Thacker reportedly died on Monday, June 12, 2017.
This journal on that date —
Thacker retired from Microsoft in February.
Thacker reportedly died on Monday, June 12, 2017.
This journal on that date —
Thacker retired from Microsoft in February.
The Cube
CodePen logo, pictured here on May 28, 2017 —
From YouTube, "The Cube," published on April 6, 2016 —
Meanwhile, also on April 6, 2016, at 2:01 AM ET …
* See The Pinterest Directive and Expanding the Spielraum.
"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."
—Staff writer Kamila Czachorowski, Harvard Crimson , March 29
1984 —
2010 —
Logo design for Stack Exchange Math by Jin Yang
Recent posts now tagged Crimson Abyss suggest
the above logo be viewed in light of a certain page 29 —
"… as if into a crimson abyss …." —
Update of 9 PM ET March 29, 2017:
Prospero's Children was first published by HarperCollins,
London, in 1999. A statement by the publisher provides
an instance of the famous "much-needed gap." —
"This is English fantasy at its finest. Prospero’s Children
steps into the gap that exists between The Lion, the Witch
and the Wardrobe and Clive Barker’s Weaveworld , and
is destined to become a modern classic."
Related imagery —
See also "Hexagram 64 in Context" (Log24, March 16, 2017).
Hexagram 29,
The Abyss (Water)
This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —
In that post, the designer quotes the Wilhelm/Baynes I Ching to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —
"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."
See also this journal on Walpurgisnacht (April 30), 2010 —
Hexagram 29:
|
Hexagram 30: |
A thought from another German-speaking philosopher —
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.
Another view of the previous post's art space —
More generally, see Solomon's Cube in Log24.
See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above
cube arrangement from "Affine groups on small binary spaces" (1984).
New York Times headline about a death
on Friday, March 3, 2017 —
René Préval, President of Haiti
in 2010 Quake, Dies at 74
See also …
This way to the egress.
"Bertram Kostant, professor emeritus of mathematics at MIT,
died at the Hebrew Senior Rehabilitation Center in Roslindale,
Massachusetts, on Thursday, Feb. 2, at the age of 88."
— MIT News, story dated Feb. 16, 2017
See also a search for Kostant in this journal.
Regarding the discussions of symmetries and "facets" found in
that search —
Kostant:
“A word about E(8). In my opinion, and shared by others,
E(8) is the most magnificent ‘object’ in all of mathematics.
It is like a diamond with thousands of facets. Each facet
offering a different view of its unbelievable intricate internal
structure.”
Cullinane:
In the Steiner system S(5, 8, 24) each octad might be
regarded as a "facet," with the order of the system's
automorphism group, the Mathieu group M24 , obtained
by multiplying the number of such facets, 759, by the
order of the octad stabilizer group, 322,560.
Analogously …
The title was suggested by the previous post and by
a phrase in Four Quartets.
Author Silvia Jonas tonight at Arts & Letters Daily —
The Inarticulate —
Detail of The Inarticulate —
The Raid —
Logo on the cover of
Joyce's Visible Art
From mathematician Izabella Laba today —
From Harry T. Antrim’s 1967 thesis on Eliot —
“That words can be made to reach across the void
left by the disappearance of God (and hence of all
Absolutes) and thereby reestablish some basis of
relation with forms existing outside the subjective
and ego-centered self has been one of the chief
concerns of the first half of the twentieth century.”
… And then there is the Snow White void —
A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —
The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).
See posts tagged Spiegel-Spiel.
"Mirror, Mirror …." —
A logo that may be interpreted as one-eighth of
a 2x2x2 array of cubes —
The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).
Log24 in review — Logos and Logic, Crystal and Dragon .
For a Monkey Grammarian (Viennese Version)
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —
The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).
Shown below are a few variations on the figure by VCQ,
the Vienna Center for Quantum Science and Technology —
(Click image to enlarge.)
In this post, "Omega" denotes a generic 4-element set.
For instance … Cullinane's
or Schmeikal's
.
The mathematics appropriate for describing
group actions on such a set is not Schmeikal's
Clifford algebra, but rather Galois's finite fields.
Related material from the same day —
See also …
Cube Bricks 1984 —
The above bricks appeared in some earlier Log24 posts.
Previous references in this journal to the "Church of Synchronology"
suggest a review of that phrase's source —
"The fine line between hokum and rational thinking
is precisely the point of The Lost Time Accidents ;
a brick of a book not just because of its length but
because of the density of both the prose and the
ideas it contains.
It is, in a nutshell, a sweeping historical novel that's
also a love story but is rooted in time-travel
science fiction and takes on as its subject
the meaning of time itself. This is no small endeavor."
— Janelle Brown in The Los Angeles Times
on February 4, 2016
See also …
For Galatea 2.2 on Eliza Doolittle Day
My Google searches are set to ignore my own private
search history. Still, I am not sure whether others would
see the same results as those below, which do seem to
reflect rather closely my own interests. Google-as-Galatea
perhaps based the search results partly on associations
from this weblog. An exception: the "Family Circus " novel
in the list below. I have not heard of this book before, but
it seems to be a tale analogous to Stephen King's It ,
from which the searched-for quotation below is drawn.
I prefer a different Family Circus.
* A phrase coined by the late John Archibald Wheeler.
"… I would drop the keystone into my arch …."
— Charles Sanders Peirce, "On Phenomenology"
" 'But which is the stone that supports the bridge?' Kublai Khan asks."
— Italo Calvino, Invisible Cities, as quoted by B. Elan Dresher.
(B. Elan Dresher. Nordlyd 41.2 (2014): 165-181,
special issue on Features edited by Martin Krämer,
Sandra Ronai and Peter Svenonius. University of Tromsø –
The Arctic University of Norway.
http://septentrio.uit.no/index.php/nordlyd)
Peter Svenonius and Martin Krämer, introduction to the
Nordlyd double issue on Features —
"Interacting with these questions about the 'geometric'
relations among features is the algebraic structure
of the features."
For another such interaction, see the previous post.
This post may be viewed as a commentary on a remark in Wikipedia —
"All of these ideas speak to the crux of Plato's Problem…."
See also The Diamond Theorem at Tromsø and Mere Geometry.
(A sequel to today's earlier posts Cube for Berlin and Midnight for Paris.)
See London in this journal.
That search yields …
“The more intellectual, less physical,
the spell of contemplation
the more complex must be the object,
the more close and elaborate
must be the comparison
the mind has to keep making
between the whole and the parts,
the parts and the whole.”
— The Journals and Papers of Gerard Manley Hopkins ,
ed. by Humphry House (London: Oxford University Press, 1959),
as quoted by Philip A. Ballinger in The Poem as Sacrament
(From the post The Inscape of 24, April 24, 2014. The 14 blocks in
the design S(3, 4, 8) of today's previous post are analogous to the 759
blocks in the design S(5, 8, 24).)
From the New York Times philosophy column "The Stone"
yesterday morning —
"Our knowledge of the universe and ourselves expands
like a ripple surrounding a pebble dropped in a pool.
As we move away from the center of the spreading circle,
its area, representing our secure knowledge, grows.
But so does its circumference, representing the border
where knowledge blurs into uncertainty and speculation,
and methodological confusion returns. Philosophy patrols
the border, trying to understand how we got there and to
conceptualize our next move. Its job is unending."
— Scott Soames, "Philosophy's True Home"
Related ripples —
From the previous Log24 post:
From a passage by Nietzsche quoted here on June 9, 2012:
For Soames's "unending" job of philosophy and Nietzsche's
"maieutic and educational influences on noble youths,"
consult the lyrics played over the end credits of "Monster" —
"Oh, the movie never ends
It goes on, and on, and on, and on"
On film director Stanley Kubrick:
From "Kubrick," by Michael Herr, Vanity Fair , August 1999— "He disliked the usual references to his having been a 'chess hustler' in his Greenwich Village days, as though this impugned the gravity and beauty of the exercise, the suggestion that his game wasn’t pour le sport or, more correctly, pour l’art . To win the game was important, to win the money was irresistible, but it was nothing compared with his game, with the searching, endless action of working on his game. But of course he was hustling, he was always hustling; as he grew older and moved beyond still photography, chess became movies, and movies became chess by other means. I doubt that he ever thought of chess as just a game, or even as a game at all. I do imagine that a lot of people sitting across the board from him got melted, fried, and fragmented when Stanley let that cool ray come streaming down out of his eyes— talk about penetrating looks and piercing intelligence; here they’d sat down to a nice game of chess, and all of a sudden he was doing the thinking for both of them." |
On physics writer Peter Woit:
From Part II of an interview with Peter Woit by Gerald Alper "For just a moment, he allows himself to become self reflective: 'I was always a smart kid. A very smart kid. I suppose if I ever took a standardized test I would do very well, especially, in the area of abstract reasoning.' Peter Woit says this as matter-of-factly as if he said, 'When I was a kid my father drove a Chevrolet.' He says it as Kareem Abdul-Jabbar, if asked to describe how he became the person he is, might have said 'I was always a tall kid. A very tall kid. In school, short kids bored me.' I felt I had to say, 'but there must be a few million people in the United States who would also score very high in abstract thinking in the standardized tests and none of them have your interests.' 'The people around here all do. And there are thousands of us all around the world.' 'But there are 7 billion people in the world.' Peter Woit had to concede the mathematical point, but I don't think he appreciated the psychological distinction I was alluding to. There is an astonishing divide between the culture of science and the culture of humanities that C.P. Snow famously alluded to. There is even a greater divide between the culture of pure mathematics and the culture of the earthbound evolutionarily programmed biological world into which we are born. There is a celebrated quip by Dick Cavett that encapsulates this. Reflecting on his famous interview of the then reigning world chess champion, Bobby Fischer, he observed: 'Throughout the interview I could feel the force of his IQ.' Paraphrasing this I could say that throughout the interview, which was at times exhilarating, at times daunting, I could feel the force of his two hundred QMIQ (quantum mechanics IQ). Norman Mailer once commented that the immediacy of television— the fact that most influential people in the world can be brought into your living room— creates the illusion that you have thereby been included in their inner power circle, and to that extent vicariously empowered. But you are no closer to the corridors of power then you were before. Analogously, you can sit just a few feet away from a world-class expert, close enough to reach out and touch them, but you are no closer to their accumulated wisdom— unless you are willing to go home and put in ten thousand hours of hard work trying to raise the level of your understanding." |
Illustration from a post of
Schicksalstag 2009
"The study of social memory allows scholars to
understand how different memories form within
a collective group, thus exploring the societal
and ideological elements of disparate groups
that form the over-arching memory of Melkisedeq."
— The Melkisedeq Memoirs , by Cale Staley,
2015 master's thesis at the University of Iowa
Elements of groups that I prefer —
"Right through hell
there is a path…."
— Malcolm Lowry,
Under the Volcano
Norwegian Sculpture Biennial 2015 catalog, p. 70 —
" 'Ambassadørene' er fysiske former som presenterer
ikk-fysiske fenomener. "
Translation by Google —
" 'Ambassadors' physical forms presents
nonphysical phenomena. "
Related definition —
Are the "line diagrams" of the diamond theorem and
the analogous "plane diagrams" of the eightfold cube
nonphysical entities? Discuss.
Sarah Larson in the online New Yorker on Sept. 3, 2015,
discussed Google’s new parent company, “Alphabet”—
“… Alphabet takes our most elementally wonderful
general-use word—the name of the components of
language itself*—and reassigns it, like the words
tweet, twitter, vine, facebook, friend, and so on,
into a branded realm.”
Emma Watson in “The Bling Ring”
This journal, also on September 3 —
Thursday, September 3, 2015
Filed under: Uncategorized — m759 @ 7:20 AM For the title, see posts from August 2007 Related theological remarks: Boolean spaces (old) vs. Galois spaces (new) in |
* Actually, Sarah, that would be “phonemes.”
For the title, see posts from August 2007 tagged Gyges.
Related theological remarks:
Boolean spaces (old) vs. Galois spaces (new) in
“The Quality Without a Name”
(a post from August 26, 2015) and the…
Related literature: A search for Borogoves in this journal will yield
remarks on the 1943 tale underlying the above film.
Adapted from posts tagged Cryptomorphisms
in this journal:
"Hear it not, Craven, for it is a knell
That summons thee to heaven, or to hell. “
Max von Sydow in Branded (2012)
Death of an academic on
the feast of St. Ignatius Loyola, 2015 —
"Cheuse was involved in a serious car accident
on July 14, 2015 on California State Route 17
while driving from Olympic Valley to Santa Cruz,
California. He was reported to be in a coma on
July 20, 2015 with injuries including fractured ribs,
cervical vertebrae, and an acute subdural hematoma.
He died on July 31, 2015 from his injuries at the age
of 75." — Wikipedia
Also on July 14 …
See as well Cheuse on Santa Cruz …
Home Away From Home in Santa Cruz
There are towns you are born into,
and there are towns you grow into.
Related artistic image —
Or: Swan Boat for Kristen
In the recent film "Danny Collins," Al Pacino plays aging
rock star Danny and Christopher Plummer plays his agèd
agent-manager Frank …
"… when Danny tells Frank about his burgeoning relationship
with hotel manager Mary (Annette Bening), he declares happily,
'And she's age-appropriate!' 'Not really,' frowns Frank.
'Baby steps,' Danny replies."
The previous post's link to The Lindbergh Manifesto
and Thursday's post on Basel-born artist Wolf Barth
suggest the following —
See as well a June 14 New York Times
piece on Art Basel.
The logo of the University of Basel …
… suggests a review of The Holy Field —
From MAA columnist Keith Devlin yesterday :
"All very depressing. I fear that this state of affairs
will continue all the time US education continues to be
treated as a political football, with our nation’s children
and their teachers treated as pawns while various
groups fight political battles…."
Review:
Illustrating the Spiegel-Spiel des Gevierts
"At the point of convergence
by Octavio Paz, translated by |
Friday December 5, 2008
|
"Visibilities are not forms of objects, nor even forms
that would show up under light, but rather forms of
luminosity which are created by the light itself and
allow a thing or object to exist only as a flash, sparkle
or shimmer."
— Deleuze, Foucault
Clap if you believe in Plotnitsky .
From his "Teaching" page —
Capitalism and Paranoia, Capitalism and Schizophrenia: Foucault, Deleuze, and Modernist Novel. The course offers a comprehensive examination of the works of Michel Foucault and Gilles Deleuze, and of the relationships between their ideas and the culture of modernity and, then, postmodernity, as the culture of capitalism. The course also considers, through the optics of Foucault's and Deleuze's work, how this culture is reflected in modernist and postmodernist novels of the twentieth century, and in the genre of the novel itself, which has been the dominant and indeed defining literary genre of this culture, from early to late capitalism. While Foucault's and Deleuze's work may be seen as a radical philosophical critique of modernity and capitalism by the philosophical means, the novel enacts an analogous and often equally radical literary critique. The works to be discussed include selections from Marx, Nietzsche, and Freud; Foucault's The Order of Things, Discipline and Punish, History of Sexuality, vol.1, and selected essays; and substantive selections from such works by Deleuze (and Deleuze and Guattari) as Anti-Oedipus, A Thousand Plateaus, and Foucault, as well as several shorter essays. Among the works of fiction to be considered are Joyce's A Portrait of the Artist as a Young Man; Kafka's The Trial; Woolf's Orlando; and Pynchon's The Crying of Lot 49. |
For Mark Steinberg, sports agent .
From Field Notes (9:29 AM ET Saturday, Nov. 28, 2009) —
From the heraldic crest of Steinberg's fraternity :
"Remember me to Herald Square."
From "How the Guggenheim Got Its Visual Identity,"
by Caitlin Dover, November 4, 2013 —
For the square and half-square in the above logo
as independent design elements, see
the Cullinane diamond theorem.
For the circle and half-circle in the logo,
see Art Wars (July 22, 2012).
For a rectangular space that embodies the name of
the logo's design firm 2×4, see Octad in this journal.
The Cumberbatch Conundrum
A quote from Benedict Cumberbatch in this journal
on Nov. 15 last year:
"… this film’s been up my ass
for the last five years.”
The quote, in connection with today's previous post,
suggests a check of this journal five years ago.
The check yields a paper at the new research site InvenZone.
Bogus religion from a bogus "research lab" —
Journal of Scientific Exploration,
Princeton Engineering Anomalies Research "… Consequently, the inferred models of reality are limited to those substances, processes, and sources of information that constitute conventional contemporary science. In this paper we ally ourselves with the sharply contrary position that there exists a much deeper and more extensive source of reality, which is largely insulated from direct human experience, representation, or even comprehension. It is a domain that has long been posited and contemplated by metaphysicians and theologians, Jungian and Jamesian psychologists, philosophers of science, and a few contemporary progressive theoretical physicists, all struggling to grasp and to represent its essence and its function. A variety of provincial labels have been applied, such as 'Tao,' 'Qi,' 'prana,' 'void,' 'Akashic record,' 'Unus Mundi,' 'unknowable substratum,' 'terra incognita,' 'archetypal field,' 'hidden order,' 'aboriginal sensible muchness,' 'implicate order,' 'zero-point vacuum,' 'ontic (or ontological) level,' 'undivided timeless primordial reality,' among many others, none of which fully captures the sublimely elusive nature of this domain. In earlier papers we called it the 'subliminal seed regime,' (2,3) but for our present purposes we shall henceforth refer to it simply as the 'Source.' "* References:
2. Jahn, R. G., & Dunne, B. J. (2001). A modular model of mind/matter manifestations (M5). Journal of Scientific Exploration , 15(3), 299–329. Note: * This assortment of contexts, labels, or models should not be regarded as mutually exclusive or hierarchical; nor are they isomorphic to one another. Rather, they represent different perspectives on the same basic search, and hence should be respected as collectively complementary. Where they reinforce one another, or display common features, this may indicate some degree of basic insight. Where they disagree on details, testable hypotheses may present themselves. |
This was quoted approvingly in a recent book by
Joseph Jaworski, Source (Berrett-Koehler Publishers,
1st ed. Jan. 11, 2012, pp. 2-3).
Jaworski, a lawyer-turned-guru,
in 1980 founded a cult for executives
called the American Leadership Forum.
A synchronicity cult I prefer —
the Roman Catholic Church:
Related material: This morning's NY Times obituaries—
Scully reportedly died on Dec. 16, 2014.
See that date in this journal —
For previous remarks on this topic, as it relates to
symmetry axes of the cube, see previous posts tagged Interplay.
The above posts discuss, among other things, the Galois
projective plane of order 3, with 13 points and 13 lines.
These Galois points and lines may be modeled in Euclidean geometry
by the 13 symmetry axes and the 13 rotation planes
of the Euclidean cube. They may also be modeled in Galois geometry
by subsets of the 3x3x3 Galois cube (vector 3-space over GF(3)).
The 3×3×3 Galois Cube
Exercise: Is there any such analogy between the 31 points of the
order-5 Galois projective plane and the 31 symmetry axes of the
Euclidean dodecahedron and icosahedron? Also, how may the
31 projective points be naturally pictured as lines within the
5x5x5 Galois cube (vector 3-space over GF(5))?
Update of Nov. 30, 2014 —
For background to the above exercise, see
pp. 16-17 of A Geometrical Picture Book ,
by Burkard Polster (Springer, 1998), esp.
the citation to a 1983 article by Lemay.
"To every man upon this earth,
Death cometh soon or late.
And how can man die better
Than facing fearful odds,
For the ashes of his fathers,
and the temples of his gods…?"
— Macaulay, quoted in the April 2013 film "Oblivion"
"Leave a space." — Tom Stoppard, "Jumpers"
Related material: The August 16, 2014, sudden death in Scotland
of an architect of the above Cardross seminary, and a Log24 post,
Plato's Logos, from the date of the above photo: June 26, 2010.
See also…
Here “eidolon” should instead be “eidos .”
An example of eidos — Plato's diamond (from the Meno ) —
Some illustrations:
Chess Knight
(in German, Springer)
See also…
More technically (click image for details):
The title is both a legal phrase and a phrase
used by Tom Wolfe in his writings on art.
See, too, the pattern of nine triangular half-squares
arranged in a 3×3 square used in the logo of the
Jean Stephen art galleries in Minneapolis…
… and in a print at the Tate in London (click to enlarge)—
See as well an obit of the print’s artist, Justin Knowles, who reportedly died
on Feb. 24, 2004.
Some instances of that date in this journal are related to Knowles’s aesthetics.
Despite the blocking of Doodles on my Google Search
screen, some messages get through.
Today, for instance —
"Your idea just might change the world.
Enter Google Science Fair 2014"
Clicking the link yields a page with the following image—
Clearly there is a problem here analogous to
the square-triangle coordinatization problem,
but with the 4×6 rectangle of the R. T. Curtis
Miracle Octad Generator playing the role of
the square.
I once studied this 24-triangle-hexagon
coordinatization problem, but was unable to
obtain any results of interest. Perhaps
someone else will have better luck.
* For a rather different use of this word,
see Hermann Weyl in the Stanford
Encyclopedia of Philosophy.
Moss on the Wall (Continued)
Tom Cruise at the Vatican in Mission: Impossible III (2006) —
Starring Tom Cruise as Ezekiel Moss, "a mysterious drifter
with the divine ability to channel and physically inhabit
the spirits of the dead."
— The quote is from "Philip Seymour Hoffman
Project 'Ezekiel Moss' Will Not Be Sold In Berlin*"
at Deadline.com.
See also Hereafter + Damon in this journal, as well as
the upload date for the above clip: Oct. 6, 2011.
* Here "Berlin" refers to the upcoming
European Film Market, Feb. 6-14
"When will they ever learn?"
— Rhetorical question by the late Pete Seeger
NY Times logo for its Learning Network feature —
Frances McDormand in Burn After Reading —
The Times pieces that inspired the above selection —
See also Mr. Arlington's date of death, January 16,
and Mr. Burns's date of death, January 26.
From the Bacardi website—
"Hamilton, Bermuda, December 13, 2012 —
Bacardi Limited caps off the yearlong celebration
of its 150th anniversary with the creation of a
commemorative time capsule…."
See also this journal on that date.
For Amy Adams, who in a recent
Superman film posed the question…
"What's the S stand for?"
This logo appears on the new game
Beyond: Two Souls . (See this evening's
earlier post on the game.)
In a more appealing sort of computer
entertainment, the S might stand for Scarlett.
"Please wait as your operating system is initiated."
(From the October 5th post Dream Girls.)
(Continued from High White Noon,
Finishing Up at Noon, and A New York Jew.)
Above: Frank Langella in "Starting Out in the Evening"
Below: Frank Langella and Johnny Depp in "The Ninth Gate"
"Not by the hair on your chinny-chin-chin."
Above: Detail from a Wikipedia photo.
For the logo, see Lostpedia.
For some backstory, see Noether.
Those seeking an escape from the eightfold nightmare
represented by the Dharma logo above may consult
the remarks of Heisenberg (the real one, not the
Breaking Bad version) to the Bavarian Academy
of Fine Arts.
Those who prefer Plato's cave to his geometry are
free to continue their Morphean adventures.
(Continued from this morning)
The above stylized "N," based on
an 8-cycle in the 9-element Galois field
GF(9), may also be read as an Aleph.
Graphic designers may prefer a simpler,
bolder version:
This is the weekend for Comic-Con International in San Diego.
The convention includes an art show. (Click above image to enlarge.)
Related material from Norway…
Suggested nominations for a Kavli Prize:
1. Josefine Lyche's highly imaginative catalog page for
the current Norwegian art exhibition I de lange nætter,
which mentions her interest in sacred geometry
2. Sacred Geometry: Drawing a Metatron Cube
… and from San Diego—
The Kavli Institutes logo:
A Brainstorm for Jo Lyxe :
Swastika logo of the Kavli Institute for Brain and Mind
at the University of California, San Diego.
Soundtrack: Under the Iron Sky .
"What on earth is
— Said to be an annotation |
In the spirit of the late Thomas Guinzburg…
See also "Concrete Universal" in this journal.
Related material— From a Bloomsday reply
to a Diamond Theory reader's comment, an excerpt—
The reader's comment suggests the following passages from
the book by Stirling quoted above—
Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow in 1974.
Continued from the previous post (June 27),
about the death of the founder of the
Future of Humanity Institute (FHI) at Oxford…
From Oxford Today , June 26, 2013—
(See also a June 11 Independent story on the same topic.)
Update of 6:42 PM ET June 29:
Any similarity between the FHI logo and Plato's diamond
is of course purely coincidental—
The body of James Martin, 79, founder of the Oxford Martin School,
was reportedly found floating in the sea near his private island
off Bermuda on Monday, June 24, 2013.
In his memory— A Log24 post from last December.
Yesterday's post The Belicic Problem suggests
a review of a Log24 post from October 29, 2007:
The extremely loose plot of Anthony Hopkins's
pet project "Slipstream" was in part inspired by
the events of 1956 in Santa Mira.
In keeping with Hopkins's strange plot logic, and
with the strange visual logic of the New York Times
editorial logo in yesterday's Santa Mira post,
here is a "diamond pivot bright"—
Click image for an explanation.
Andrew Rosenthal on a government official
in "Taking Note," the New York Times editorial
page editor's blog, at 3:12 PM today:
"… we are going to have to parse his meanings
of complex words like 'yes' and 'no.'"
Parse this, Rosenthal:
For some help, do a Google image search on "semaphore."
"There is such a thing as a tesseract." —A novel from Crosswicks
Related material from a 1905 graduate of Princeton,
"The 3-Space PG(3,2) and Its Group," is now available
at Internet Archive (1 download thus far).
The 3-space paper is relevant because of the
connection of the group it describes to the
"super, overarching" group of the tesseract.
Google search result at 1 PM ET April 24, 2013:
New York Stage and Film 2013 Musicals – EPA – Playbill
www.playbill.com/jobs/find/job_detail/51922.html
14 hours ago – BRIGHT STAR
Casting: Howie Cherpakov
Music by Edie Brickell and Steve Martin
Lyrics by Edie Brickell Book by Steve Martin…
The musical is set in North Carolina.
From Howie Cherpakov:
From North Carolina:
Archibald Henderson monument, Chestnut Hill Cemetery, Salisbury, NC
Henderson died in 1963 on the Feast of St. Nicholas.
Related material: Santa vs. the Obelisk.
Meanwhile…
Daily Princetonian @princetonian
Related material:
A sermon by the man named today the new President of Princeton.
The sermon is from October 7, 2012. See also Log24 on that date.
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.
"First published between 1922 and 1925,
the six-volume Principles of Geometry was
a synthesis of Baker's lecture series on geometry…."
From a different university press, a new logo
can be seen either as six volumes or as
the letter H —
"What is the H for?"
"Preparation."
The Square Fish logo was designed by Filomena Tuosto.
… In gratitude for his book Real Presences—
A related shell game:
Ad for a talk at Harvard by Nick Bostrom in April 2010—
Click ad for background on the April 10 , 2010, symposium.
See also Bostrom on the The Simulation Argument
and the Log24 April 12, 2010, Shell Game post above.
Note the black diamond logo of Bostrom's Oxford institute.
Jennifer Scott at IT Pro , Feb. 16, 2012, on Autonomy—
Mike Lynch, founder of Autonomy and vice president
of information management at HP, took to the stage
at his new parent company’s global partner conference
to impart his philosophy to the 3,000 partners gathered.
‘It is no longer about the data but about the meaning
of that data,’ he said. ‘There is a fundamental revolution
going on in information and the industry is now about
the “I” not the “T” in IT.'”
Click on the logo below for the source.
See also today’s previous post and…
“After A Wrinkle in Time was finally published, |
The December 2012 Notices of the American
Mathematical Society has an ad on page 1564
(in a review of two books on vulgarized mathematics)
for three workshops next year on “Low-dimensional
Topology, Geometry, and Dynamics”—
(Only the top part of the ad is shown; for further details
see an ICERM page.)
(ICERM stands for Institute for Computational
and Experimental Research in Mathematics.)
The ICERM logo displays seven subcubes of
a 2x2x2 eight-cube array with one cube missing—
The logo, apparently a stylized image of the architecture
of the Providence building housing ICERM, is not unlike
a picture of Froebel’s Third Gift—
© 2005 The Institute for Figuring
Photo by Norman Brosterman from the Inventing Kindergarten
exhibit at The Institute for Figuring (co-founded by Margaret Wertheim)
The eighth cube, missing in the ICERM logo and detached in the
Froebel Cubes photo, may be regarded as representing the origin
(0,0,0) in a coordinatized version of the 2x2x2 array—
in other words the cube invariant under linear , as opposed to
more general affine , permutations of the cubes in the array.
These cubes are not without relevance to the workshops’ topics—
low-dimensional exotic geometric structures, group theory, and dynamics.
See The Eightfold Cube, A Simple Reflection Group of Order 168, and
The Quaternion Group Acting on an Eightfold Cube.
Those who insist on vulgarizing their mathematics may regard linear
and affine group actions on the eight cubes as the dance of
Snow White (representing (0,0,0)) and the Seven Dwarfs—
.
The title refers to today's previous post,
"In the Widening Gyre."
"In modal logic, specifically when representing
possible worlds, @ is sometimes used as
a logical symbol to denote the actual world
(the world we are 'at')." —Wikipedia
"What might have been and what has been
Point to one end, which is always present."
— Four Quartets
Click the gyre on the book cover above for further details.
Leading this morning's online New York Times
obituaries list is one for a leftist Episcopal priest.
That obituary contains a link to a 1996 Times story —
Old Friends, New Foes:
President and a Preacher;
One 60's Activist Runs Columbia;
One Fights It
A check for background on the Columbia president
in that story yields the following from a leftist journalist's
website in a 2012 post dated October 26 (date of the
1917 October Revolution in Russia)—
Click for further details of this leftist allegation, which is
clearly false (because based on a ludicrously bad
misreading of a Rice University puff piece), and would
be libelous if its target were alive.
See a Rice University obituary for the "Nazi spy"
in question, who died on May 25, 2010. (See also
this journal on that date.)
The same leftist webpage contains a link to another leftist's
attack on a respected charitable organization that may
or may not have, or have had, CIA connections—
The International Rescue Committee (IRC).
In the spirit of Leonard Cohen's "then we take Berlin" lyric,
here is a note on how the IRC logo
might be rendered in a way that is, though less visually appealing,
more logical— i.e., more purely an example of Bauhaus style—
See also the recent Black October post
on a Columbia enthusiast of the October Revolution—
"We live together, we act on, and react to, one another; but always and in all circumstances we are by ourselves. The martyrs go hand in hand into the arena; they are crucified alone. Embraced, the lovers desperately try to fuse their insulated ecstasies into a single self-transcendence; in vain. By its very nature every embodied spirit is doomed to suffer and enjoy in solitude. Sensations, feelings, insights, fancies – all these are private and, except through symbols and at second hand, incommunicable. We can pool information about experiences, but never the experiences themselves. From family to nation, every human group is a society of island universes. Most island universes are sufficiently like one another to permit of inferential understanding or even of mutual empathy or "feeling into." Thus, remembering our own bereavements and humiliations, we can condole with others in analogous circumstances, can put ourselves (always, of course, in a slightly Pickwickian sense) in their places. But in certain cases communication between universes is incomplete or even nonexistent. The mind is its own place, and the places inhabited by the insane and the exceptionally gifted are so different from the places where ordinary men and women live, that there is little or no common ground of memory to serve as a basis for understanding or fellow feeling. Words are uttered, but fail to enlighten. The things and events to which the symbols refer belong to mutually exclusive realms of experience."
"Greet guests with a touch of glass."
(Continued from July 19, 2008)
From the Diamond 16 Puzzle —
The resemblance between the "quadrants" part of
the above picture and the new Microsoft symbol—
— is of course purely coincidental, as is the fact
that the new symbol illustrates four colors.
The second Logos figure in the previous post
summarized affine group actions on partitions
that generate a group of about 1.3 trillion
permutations of a 4x4x4 cube (shown below)—
Click for further details.
(Continued from July 22)
Manhattan, July 22, 2012 — "Once upon a time, in a quiet corner
of the Middle East, there lived a shepherd named Gyges. Despite
the hardships in his life Gyges was relatively satisfied with his meager
existence. Then, one day, he found a ring buried in a nearby cave."
Read more…
Heidegger, "Hölderlin and the Essence of Poetry,"
translated by Douglas Scott, in Existence and Being ,
Regnery, 1949, pp. 291-316—
See also Hexagram 36.
This post was suggested by Paradigms Lost
(a post cited here a year ago today),
by David Weinberger's recent essay "Shift Happens,"
and by today's opening of "The Raven."
David Weinberger in The Chronicle of Higher Education , April 22—
"… Kuhn was trying to understand how Aristotle could be such a brilliant natural scientist except when it came to understanding motion. Aristotle's idea that stones fall and fire rises because they're trying to get to their natural places seems like a simpleton's animism.
Then it became clear to Kuhn all at once. Ever since Newton, we in the West have thought movement changes an object's position in neutral space but does not change the object itself. For Aristotle, a change in position was a change in a quality of the object, and qualitative change tended toward an asymmetric actualization of potential: an acorn becomes an oak, but an oak never becomes an acorn. Motion likewise expressed a tendency for things to actualize their essence by moving to their proper place. With that, 'another initially strange part of Aristotelian doctrine begins to fall into place,' Kuhn wrote in The Road Since Structure ."
Dr. John Raven (of Raven's Progressive Matrices)—
"… these tools cannot be immediately applied within our current workplaces, educational systems, and public management systems because the operation of these systems is determined, not by personal developmental or societal needs, but by a range of latent, rarely discussed, and hard to influence sociological forces.
But this is not a cry of despair: It points to another topic which has been widely neglected by psychologists: It tells us that human behaviour is not mainly determined by internal properties— such as talents, attitudes, and values— but by external social forces. Such a transformation in psychological thinking and theorising is as great as the transformation Newton introduced into physics by noting that the movement of inanimate objects is not determined by internal, 'animistic,' properties of the objects but by invisible external forces which act upon them— invisible forces that can nevertheless be mapped, measured, and harnessed to do useful work for humankind.
So this brings us to our fourth conceptualisation and measurement topic: How are these social forces to be conceptualised, mapped, measured, and harnessed in a manner analogous to the way in which Newton made it possible to harness the destructive forces of the wind and the waves to enable sailing boats to get to their destinations?"
Before Newton, boats never arrived?
(Not Olympus )
(Continued from Mythopoetic, a post of April 12)
This post was suggested by a 2010 film about fictional Olympians,
by today's New York Times obituaries, and by a bar brawl at the Olympian
New York Athletic Club in "the wee hours of April 13."
Rick Riordan in the image below advertises another large
"Demigod Gathering" on October 12, 2010.
The Riordan image is from a post at ComposersCave.com
made on October 3, 2010.
Applying Jung's principle of synchronicity to this demigod material,
we find the October 3, 2010, Log24 post Search for the Basic Picture
and the October 12, 2010, Log24 post King Solomon's Mind.
Note that the latter October date is that of the traditional
Columbus Day, and that the 2010 film of The Lightning Thief
was directed by Chris Columbus of 1492 Pictures.
The film's release was earlier in 2010, on February 12.
See George Steiner on Autistic Enchantment, as well as…
(Click images for further details.)
This year, Autism Awareness Day was April 2.
"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.
CBS Sunday Morning 's piece on
the number pi today suggested…
Hexagram 20, Contemplation/View,
from the website Rightreading.com
Dick Tufeld, Robot Voice in TV’s ‘Lost in Space,’ Dies at 85
Wed Jan 25, 2012 23:42 from NYT Obituaries By Bruce Weber
"Mr. Tufeld possessed one of Hollywood’s most often-heard
disembodied voices, especially from the 1950s through the 1970s."
"Design is how it works." —Steve Jobs
Website logo—
Screenshot from How Stuff Works—
(Click image for details.)
From "A Device Worthy of a Gothic Novel,"
Chapter XVI of The Club Dumas,
by Arturo Perez-Reverte (1993),
Vintage International, April 1998….
the basis of the 1999 Roman Polanski film
The Ninth Gate —
Aren't you going to give me a document to sign?"
"A document?"
"Yes. It used to be called a pact. Now it would be a contract
with lots of small print, wouldn't it? 'In the event of litigation,
the parties are to submit to the jurisdiction of the courts of…'
That's a funny thing. I wonder which court covers this."
Perhaps the best obituary for the late Morris Philipson
(see Nov. 10) is this text, by writer W.P. Norton
(not to be confused with the publishing firm W.W. Norton).
For the text in context, see a screenshot of the Norton
weblog (which was very slow to load this morning).
The Blogspot loading logo that did appear at Norton's
weblog suggests the following image—
LOGOS
The logo on the right is that of
The New York Times 's
philosophy weblog "The Stone."
Philipson, incidentally, reportedly died on the morning of November 3.
See the remarks of Tom Wolfe quoted here on that date.
Between the idea
And the reality
Between the motion
And the act
Falls the Shadow
— T. S. Eliot, "The Hollow Men"
A passage quoted here on this date in 2005—
Douglas Hofstadter on his magnum opus:
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions
by some central solid essence."
This refers to Hofstadter's cover image:
Also from this date in 2005:
"Design is how it works." — Steven Jobs
A comment on the life of Jobs —
Paola Antonelli
Photo Credit: Andrea Ciotti
Paola Antonelli, senior curator of architecture and design
at the Museum of Modern Art in New York—
“NeXT was a risk and a beautiful failure."
Related material—
and 2008 posts of
(Click logo for details.)
NeXT in action:
This morning's post Opening Act suggests the following scholium—
To Purgatory fire you'll come at last;
And Christ receive your soul.
If ever you gave meat or drink,
Every night and all,
The fire will never make you shrink;
And Christ receive your soul.
See also The Wall Street Journal 's Ice Water in Hell story.
Followup scholium — "Vague but exciting …" —
Google Translate version of a recent Norwegian art review—
Josefine Lyche show is working on the basis of crop circles occur in Pewsey, Wiltshire in England for exactly one year ago on 21 June. Three circulars forms of aluminum quote forms from the field in England. With this as a starting point invites Lyche viewer to explore the sacred shapes and patterns through painting, floor work and sculpture. In the monumental painting "Wisdom Luxury Romance" draws Lyche lines to both Matisse and Baudelaire in his poem
From the artist's website, JosefineLyche.com—
WISDOM LUXURY ROMANCE
From elsewhere—
Related material—
From Antichristmas 2002— Aluminum, Your Shiny Friend.
From Sept. 22, 2004— Tribute… in the context of
today's previous entry and of the conclusion of the story
that later became Childhood's End —
The AND Publishing weblog page referred to in
a Sunday post has been changed to reflect the
source— my finite-geometry website— of pages
copied and altered by London artist Steve Richards
that are a large part of his contribution to the
AND Publishing Piracy Project.
The new version is as follows—
Note, however, that the cover page is a figure titled
by Richards "metalibrarianship" that has nothing
whatever to do with the concepts in the pages he copied
from my site, finitegeometry.org/sc.
Other pages within Richards's contribution to the
Piracy Project are similarly completely unrelated to
the content of my own site, which deals with geometry.
The image on the cover page also appears, it turns out,
on a website called intertwining.org.
At that site, it occurs in the following resume item:
The links in the resume item do not work,
but some background is available at a page titled
"Circularity, Practicality and Philosophy of Librarianship, or
The Making of 'The Nitecki Trilogy'" by Joanne Twining.
Other images in Richards's contribution to the Piracy Project also occur
in Twining's webpage "Dimensional Advances for Information Architecture."
I never heard of Twining or Nitecki before I encountered Richards's
Piracy Project contribution, and I do not wish to be associated
again in any way with Twining, with Nitecki, or with Richards.
The source of the mysterious generic
3×3 favicon with one green cell —
— has been identified.
For minimalists, here is a purer 3×3 matrix favicon—
This may, if one likes, be viewed as the "nothing"
present at the Creation. See Jim Holt on physics.
See also Visualizing GL(2,p), Coxeter and the Aleph, and Ayn Sof.
Perfect Symmetry (Oct. 2008) and Perfect Symmetry single (Dec. 2008)—
Related science…
Heinz Pagels in Perfect Symmetry (paperback, 1985), p. xvii—
The penultimate chapter of this third part of the book—
as far as speculation is concerned— describes some
recent mathematical models for the very origin of the
universe—how the fabric of space, time and matter can
be created out of absolutely nothing. What could have more
perfect symmetry than absolute nothingness? For the first
time in history, scientists have constructed mathematical
models that account for the very creation of the universe
out of nothing.
On Grand Unified Theories (GUT's) of physics (ibid., 284)—
In spite of the fact that GUTs leave deep puzzles unsolved,
they have gone a long way toward unifying the various
quantum particles. For example, many people are disturbed
by the large numbers of gluons, quarks and leptons. Part of
the appeal of the GUT idea is that this proliferation of
quantum particles is really superficial and that all the gluons
as well at the quarks and leptons may be simply viewed as
components of a few fundamental unifying fields. Under the
GUT symmetry operation these field components transform
into one another. The reason quantum particles appear to
have different properties in nature is that the unifying
symmetry is broken. The various gluons, quarks and leptons
are analogous to the facets of a cut diamond, which appear
differently according to the way the diamond is held but in
fact are all manifestations of the same underlying object.
Related art— Puzzle and Particles…
The Diamond 16 Puzzle (compare with Keane art above)—
—and The Standard Model of particle theory—
The fact that both the puzzle and the particles appear
within a 4×4 array is of course completely coincidental.
See also a more literary approach— "The Still Point and the Wheel"—
"Anomalies must be expected along the conceptual frontier between the temporal and the eternal."
— The Death of Adam , by Marilynne Robinson, Houghton Mifflin, 1998, essay on Marguerite de Navarre
From a story about mathematician Emmy Noether and 1882, the year she was born—
"People were then slowly becoming 'modern'— fortunately they had finally discovered not just that there are no Easter bunnies and Santa Claus, but also that there probably never were women who were led to evil ways by their curiosity and ended up, depending on their level of education, as common witches, as 'wiccans,' or as those particularly mysterious 'benandanti.'"
"… in the Balkans people believe that the souls of the dead rise to heaven in the guise of butterflies."
— "The Fairytale of the Totally Symmetrical Butterfly," by Dietmar Dath, in Intoxicating Heights (Eichborn AG, Frankfurt 2003)
An insect perhaps more appropriate for the afternoon of Good Friday— the fly in the logo of Dath's publisher—
Related material— Holy Saturday of 2004 and Wittgenstein and the Fly Bottle.
(After clicking, scroll down to get past current post.)
Click on the logo for a story about
witches' response to Charlie Sheen's
"warlock" campaign.
Related material—
Dennis Overbye on the manipulation
of science news.
(Link thanks to Not Even Wrong .)
From "Mathematicians and Poets," by Cai Tianxin, in the April 2011 AMS Notices—
Gauss, “the prince of mathematics”, wrote to tell a
friend, after solving a problem (symbols of Gaussian
summation) that had been bothering him for
years, “Finally, two days ago, I succeeded—not on
account of my hard efforts, but by the grace of the
Lord. Like a sudden flash of lightning, the riddle
was solved. I am unable to say what the conducting
thread was that connected what I previously knew
with what made my success possible.”
Gauss appears also in the results of the search for the phrase "only connect"
in this morning's Ides of Art post.
See as well the Grateful Dead logo in that post, and the following ad
shown today at Secret Blogging Seminar's Oct. 11, 2008, post
"The Sign of the Gauss Sum"—
In memory of John Miner —
See also |
AMS logo—Note resemblance Click on pictures for details. |
This morning's LA Times —
Related remarks —
"I’ve heard of affairs that are strictly plutonic,
But diamonds are a girl’s best friend!"
"In this talk, we will prove the diamond theorem and explore symmetries…."
– Log24 on the date of John Miner's death
Also known, roughly speaking, as confluence or the Church-Rosser property.
From “NYU Lambda Seminar, Week 2” —
[See also the parent page Seminar in Semantics / Philosophy of Language or:
What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn’t Know To Ask)]
A computational system is said to be confluent, or to have the Church-Rosser or diamond property, if, whenever there are multiple possible evaluation paths, those that terminate always terminate in the same value. In such a system, the choice of which sub-expressions to evaluate first will only matter if some of them but not others might lead down a non-terminating path.
The untyped lambda calculus is confluent. So long as a computation terminates, it always terminates in the same way. It doesn’t matter which order the sub-expressions are evaluated in.
A computational system is said to be strongly normalizing if every permitted evaluation path is guaranteed to terminate. The untyped lambda calculus is not strongly normalizing: ω ω
doesn’t terminate by any evaluation path; and (\x. y) (ω ω)
terminates only by some evaluation paths but not by others.
But the untyped lambda calculus enjoys some compensation for this weakness. It’s Turing complete! It can represent any computation we know how to describe. (That’s the cash value of being Turing complete, not the rigorous definition. There is a rigorous definition. However, we don’t know how to rigorously define “any computation we know how to describe.”) And in fact, it’s been proven that you can’t have both. If a computational system is Turing complete, it cannot be strongly normalizing.
There is no connection, apart from the common reference to an elementary geometric shape, between the use of “diamond” in the above Church-Rosser sense and the use of “diamond” in the mathematics of (Cullinane’s) Diamond Theory.
Any attempt to establish such a connection would, it seems, lead quickly into logically dubious territory.
Nevertheless, in the synchronistic spirit of Carl Jung and Arthur Koestler, here are some links to such a territory —
Link One — “Insane Symmetry” (Click image for further details)—
See also the quilt symmetry in this journal on Christmas Day.
Link Two — Divine Symmetry
(George Steiner on the Name in this journal on Dec. 31 last year (“All about Eve“)) —
“The links are direct between the tautology out of the Burning Bush, that ‘I am’ which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That ‘I am’ has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes ‘a dead letter.'”
– George Steiner, Grammars of Creation
(See also, from Hanukkah this year, A Geometric Merkabah and The Dreidel is Cast.)
Link Three – Spanning the Arc —
Part A — Architect Louis Sullivan on “span” (see also Kindergarten at Stonehenge)
Part B — “Span” in category theory at nLab —
Also from nLab — Completing Spans to Diamonds
“It is often interesting whether a given span in some partial ordered set can be completed into a diamond. The property of a collection of spans to consist of spans which are expandable into diamonds is very useful in the theory of rewriting systems and producing normal forms in algebra. There are classical results e.g. Newman’s diamond lemma, Širšov-Bergman’s diamond lemma (Širšov is also sometimes spelled as Shirshov), and Church-Rosser theorem (and the corresponding Church-Rosser confluence property).”
The concepts in this last paragraph may or may not have influenced the diamond theory of Rudolf Kaehr (apparently dating from 2007).
They certainly have nothing to do with the Diamond Theory of Steven H. Cullinane (dating from 1976).
For more on what the above San Francisco art curator is pleased to call “insane symmetry,” see this journal on Christmas Day.
For related philosophical lucubrations (more in the spirit of Kaehr than of Steiner), see the New York Times “The Stone” essay “Span: A Remembrance,” from December 22—
“To understand ourselves well,” [architect Louis] Sullivan writes, “we must arrive first at a simple basis: then build up from it.”
Around 300 BC, Euclid arrived at this: “A point is that which has no part. A line is breadthless length.”
See also the link from Christmas Day to remarks on Euclid and “architectonic” in Mere Geometry.
"An image comes to mind of a white, ideal space
that, more than any single picture, may be
the archetypal image of 20th-century art."
"May be" —
Image from this journal
at noon (EST) Tuesday
"The geometry of unit cubes is a meeting point
of several different subjects in mathematics."
— Chuanming Zong
"A meeting point" —
The above death reportedly occurred "early Wednesday in Beijing."
Another meeting point —
(Click on logo and on meeting image for more details.)
See also "no ordinary venue."
Detail from Google logo of Nov. 13, 2010
Related material: After Eden and Voyage of the Dawn Treader.
Continued from May 18, 2010.
Previous logo for the New York Times feature "The Stone"—
Today's new logo, appearing retroactively—
Comparison—
From the October 3 "The Stone," Hegel on Wall Street—
The “Phenomenology” is a philosophical portrait gallery that presents depictions, one after another, of different, fundamental ways in which individuals and societies have understood themselves. Each self-understanding has two parts: an account of how a particular kind of self understands itself and, then, an account of the world that the self considers its natural counterpart. Hegel narrates how each formation of self and world collapses because of a mismatch between self-conception and how that self conceives of the larger world. Hegel thinks we can see how history has been driven by misshapen forms of life in which the self-understanding of agents and the worldly practices they participate in fail to correspond. With great drama, he claims that his narrative is a “highway of despair.”
— J.M. Bernstein of the New School for Social Research
A two-part self-understanding that is not from Hegel—
1. An account of how a particular kind of self understands itself:
… world’s wildfire, leave but ash: | |
In a flash, at a trumpet crash, | |
I am all at once what Christ is, ' since he was what I am, and | |
This Jack, joke, poor potsherd, ' patch, matchwood, immortal diamond, | |
Is immortal diamond. |
2. An account of the world that the self considers its natural counterpart:
CLOUD-PUFFBALL, torn tufts, tossed pillows ' flaunt forth, then chevy on an air- | |
built thoroughfare: heaven-roysterers, in gay-gangs ' they throng; they glitter in marches. | |
Down roughcast, down dazzling whitewash, ' wherever an elm arches, | |
Shivelights and shadowtackle in long ' lashes lace, lance, and pair. | |
Delightfully the bright wind boisterous ' ropes, wrestles, beats earth bare | |
Of yestertempest’s creases; in pool and rut peel parches | |
Squandering ooze to squeezed ' dough, crust, dust; stanches, starches | |
Squadroned masks and manmarks ' treadmire toil there | |
Footfretted in it. Million-fuelèd, ' nature’s bonfire burns on. |
“Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word….”
– Notes Toward a Supreme Fiction
(Quoted here four years ago on October 2, 2006.)
"…to seek one's true nature is, as one Zen master has said,
'a way to lead you to your long lost home.'"
— Peter Matthiessen, Nine-Headed Dragon River
See also Matthiessen in Dead Viking.
"It's a Barnum and Bailey world…"
* See Jazz Standards.
** "Just as phony as it can be"
*** A search for Jung and "the square inch space"
leads to March 15, 2009, and preceding posts.
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