long o, omega) has nothing to do with “the Greek word for dance,” which is spelt with a short o (omicron). As a technical term in trinitarian theology, perichoresis means “interpenetration.”
Interpenetration in Arthur Machen
Interpenetration in T. S. Eliot:
“Between two worlds
become much like each other….”
On the Novels of Charles Williams
Coinherence in Charles Williams
The Per Speculum link is to a discussion of coinherence and the four last films of Kieslowski —
La Double Vie de Veronique (1991),
Trois Couleurs: Bleu (1993),
Trois Couleurs: Blanc (1993), and
Trois Couleurs: Rouge (1994).
See, too, previous log24 entries related to Kieslowski’s work and to coinherence:
Moulin Bleu (12/16/03),
Quarter to Three (12/20/03), and
White, Geometric, and Eternal (12/20/03).
|
Plato's |
|
From The Unknowable (1999), by Gregory J. Chaitin, who has written extensively about his constant, which he calls Omega:
"What is Omega? It's just the diamond-hard distilled and crystallized essence of mathematical truth! It's what you get when you compress tremendously the coal of redundant mathematical truth…"
Charles H. Bennett has written about Omega as a cabalistic number.
Here is another result with religious associations which, historically, has perhaps more claim to be called the "diamond-hard essence" of mathematical truth: The demonstration in Plato's Meno that a diamond inscribed in a square has half the area of the square (or that, vice-versa, the square has twice the area of the diamond).
From Ivars Peterson's discussion of Plato's diamond and the Pythagorean theorem:
"In his textbook The History of Mathematics, Roger Cooke of the University of Vermont describes how the Babylonians might have discovered the Pythagorean theorem more than 1,000 years before Pythagoras.
Basing his account on a passage in Plato's dialogue Meno, Cooke suggests that the discovery arose when someone, either for a practical purpose or perhaps just for fun, found it necessary to construct a square twice as large as a given square…."
From "Halving a Square," a presentation of Plato's diamond by Alexander Bogomolny, the moral of the story:
SOCRATES: And if the truth about reality is always in our soul, the soul must be immortal….
From "Renaissance Metaphysics and the History of Science," at The John Dee Society website:
Galileo on Plato's diamond:
"Cassirer, drawing attention to Galileo's frequent use of the Meno, particularly the incident of the slave's solving without instruction a problem in geometry by 'natural' reason stimulated by questioning, remarks, 'Galileo seems to accept all the consequences drawn by Plato from this fact…..'"
Roger Bacon on Plato's diamond:
"Fastening on the incident of the slave in the Meno, which he had found reproduced in Cicero, Bacon argued from it 'wherefore since this knowledge (of mathematics) is almost innate and as it were precedes discovery and learning or at least is less in need of them than other sciences, it will be first among sciences and will precede others disposing us towards them.'"
It is perhaps appropriate to close this entry, made on All Hallows' Eve, with a link to a page on Dr. John Dee himself.
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