A sequel to last night's Chess Problem —
See as well a related CV .
A Meditation on Two Dates
The dates are October 14, 2016, the release date of
the new film "The Accountant" —
"… clearer, more economical and formal, more liturgical."
— David Remnick on lyrics of Leonard Cohen
vs. those of Bob Dylan, quoted here on Oct. 14
— and May 12, 2016, the publication date of
a YouTube trailer for "The Accountant."
Also quoted in the May 12 post —
See as well the Ape with Skull (Affe mit Schädel) statue in
the Oct. 17 post Memorial Encounter. The version of the statue
pictured there omits the inscription "ERITIS SICUT DEUS"
in a book at the statue's base. There are related remarks on
Mephistopheles and Faust at a different weblog.
The term "parametrization," as discussed in Wikipedia,
seems useful for describing labelings that are not, at least
at first glance, of a vector-space nature.
Examples: The labelings of a 4×4 array by a blank space
plus the 15 two-subsets of a six-set (Hudson, 1905) or by a
blank plus the 5 elements and the 10 two-subsets of a five-set
(derived in 2014 from a 1906 page by Whitehead), or by
a blank plus the 15 line diagrams of the diamond theorem.
Thus "parametrization" is apparently more general than
the word "coodinatization" used by Hermann Weyl —
“This is the relativity problem: to fix objectively
a class of equivalent coordinatizations and to
ascertain the group of transformations S
mediating between them.”
Note, however, that Weyl's definition of "coordinatization"
is not limited to vector-space coordinates. He describes it
as simply a mapping to a set of reproducible symbols .
(But Weyl does imply that these symbols should, like vector-space
coordinates, admit a group of transformations among themselves
that can be used to describe transformations of the point-space
"There is such a thing as a counting-pattern."
— Saying adapted from a young-adult novel
See also the previous post and …
Pentagram Meets Counting-Pattern
See also MIT News today —
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 —
"I love those Bavarians." — Don Henley, "The Garden of Allah"
Related religious imagery —
Click image for a better view of the original.
There are, of course, more sophisticated approaches
to the place of perspective in the history of art.
A brief tale by Dario Fo, winner of the 1997 Nobel Prize in Literature —
. . . .
"Cohen’s links to Dylan were obvious—Jewish, literary,
a penchant for Biblical imagery, Hammond’s tutelage—
but the work was divergent. Dylan, even on his earliest
records, was moving toward more surrealist, free-
associative language and the furious abandon of
rock and roll. Cohen’s lyrics were no less imaginative
or charged, no less ironic or self-investigating, but he
was clearer, more economical and formal, more liturgical."
See also …
"…Hashem has guaranteed our eternity…."
— Hineni founder Esther Jungreis, quoted in obit
by Matthew Williams in Tablet (Aug. 24, 2016).
A phrase from the date of Jungreis's reported death —
The above cycle may have influenced the design
of Carl Jung's symbol of the self —
Related art by
Steven H. Cullinane
See also Levi-Strauss Formula in this journal.
On the 10th day of the Jewish month of Tishri comes Yom Kippur, meaning the 'Day of Atonement'. It's the holiest day of the year.
To mark the 'Sabbath of Sabbaths', Jews fast for 25 hours and pray devoutly for most of the day, with five different sessions – Maariv, Shacharit, Musaf, Minchah and Neilah. [Link added.]
When is Yom Kippur?
* For the title, see yesterday's post "Noto." See also yesterday's
"Saturday Dialectics." For further background, see an October 2
Rosh Hashanah piece in Politico Magazine by Ben Wofford.
From "Saturday Dialectics" —
"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"
Neusner reportedly died on Saturday, Oct. 8, 2016.
For Log24 on that date, see posts now tagged
"Sultan" was a pseudonym of Peter Lindbergh, now a
well-known fashion photographer. Click image for the source.
Richard Wilhelm’s grave:
Note the eight I Ching
See a 1.5 MB Google Image Search for
Jumpers + Stoppard + "Leave a Space".
For the source of some of the images,
see a Log24 search for "Leave a Space."
See also Talman in this journal.
George Steiner's phrase "the language animal" as examined by
Charles Taylor —
Steiner attributes his "language animal" phrase, in the transliterated
form "zoon phonanta," to the ancient Greeks. This attribution
is apparently bogus. See Steiner on Language (March 30, 2012).*
* More generally — See Steiner + Language + Animal in this journal.
The "unity" of the title was suggested by this morning's update
at the end of yesterday's post Paz.
For the Plato of the title, see the Sept. 27, 2016, post
The above video promotes Google's new open-source "Noto" font —
The Paz quote below is from the last chapter
of his book, titled "The Dialectic of Solitude."
The phrase "dialectic of solitude" has been applied also to a 1967
book by the Colombian writer Gabriel García Márquez:
The conclusion of One Hundred Years of Solitude ,
"He was so absorbed that he did not feel the second surge of wind either as its cyclonic strength tore the doors and windows off their hinges, pulled off the roof of the east wing, and uprooted the foundations. Only then did he discover that Amaranta Úrsula was not his sister but his aunt, and that Sir Francis Drake had attacked Riohacha only so that they could seek each other through the most intricate labyrinths of blood until they would engender the mythological animal that was to bring the line to an end. Macondo was already a fearful whirlwind of dust and rubble being spun about by the wrath of the biblical hurricane when Aureliano skipped eleven pages so as not to lose time with facts he knew only too well, and he began to decipher the instant that he was living, deciphering it as he lived it, prophesying himself in the act of deciphering the last page of the parchments, as if he were looking into a speaking mirror. Then he skipped again to anticipate the predictions and ascertain the date and circumstances of his death. Before reaching the final line, however, he had already understood that he would never leave that room, for it was foreseen that the city of mirrors (or mirages) would be wiped out by the wind and exiled from the memory of men at the precise moment when Aureliano Babilonia would finish deciphering the parchments, and that everything written on them was unrepeatable since time immemorial and forever more, because races condemned to one hundred years of solitude did not have a second opportunity on earth."
Update of Saturday, October 8:
I do not recommend taking very seriously the work of Latin American leftists
(or American academics) who like to use the word "dialectic."
A related phrase does, however, have a certain mystic or poetic charm,
as pointed out by Wikipedia —
See also Bullshit Studies.
The title refers to the previous post.
From Middlemarch (1871-2), by George Eliot, Ch. III —
"Dorothea by this time had looked deep into the ungauged reservoir of Mr. Casaubon's mind, seeing reflected there in vague labyrinthine extension every quality she herself brought; had opened much of her own experience to him, and had understood from him the scope of his great work, also of attractively labyrinthine extent. For he had been as instructive as Milton's 'affable archangel;' and with something of the archangelic manner he told her how he had undertaken to show (what indeed had been attempted before, but not with that thoroughness, justice of comparison, and effectiveness of arrangement at which Mr. Casaubon aimed) that all the mythical systems or erratic mythical fragments in the world were corruptions of a tradition originally revealed. Having once mastered the true position and taken a firm footing there, the vast field of mythical constructions became intelligible, nay, luminous with the reflected light of correspondences. But to gather in this great harvest of truth was no light or speedy work."
See also the term correspondence in this journal.
According to Octavio Paz and Claude Lévi-Strauss
"Poetry…. conceives of the text as a series of transparent strata
within which the various parts—the different verbal and semantic
currents— produce momentary configurations as they intertwine
or break apart, as they reflect each other or efface each other.
Poetry contemplates itself, fuses with itself, and obliterates itself
in the crystallizations of language. Apparitions, metamorphoses,
volatilizations, precipitations of presences. These configurations
are crystallized time…."
— Octavio Paz in The Monkey Grammarian (written in 1970)
"Strata" also seem to underlie the Lévi-Strauss "canonic formula" of myth
in its original 1955 context, described as that of permutation groups —
I do not recommend trying to make sense of the above "formula."
Related material —
Wednesday, January 29, 2014
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)).
Goes to Feynman, Epstein, and Kaplan
"A self-replicating swarm of predatory molecules
is rapidly evolving outside the plant."
— Amazon.com synopsis of Michael Crichton's
2002 novel Prey
Washington Post online today —
" The physicist and Nobel laureate Richard Feynman
gave a seminal lecture on the subject in 1959,
envisioning a 'great future' in which 'we can arrange
the atoms the way we want; the very atoms,
all the way down.' " — Sarah Kaplan
"How do we write small?"
Related material quoted here on Sunday morning, Oct. 2, 2016 —
" Westworld is especially impressive because it builds two worlds
at once: the Western theme park and the futuristic workplace.
The Western half of Westworld might be the more purely
entertaining of the two, with its shootouts and heists and chases
through sublime desert vistas. Behind the scenes, the theme park’s
workers show how the robot sausage is made. And as a dystopian
office drama, the show does something truly original."
— Adam Epstein at QUARTZ, October 1, 2016
From a Google image search yesterday —
Sources (left to right, top to bottom) —
Math Guy (July 16, 2014)
The Galois Tesseract (Sept. 1, 2011)
The Full Force of Roman Law (April 21, 2014)
A Great Moonshine (Sept. 25, 2015)
A Point of Identity (August 8, 2016)
Pascal via Curtis (April 6, 2013)
Correspondences (August 6, 2011)
Symmetric Generation (Sept. 21, 2011)
The New York Times today on the late LA theater director
Gordon Davidson —
" When Mr. Davidson announced his retirement in 2002,
Mr. Eustis summed up his achievement succinctly.
Mr. Davidson, he told The Los Angeles Times ,
'has managed to make serious theater in the eye of
the celebrity hurricane.' " — William Grimes
From a Google image search today for "Mobius 8 4" Configuration —
The title refers to a Log24 post of 9:45 AM ET Sunday, Oct. 2.
From the "Westworld" post of Sunday, Oct. 2 —
"It was rather like watching a play."
The discovery of "square ice" is discussed in
Nature 519, 443–445 (26 March 2015).
Remarks related, if only by squareness —
this journal on that same date, 26 March 2015 —
The above figure is part of a Log24 discussion of the fact that
adjacency in the set of 16 vertices of a hypercube is isomorphic to
adjacency in the set of 16 subsquares of a square 4×4 array,
provided that opposite sides of the array are identified. When
this fact was first observed, I do not know. It is implicit, although
not stated explicitly, in the 1950 paper by H.S.M. Coxeter from
which the above figure is adapted (blue dots added).
Friday, July 11, 2014
The Washington Post online today —
See also Log24 posts from the above reported date of death —
posts now tagged Wittgenstein's Pentagram.
"I don't care about what anything was designed to do,
I care about what it can do."
On a new HBO series that opens at 9 PM ET tonight —
Watching Westworld , you can sense a grand mythology unfolding before your eyes. The show’s biggest strength is its world-building, an aspect of screenwriting that many television series have botched before. Often shows will rush viewers into plot, forgetting to instill a sense of place and of history, that you’re watching something that doesn’t just exist in a vacuum but rather is part of some larger ecosystem. Not since Lost can I remember a TV show so committed to immersing its audience into the physical space it inhabits. (Indeed, Westworld can also be viewed as a meta commentary on the art of screenwriting itself: brainstorming narratives, building characters, all for the amusement of other people.)
Westworld is especially impressive because it builds two worlds at once: the Western theme park and the futuristic workplace. The Western half of Westworld might be the more purely entertaining of the two, with its shootouts and heists and chases through sublime desert vistas. Behind the scenes, the theme park’s workers show how the robot sausage is made. And as a dystopian office drama, the show does something truly original.
— Adam Epstein at QUARTZ, October 1, 2016
"… committed to immersing its audience
into the physical space it inhabits…."
See also, in this journal, the Mimsy Cube —
"… he lifted a square, transparent crystal block, small enough to cup in his palm– much too small to contain the maze of apparatus within it. In a moment Scott had solved that problem. The crystal was a sort of magnifying glass, vastly enlarging the things inside the block. Strange things they were, too. Miniature people, for example– They moved. Like clockwork automatons, though much more smoothly. It was rather like watching a play."
The previous post presented Plato's Meno diagram as
an illustration of (superimposed) yin and yang.
For those who prefer a more fluid approach to yin and yang —
From a June 15, 2016, Caltech news release on gravitational waves —
The "chirp" tones of the two LIGO detections are available for download. Formats are suitable as ringtones for either iPhone or Android devices. (Instructions for installing custom ringtones)
September 2015 Detection
December 2015 Detection
Related commentary from July 2015 and earlier —
See posts tagged Haiku.
A different perspective —
The title is from a book quoted in the previous post.
A related illustration from 7:31 AM Tuesday, September 27 —
"The matrix at left below represents the feminine yin principle
and the diamond at right represents the masculine yang ."
An image from last night's post Brand Name —
"Squared into a matrix of four"
YouTube data suggested by the above passage —
Related literary remarks —
— A Heart for the Gods of Mexico , Conrad Aiken, 1939
The author of the review in the previous post supplies a midrash
on "desmic," a term derived from the Greek desme ( δεσμή , bundle,
sheaf, or, in the mathematical sense, pencil — French faisceau ),
which is apparently related to the term desmos , bond …
(The term "desmic," as noted earlier, is relevant to the structure of
Heidegger's Sternwürfel .)
The Horn midrash —
See "desmic" in this journal.
From a review by Dara Horn of …
Critics, Monsters, Fanatics, & Other Literary Essays
by Cynthia Ozick
Houghton Mifflin Harcourt, 224 pp., $25
"… the credo that has emerged throughout her career:
against idolatry, yes, but also in favor of the particular,
context, rootedness, the profound archaeological wells
from which no writer can be removed without removing
his or her greatest powers.
For Ozick herself, that archaeological well is not only Anglo-
American literature, but the far deeper well of Judaism."
— "Cynthia Ozick: Or, Immortality,"
Jewish Review of Books , Fall 2016
See also Michener's The Source in this journal.
Cassirer vs. Heidegger at Harvard —
A remembrance for Michaelmas —
A version of Heidegger's "Sternwürfel " —
From Log24 on the upload date for the above figure —
A review of …
Continental Divide : Heidegger, Cassirer, Davos
By Peter E. Gordon
(Harvard University Press, 426 pp., $39.95)
The reviewer: David Nirenberg in The New Republic .
The review, dated January 13, 2011, ran in the
February 3, 2011, issue of the magazine.
See also Jews Telling Stories.
From RIP, a post of Wednesday, March 16, 2016 —
See also earlier posts tagged Sermon Weekend.
From Balboa Press —
More than a pretty face designed to identify a product, a logo combines powerful elements super boosted with sophisticated branding techniques. Logos spark our purchasing choice and can affect our wellbeing.
Lovingly detailed, researched and honed to deliver a specific intention, a logo contains a unique dynamic that sidesteps our conscious mind. We might not know why we prefer one product over another but the logo, designed to connect the heart of the brand to our own hearts, plays a vital part in our decision to buy.
The power of symbols to sway us has been recognised throughout history. Found in caves and in Egyptian temples they are attributed with the strength to foretell and create the future, connect us with the divine and evoke emotions, from horror to ecstasy, at a glance. The new symbols we imbue with these awesome powers are our favourite brand logos.
• Discover the unconscious effect of these modern symbols that thrust our most successful global corporations into the limelight and our lives.
• Learn to make informed choices about brands.
• Find out how a logo reflects the state of the brand and holds it to account.
Or: Philosophy for Jews
From a New Yorker weblog post dated Dec. 6, 2012 —
"Happy Birthday, Noam Chomsky" by Gary Marcus—
"… two titans facing off, with Chomsky, as ever,
defining the contest"
"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."
Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).
Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…
The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
The matrix at left below represents the feminine yin principle
and the diamond at right represents the masculine yang .
From a post of Sept. 22,
"Binary Opposition Illustrated" —
A symbol of the unity of yin and yang —
A much more sophisticated approach to the "deep structure" of the
Meno diagram —
From this morning's 3:33 AM ET post —
Adapted from a post of Dec. 8, 2012, "Defining the Contest" —
From a post of Sept. 22,
"Binary Opposition Illustrated" —
From Sunday's news —
Stanford Encyclopedia of Philosophy
on the origins of Pragmatism:
"Pragmatism had been born in the discussions at
a ‘metaphysical club’ in Harvard around 1870
(see Menand…*). Peirce and James participated
in these discussions along with some other philosophers
and philosophically inclined lawyers. As we have
already noted, Peirce developed these ideas in his
publications from the 1870s."
From "How to Make Our Ideas Clear,"
"The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought. It is most easily learned by those whose ideas are meagre and restricted; and far happier they than such as wallow helplessly in a rich mud of conceptions. A nation, it is true, may, in the course of generations, overcome the disadvantage of an excessive wealth of language and its natural concomitant, a vast, unfathomable deep of ideas. We may see it in history, slowly perfecting its literary forms, sloughing at length its metaphysics, and, by virtue of the untirable patience which is often a compensation, attaining great excellence in every branch of mental acquirement. The page of history is not yet unrolled which is to tell us whether such a people will or will not in the long-run prevail over one whose ideas (like the words of their language) are few, but which possesses a wonderful mastery over those which it has. For an individual, however, there can be no question that a few clear ideas are worth more than many confused ones. A young man would hardly be persuaded to sacrifice the greater part of his thoughts to save the rest; and the muddled head is the least apt to see the necessity of such a sacrifice. Him we can usually only commiserate, as a person with a congenital defect. Time will help him, but intellectual maturity with regard to clearness comes rather late, an unfortunate arrangement of Nature, inasmuch as clearness is of less use to a man settled in life, whose errors have in great measure had their effect, than it would be to one whose path lies before him. It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty. Many a man has cherished for years as his hobby some vague shadow of an idea, too meaningless to be positively false; he has, nevertheless, passionately loved it, has made it his companion by day and by night, and has given to it his strength and his life, leaving all other occupations for its sake, and in short has lived with it and for it, until it has become, as it were, flesh of his flesh and bone of his bone; and then he has waked up some bright morning to find it gone, clean vanished away like the beautiful Melusina of the fable, and the essence of his life gone with it. I have myself known such a man; and who can tell how many histories of circle-squarers, metaphysicians, astrologers, and what not, may not be told in the old German story?"
* Menand, L., 2001. The Metaphysical Club : A Story of
Ideas in America , New York: Farrar, Straus and Giroux
From Hermann Weyl's 1952 classic Symmetry —
"Galois' ideas, which for several decades remained
a book with seven seals but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
Some Galois geometry —
See the previous post for more narrative.
For the director of "Interstellar" and "Inception" —
At the core of the 4x4x4 cube is …
Last night, Thursday, Sept. 22, 2016, at Harvard's Sanders Theatre,
the annual Ig Nobel prizes were awarded.
This journal earlier that day —
Related material —
Click the above image for remarks on
"deep structure" and binary opposition.
See also the eightfold cube.
"The Genesis of an Icon:
The Taiji Diagram's Early History"
By François Louis
Harvard Journal of Asiatic Studies
Vol. 63, No. 1 (June 2003), pp. 145-196
See also "arrowy, still strings" in this journal.
The phrase "binary opposition" in the previous post suggests
a review of some binary-related concepts —
From a post on St. Finbarr's Day 2015 —
Buffy: So, Giles! Got anything that can make this day any worse?
Giles: This is what we know. Some sixty years ago, a very old, very powerful vampire came to this shore, not just to feed.
From "The Cerebral Savage," by Clifford Geertz —
As the Key to All Mythologies
For the theorem of the title, see "Diamond Theorem" in this journal.
"These were heavy impressions to struggle against,
and brought that melancholy embitterment which
is the consequence of all excessive claim: even his
religious faith wavered with his wavering trust in his
own authorship, and the consolations of the Christian
hope in immortality seemed to lean on the immortality
of the still unwritten Key to all Mythologies."
Related material from Sunday's print New York Times —
Sunday's Log24 sermon —
The "points" and "lines" of finite geometry are abstract
entities satisfying only whatever incidence requirements
yield non-contradictory and interesting results. In finite
geometry, neither the points nor the lines are required to
lie within any Euclidean (or, for that matter, non-Euclidean)
Models of finite geometries may, however, embed the
points and lines within non -finite geometries in order
to aid visualization.
For instance, the 15 points and 35 lines of PG(3,2) may
be represented by subsets of a 4×4 array of dots, or squares,
located in the Euclidean plane. These "lines" are usually finite
subsets of dots or squares and not* lines of the Euclidean plane.
Example — See "4×4" in this journal.
Some impose on configurations from finite geometry
the rather artificial requirement that both points and lines
must be representable as those of a Euclidean plane.
Example: A Cremona-Richmond pentagon —
A square version of these 15 "points" —
A 1905 square version of these 15 "points"
with digits instead of letters —
See Parametrizing the 4×4 Array
(Log24 post of Sept. 13, 2016).
Update of 8 AM ET Sunday, Sept. 25, 2016 —
For more illustrations, do a Google image search
on "the 2-subsets of a 6-set." (See one such search.)
* But in some models are subsets of the grid lines
that separate squares within an array.
"Symmetry, yes, but logic?"
— Photo caption in the New York Times review of the 2008 Albee play
at Princeton titled "Me, Myself & I"
Above: Albee rests on Wittgenstein.
The late Edward Albee, as quoted today in The Telegraph :
“I tell my students, if you want to know something
about the structure of a play, listen to some Bach
preludes and fugues. I discovered classical music
when I was eight, nine, 10 years old, and I think
I learnt something about the nature of dramatic
structure from the nature of the music I was
listening to. I probably think of myself half the
time as a composer.”
Related material —
See the story of a British man who reportedly had a doctorate in
physics and mathematics and became a witchcraft enthusiast.
He is said to have died at 85 on September 11, 2016.
As Wittgenstein noted, it is not always clear whether the pentagram
expresses a mathematical or an experiential proposition.
For some mathematical propositions related to the pentagram,
see (for instance) John Baez's slides for his 2008 Glasgow
lecture on the number 5.
For som experiential propositions, see Pentagram in this journal.
Dolgachev and Keum, 2002
For some related material, see posts tagged Priority.
The smallest perfect number,* six, meets
"the smallest perfect universe,"** PG(3,2).
* For the definition of "perfect number," see any introductory
number-theory text that deals with the history of the subject.
** The phrase "smallest perfect universe" as a name for PG(3,2),
the projective 3-space over the 2-element Galois field GF(2),
was coined by math writer Burkard Polster. Cullinane's square
model of PG(3,2) differs from the earlier tetrahedral model
discussed by Polster.
See the three dead Solomons in a Log24 post of May 8, 2016.
A sample of the work of Feferman —
See also a tribute to Feferman respectively .
For Mrs. Hyman, see the October Atlantic.
The 4×4 array may also be parametrized by the symbol
0 along with the fifteen 2-subsets of a 6-set, as in Hudson's
1905 classic Kummer's Quartic Surface —
Hudson in 1905:
These two ways of parametrizing the 4×4 array — as a finite space
and as an array of 2-element sets — were related to one another
by Cullinane in 1986 in describing, in connection with the Curtis
"Miracle Octad Generator," what turned out to be 15 of Hudson's
1905 "Göpel tetrads":
A recap by Cullinane in 2013:
Click images for further details.
The previous post quoted Tom Wolfe on Chomsky's use of
the word "array."
An example of particular interest is the 4×4 array
(whether of dots or of unit squares) —
Some context for the 4×4 array —
The following definition indicates that the 4×4 array, when
suitably coordinatized, underlies the Kummer lattice .
Further background on the Kummer lattice:
Alice Garbagnati and Alessandra Sarti,
"Kummer Surfaces and K3 surfaces
with $(Z/2Z)^4$ symplectic action."
To appear in Rocky Mountain J. Math. —
The above article is written from the viewpoint of traditional
algebraic geometry. For a less traditional view of the underlying
affine 4-space from finite geometry, see the website
Finite Geometry of the Square and Cube.
Some further context …
"To our knowledge, the relation of the Golay code
to the Kummer lattice … is a new observation."
— Anne Taormina and Katrin Wendland,
"The overarching finite symmetry group of
Kummer surfaces in the Mathieu group M24 "
As noted earlier, Taormina and Wendland seem not to be aware of
R. W. H. T. Hudson's use of the (uncoordinatized*) 4×4 array in his
1905 book Kummer's Quartic Surface. The array was coordinatized,
i.e. given a "vector space structure," by Cullinane eight years prior to
the cited remarks of Curtis.
(C. K. Williams and Crazy Eddie)
Todd Gitlin on C. K. Williams, dead on 9/20, 2015 —
'I was traversing the maze of my brain;
corridors, corners, strange, narrow caverns, dead ends.
Then all at once my being like this in my brain,
this sense of being my brain, became unbearable to me.
I began to wonder in dismay if the conclusion
I’d long ago come to that there can be nothing
that might reasonably be postulated as
the soul apart from body and mind
was entirely valid.' "
Times Square on Crazy Eddie, reportedly dead on Sept. 10, 2016 —
His prices …
— Cover of a novel, Graveland
Or: Elegy for Wiener Neustadt
That town outside Vienna was rather different in 1924,
the reported year of birth there of a woman whose obituary
appears in this evening's New York Times .
From the woman's reported date of death —
"After trying magic mushrooms in Cuernavaca, in 1960,
Leary conceived the Harvard Psilocybin Project, to study
the therapeutic potential of hallucinogens. His involvement
with LSD came a few years later."
Related viewing —
For the cocktail, see the following illustration, taken from
The New Yorker issue dated Sept. 12, 2016.
(The article accompanying the illustration is not recommended.)
* For more on the concept of "cocktail," search this journal for
Casablanca + Cocktail.
"A version of this article appears in print on September 11, 2016,
on page BR9 of the Sunday Book Review …."
"What genres do you prefer? And which do you avoid?"
"To be honest, having worked in genre for so long, I’m happiest
when I’m outside it altogether, or perhaps more accurately,
when I can conjure multiple genres all at once, in accordance
with my theory (now available, I believe, as a greeting card and
fridge magnet) that human life as we experience it is a
simultaneous multiplicity of genres. I put it much more elegantly
on the magnet."
( Sequel to the post of 12 AM Wednesday )
The following highlighted phrase was found, with a different spelling,
in The New Yorker issue dated Sept. 12, 2016.
The article in which the phrase was embedded is not recommended.
Neither is the book (which the foolhardy explorer may easily find)
from which the above snippet was taken.
* That of Fields of the Lord .
A 1984 master's thesis (PDF, 8+ MB) —
"Language, Linguistics, and Philosophy:
A Comparison of the Work of Roman Jakobson
and the Later Wittgenstein, with Some Attention
to the Philosophy of Charles Saunders Peirce,"
by Miles Spencer Kimball.
Two pages from that thesis —
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