(A sequel to the previous post, Narrative for Westworld)
"That corpse you planted last year . . . ." — T. S. Eliot
Circle and Square at the Court of King Minos —
Harmonic analysis based on the circle involves the
circular functions. Dyadic harmonic analysis involves …
For some related history, see (for instance) E. M. Stein
on square functions in a 1982 AMS Bulletin article.
The Key to All Mythologies in a Cartoon Graveyard
This is a sequel to yesterday's post Review, which
suggested a look at Lévi-Strauss's The Raw and The Cooked
in Derrida's “Structure, Sign, and Play," and then a look at the …
Financial Times of February 26, 2010 —
"The metaphor for metamorphosis no keys unlock."
Continued from last night
From the American Mathematical Society, a news item
dated Thursday, March 9, 2017 —
Remarks by Schwartz quoted here on March 7—
A Yale Law professor on Saturday, March 4, 2017 —
"Donald Trump is Shiva the Destroyer."
Related dialogue from the new film "Assassin's Creed"—
Marion Cotillard— You've thought of everything.
Jeremy Irons— Not quite. My speech. It could do
with one of your elegant openings.
Marion Cotillard— "Now I've become death,
the destroyer of worlds."
Jeremy Irons—Not sure that I could make that work.
"The transformed urban interior is the spatial organisation of
an achiever, one who has crossed the class divide and who uses
space to express his membership of, not aspirations towards,
an ascendant class in our society: the class of those people who
earn their living by transformation— as opposed to the mere
reproduction— of symbols, such as writers, designers, and
academics"
— The Social Logic of Space ,
by Bill Hillier and Julienne Hanson,
Cambridge University Press, 1984
For another perspective on the achievers, see The Deceivers .
Related material —
Exhibit A:
Exhibit B:
Exhibit C:
"We tell ourselves stories in order to live." — Joan Didion
The New York Times Magazine online today —
"As a former believer and now a nonbeliever, Carrère,
seeking answers, sets out, in The Kingdom , to tell
the story of the storytellers. He is trying to understand
what it takes to be able to tell a story, any story.
And what he finds, once again, is that you have to find
your role in it."
— Wyatt Mason in The New York Times Magazine ,
online March 2, 2017
Like Tom Hanks?
Click image for related posts.
Hollywood, from the Alto Nido Apartments
to Sunset Boulevard —
See also the Jan. 31 post "Sunset Passion."
"What Yokoyama does in Six Four evokes — improbably —
the fastidious ethical parsings of a novel by Henry James,
all qualms and calibrations, and while that might not sound
like a good idea, he makes it work. He writes, fortunately,
in plain, declarative prose (ably translated by Jonathan Lloyd-Davies),
and because Mikami is such an ordinary man the mental gymnastics
he puts himself through are moving and sometimes deeply funny.
A Jamesian police procedural — 'The Wings of the Perp,' maybe?
Not exactly. But this novel is a real, out-of-the-blue original.*
I’ve never read anything like it."
— Terrence Rafferty in the online New York Times
on Tuesday, Feb. 21, 2017
Illustration from this journal on that date —
See also the previous post, "Six Four."
Update of 10 PM ET Feb. 23, 2017 —
A pathetic asterisk for, and by, Rafferty —
* A passage from Rafferty's essay
in The New York Times on July 27, 2003:
"… the message is clear: screenwriters are pathetic.
You can hear, clearly, the voice of Joe Gillis,
describing himself from beyond his watery grave:
'Nobody important, really. Just a movie writer with
a couple of B pictures to his credit. The poor dope.' "
See as well this journal on July 27, 2003.
Key sentence meets key title …
The title, Six Four , of the book under review is more interesting than
either of the headlines assigned by the Times to the review itself.
For another mystery related to the numbers six and four, see
this journal on Feb. 21.
… Namely, Scholarship and Showmanship (previous post)
"The suffix '-schaft ' (cognate with the English '-ship ')
can be added to nouns…."
— http://www.dartmouth.edu/~deutsch/
Grammatik/Wortbildung/Suffixes.html
For instance —
|
"… I’d rely on the old sociological distinction between gemeinschaft and gesellschaft . All across the world, we have masses of voters who live in a world of gemeinschaft : where relationships are personal, organic and fused by particular affections. These people define their loyalty to community, faith and nation in personal, in-the-gut sort of ways. But we have a leadership class and an experience of globalization that is from the world of gesellschaft : where systems are impersonal, rule based, abstract, indirect and formal." — David Brooks, New York Times columnist, Jan. 20, 2017 |
Peter Woit today discusses a book by one Zeeya Merali:
Some earlier remarks by Merali:
Zeeya Merali in Nature on 28 August 2013 —
"… a small band of researchers who think that
the usual ideas are not yet strange enough.
If nothing else, they say, neither of the two great
pillars of modern physics — general relativity,
which describes gravity as a curvature of space
and time, and quantum mechanics, which governs
the atomic realm — gives any account for
the existence of space and time.
. . . .
'All our experiences tell us we shouldn't have two
dramatically different conceptions of reality —
there must be one huge overarching theory,' says
Abhay Ashtekar, a physicist at Pennsylvania State
University in University Park."
See as well Overarching and Doctor Strange in this journal.
See also, on Feb. 8 in this journal, Damning.
The previous post, "Colorful Tales," on the Nov. 28, 2016, death
of one Angus Fletcher, together with the remarks indexed above,
suggest a review from …
The archives of The New York Times —
"THE ANATOMY OF INFLUENCE
Literature as a Way of Life
By Harold Bloom
357 pp. Yale University Press. $32.50.
Sam Tanenhaus is the editor of the Book Review.
A version of this review appeared in print
on May 22, 2011, on Page BR1 of the
Sunday Book Review with the headline:
'An Uncommon Reader.'"
"By this time, Bloom had burrowed into a cave,
its lamplit forms and shapes merging into
an occult mythos scarcely intelligible
even to other scholars. 'Bloom had an idea,'
Christopher Ricks said; 'now the idea has him.'
Cynthia Ozick, meanwhile, called him an 'idol-maker.'
In contrast to Cleanth Brooks . . . ."
An illustration from "The Echo in Plato's Cave" linked to
in the previous post —
Judy Davis in the Marabar Caves
Cynthia Ozick on Bloom —
See also Dharwadker in the previous post and on the Higgs boson.
Smullyan reportedly died on Monday, February 6, 2017.
|
Sixteenth-century alchemist in a novel by Balzac —
"If we eliminate God from this world, sire, |
"In those days, the occult sciences were cultivated with ardor well calculated to surprise the incredulous minds of our own sovereignly analytical age; perhaps they may detect in this historical sketch the germ of the positive sciences, widely studied in the nineteenth century, but without the poetic grandeur which was ascribed to them by the audacious investigators of the sixteenth century; who, instead of devoting their energy to industry, magnified art and made thought fruitful. The patronage universally accorded to art by the sov- ereigns of that time was justified, too, by the mar- vellous creations of inventors who started in quest of the philosopher's stone and reached amazing re- sults." — Balzac, Catherine de' Medici
Honoré de Balzac, Sur Catherine de Médicis :
— Hé! bien, sire, en ôtant Dieu de ce monde, que reste-t-il?
L’homme! Examinons alors notre domaine?
Le monde matériel est composé d’éléments, ces éléments
ont eux-mêmes des principes. Ces principes se résolvent
en un seul qui est doué de mouvement. Le nombre TROIS est
la formule de la création: la Matière, le Mouvement, le Produit!
— La preuve? Halte-là, s’écria le roi.
Illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress
(New York, The Century Co., 1912)
Quotations by and for an artist who reportedly died
on Sunday, January 15, 2017 —
"What drives my vision is a need to locate
a 'genetically felt' devotional space
in which a simultaneous multiplicity
of disparate realities coexists."
— The late Ciel Bergman, in her webpage
"Artist's Statement"
"Once a registered nurse who worked in a hospital
psychiatric ward, Ms. Bergman was a struggling
single mom of two when she couldn’t resist the pull
of her art. In 1969, she entered a painting in the
Jack London Invitational, an art contest in Oakland,
and won first prize. This compelled her to enroll at
the San Francisco Art Institute, where she earned
her master of fine arts with honors in painting."
— Sam Whiting in the San Francisco Chronicle
See also Oakland in this journal and
"Only a peculiar can enter a time loop."
"The peculiar kind of 'identity' that is attributed to
apparently altogether heterogeneous figures
in virtue of their being transformable into one another
by means of certain operations defining a group,
is thus seen to exist also in the domain of perception."
— Ernst Cassirer, quoted here on
Midsummer Eve (St. John's Eve), 2010
For some backstory, see Lottery in this journal,
esp. a post of June 28, 2007:
Real Numbers: An Object Lesson.
One such number, 8775, is suggested by
a Heinlein short story in a Jan. 25 post.
A search today for that number —
That Jan. 25 post, "For Your Consideration," also mentions logic.
Logic appears as well within a post from the above "8775" date,
August 16, 2016 —
|
Update of 10 am on August 16, 2016 —
See also Atiyah on the theology of
|
Related: Remarks by Charles Altieri on Wittgenstein in
today's previous post.
For remarks by Wittgenstein related to geometry and logic, see
(for instance) "Logical space" in "A Wittgenstein Dictionary," by
Hans-Johann Glock (Wiley-Blackwell, 1996).
From the American Mathematical Society (AMS) today,
an obituary of Hans Witsenhausen —
The obituary mentioned by the AMS (from Legacy.com) says …
"Donations in his memory may be made to the
United States Holocaust Memorial Museum,
American Society for Yad Vashem or
the American Technion Society."
From an image in this journal on Nov. 19, 2016, the date of
Witsenhausen's death, that reviewed earlier posts —
See also posts from this date, January 27, in 2005.
The New York Times online on Thursday, Jan. 19, 2017 —
" 'Split' is being released by Universal under the Blumhouse label,
a brand associated with unpretentious, clever, neo-traditionalist
scare-pictures like 'Insidious,' 'Paranormal Activity' and 'The Purge.'
That seems like the right company for Mr. Shyamalan . . . ."
A check of the Blumhouse label leads to a NY Times article
dated July 15, 2012 —
David Brooks in The New York Times today
(on the Times Wire at 3:21 AM ET) —
|
It took a lot to get us here. It took a once-in-a-century societal challenge — the stresses and strains brought by the global information age — and it took a political system that was too detached and sclerotic to understand and deal with them. There are many ways to capture this massive failure, but I’d rely on the old sociological distinction between gemeinschaft and gesellschaft. All across the world, we have masses of voters who live in a world of gemeinschaft: where relationships are personal, organic and fused by particular affections. These people define their loyalty to community, faith and nation in personal, in-the-gut sort of ways. But we have a leadership class and an experience of globalization that is from the world of gesellschaft: where systems are impersonal, rule based, abstract, indirect and formal. |
This suggests …
Schaft!
The above Schaft dates suggest in turn a review of this journal's
remarks on April 8 through April 11, 2016, which include…
The Schaft robot's world is, like the new whitehouse.gov website,
admirably "impersonal, rule based, abstract, indirect and formal."
The New York Times , on the other hand, offers the sort of
aesthetic experience so aptly described in the above William
Hamilton New Yorker cartoon.
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
Quoted here on December 16, 2006 —
See also …
Reviews of Reynolds' 2015 film "Self/Less" and of
the earlier similar film "Seconds" —
4 July 2015 9:00 AM, PDT | The Wrap |
"Ben Kingsley plays a New York real estate mogul who
pays big bucks to have his consciousness microwaved
into Ryan Reynolds' body in 'Self/less,' but the real
reheating of leftovers has already occurred: this new
science-fiction thriller borrows the foundation of a much
better film — John Frankenheimer’s 1966 'Seconds' —
and strips it of any larger meaning."
The date of the "Seconds" review above, 16 Dec. 2006, was
the reason for the requotation in the first paragraph above.
By a disciple of the late John Berger —
For further ideological remarks from this source, see the now-defunct
web journal Everyday Analysis: An International Collective.
For further remarks from the date of the above post, October 9, 2013,
see this journal on that date.
"William Christopher, best known for playing Father Mulcahy
on the hit sitcom M*A*S*H , died Saturday [Dec. 31, 2016] of
lung cancer, his agent confirmed to The Hollywood Reporter.
He was 84.
Christopher died at his home in Pasadena, with his wife by
his bedside, at 5:10 a.m. on New Year's Eve, according to a
statement from his agent."
— 5:59 PM PST 12/31/2016 by Meena Jang
Image reshown in this journal on the midnight (Eastern time)
preceding Christopher's death —
Related material —
From a Log24 search for "Deathly Hallows" —
|
Mathematics
The Fano plane block design |
Magic
The Deathly Hallows symbol— |
Those who prefer Latin with their theology
may search this journal for "In Nomine Patris."
From a Dec. 21 obituary posted by the
University of Tennessee at Knoxville —
"Wade was ordained as a pastor and served
at Oakwood Baptist Church in Knoxville."
Other information —
In a Log24 post, "Seeing the Finite Structure,"
of August 16, 2008, Wade appeared as a co-author
of the Walsh series book mentioned above —
Walsh Series: An Introduction
to Dyadic Harmonic Analysis,
by F. Schipp et al.,
Taylor & Francis, 1990
From the 2008 post —
The patterns on the faces of the cube on the cover
of Walsh Series above illustrate both the
Walsh functions of order 3 and the same structure
in a different guise, subspaces of the affine 3-space
over the binary field. For a note on the relationship
of Walsh functions to finite geometry, see
Symmetry of Walsh Functions.
These are Rothko's Swamps .
See a Log24 search for related meditations.
For all three topics combined, see Coxeter —
" There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?’ "
— Coxeter, 1987, introduction to Trudeau’s
The Non-Euclidean Revolution
Update of 10 AM ET — Related material, with an elementary example:
Posts tagged "Defining Form." The example —
“… you don’t write off an aging loved one
just because he or she becomes cranky.”
— Peter Schjeldahl on Rothko in The New Yorker ,
issue dated December 19 & 26, 2016, page 27
He was cranky in his forties too —
See Rothko + Swamp in this journal.
Related attitude —
From Subway Art for Times Square Church , Nov. 7
"Don't do anything I would do.
And definitely don't do anything I wouldn't do.
There's a little gray area in there
and that's where you operate."
See as well "Spirit and Space" (Nov. 25, 2016) —
The beginning of an essay by Emily Witt that is to appear on Sunday,
Dec. 4, 2016, in the T Magazine of The New York Times —
| "Palo santo, which means 'holy stick' in Spanish, is a tree indigenous to the Caribbean and South America. When burned, it emits a fragrance of pine and citrus. Lighting a stick of palo santo, like burning a bundle of sage or sweetgrass, is believed to chase away misfortune. Amazonian shamans use it in ayahuasca ceremonies to cleanse a ceremonial space of bad spirits. Given its mystical connotations, it’s not a scent associated with the secular world, but lately I have noticed its distinctive smoke wafting over more earthly settings, from Brooklyn dive bars to blue-chip art openings." |
The ending of an essay by T. S. Eliot that appeared in his 1921 book
titled The Sacred Wood —
Those who prefer ayahuasca ceremonies may consult
a Sept. 10 post, Cocktail of the Damned.
|
Excerpts from James C. Nohrnberg, "The Master of the Myth of Literature: An Interpenetrative Ogdoad for Northrop Frye," Comparative Literature Vol. 53, No. 1 (Winter, 2001), pp. 58-82
From page 58 — * P. 22 of Rereading Frye: The Published and Unpublished Works , ed. David Boyd and Imre Salusinszky, Frye Studies [series] (Toronto: University of Toronto Press, 1998). [Abbreviated as RF .]
From page 62 —
From page 63 —
From page 69 —
From page 71 —
From page 77 — |
Song suggested by Kellyanne Conway's remarks
in a CNN story today —
"We always felt that Hillary Clinton promising to
put coal miners out of work, or steel workers,
that wasn't going to go well in a place like
Pennsylvania. Michigan, Wisconsin, the same thing,"
she said. "So it just all started to come together."
|
From the Thursday, Oct. 13, 2016, Daily Princetonian — The ever-elusive “space” is a word spoken into a great expanse of hopes and fears and delusions: “safe spaces,” “inclusive spaces,” “open spaces,” “green spaces,” “learning spaces.” In this space, words float around abstractly, almost effortlessly, seemingly without the weight of any gravity; appearing to be a distant glimmer of an idea, a once bright and assuring light, which— without much definition— easily fades into obscurity. Coming to Princeton, it’s tempting to feel as though the rhetoric surrounding the term “space” stretches the word out, magnifies it, and tacks it onto well-designed brochures and anonymous invitations. Yet the question remains— how do you comfortably situate yourself within the incredibly abstruse concept of “space,” especially when you happen to exist in a territory that has been occupied and claimed by an endless sea of others, and which has been upheld by an impregnable and deeply rooted history? In the process of interviewing various members of the University, one thing has become clear; the question of space is an issue that is pertinent to all members of the Princeton community. |
For greater depth on this topic, see the previous post.
For less depth, see a post of January 18, 2005.
A search for "Crosswicks Curse" in this journal leads (indirectly) to …
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 —
Nobel Prize in chemistry is awarded
for molecular machines
” 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
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 —
|
Audio 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 ."
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
and possible.)
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 —
Related material:
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 —
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."
— Middlemarch , by George Eliot, Ch. XXIX
Related material from Sunday's print New York Times —
Sunday's Log24 sermon —
See also the Lévi-Strauss "Key to all Mythologies" in this journal,
as well as the previous post.
The notation "O" in the previous post suggests
a review of the new "Grease" theory in light of
a phrase from a May 2014 Oslo art exhibition —
"a desperate sense of imagined community."
Illustration (click for a video) —
"I'll have what she's having."
See as well Olivia Newton-John in this journal as the Muse of Dance.
The above clickbait was "Recommended by Outbrain." The photo
shown does not appear on the site linked to. Background on the photo —
See also Brainstorm in this journal.
The images in the previous post do not lend themselves
to any straightforward narrative. Two portions of the
large image search are, however, suggestive —
Cross and Boolean lattice.
The improvised cross in the second pair of images
is perhaps being wielded to counteract the
Boole of the first pair of images. See the heading
of the webpage that is the source of the lattice
diagram toward which the cross is directed —
Update of 10 am on August 16, 2016 —
See also Atiyah on the theology of
(Boolean) algebra vs. (Galois) geometry:
(Continued from April 2013 and later)
This is what I called "the large Desargues configuration"
in posts of April 2013 and later.
Andrew O'Hehir on July 22 —
— and on July 27 —
"Unless th' Almighty Maker them ordain
His dark materials to create more Worlds …
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look'd a while,
Pondering his Voyage…."
— John Milton, Paradise Lost , Book II
For Benedict Cumberbatch as a "warie fiend,"
see posts now tagged Both Hands.
"Per the New York Times , embattled CEO Marissa Mayer
will not be joining the company, but is expected to receive
a $40 million severance package—as always, it pays to be
the boss. But Mayer said in a Tumblr post that she planned
to stay on—while Verizon exec Marni Walden seemed to
indicate Meyer's future may still be up in the air."
— Jake Swearingen
From the midnight beginning June 27, 2016 —
This review of the above post was suggested by the
Galois-related footnote in the previous post and by
an obituary in this morning's online New York Times .
See as well a July 6 obituary for the same person in
The Martha's Vineyard Times .
|
"Poincaré said that science is no more a collection of facts than a house is a collection of bricks. The facts have to be ordered or structured, they have to fit a theory, a construct (often mathematical) in the human mind. … Mathematics may be art, but to the general public it is a black art, more akin to magic and mystery. This presents a constant challenge to the mathematical community: to explain how art fits into our subject and what we mean by beauty. In attempting to bridge this divide I have always found that architecture is the best of the arts to compare with mathematics. The analogy between the two subjects is not hard to describe and enables abstract ideas to be exemplified by bricks and mortar, in the spirit of the Poincaré quotation I used earlier."
— Sir Michael Atiyah, "The Art of Mathematics" |
A post from this journal later in 2010 —
The above post's date — May 20, 2010 — was
the date of death for mathematician Walter Rudin.
The above post from that date has a link to the
Heinlein story "And He Built a Crooked House."
A not-so-crooked house —
A search for "Purple" in this journal suggests a review of Transition,
a Log24 post of November 21, 2011. A related image —
(A sequel to the previous post, Perfect Number)
Since antiquity, six has been known as
"the smallest perfect number." The word "perfect"
here means that a number is the sum of its
proper divisors — in the case of six: 1, 2, and 3.
The properties of a six-element set (a "6-set")
divided into three 2-sets and divided into two 3-sets
are those of what Burkard Polster, using the same
adjective in a different sense, has called
"the smallest perfect universe" — PG(3,2), the projective
3-dimensional space over the 2-element Galois field.
A Google search for the phrase "smallest perfect universe"
suggests a turnaround in meaning , if not in finance,
that might please Yahoo CEO Marissa Mayer on her birthday —
The semantic turnaround here in the meaning of "perfect"
is accompanied by a model turnaround in the picture of PG(3,2) as
Polster's tetrahedral model is replaced by Cullinane's square model.
Further background from the previous post —
See also Kirkman's Schoolgirl Problem.
"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—
For the birthday of Marissa Mayer, who turns 41 today —
VOGUE Magazine,
AUGUST 16, 2013 12:01 AM
by JACOB WEISBERG —
"As she works to reverse the fortunes of a failing Silicon Valley
giant, Yahoo’s Marissa Mayer has fueled a national debate
about the office life, motherhood, and what it takes to be the
CEO of the moment.
'I really like even numbers, and
I like heavily divisible numbers.
Twelve is my lucky number—
I just love how divisible it is.
I don’t like odd numbers, and
I really don’t like primes.
When I turned 37,
I put on a strong face, but
I was not looking forward to 37.
But 37 turned out to be a pretty amazing year.
Especially considering that
36 is divisible by twelve!'
A few things may strike you while listening to Marissa Mayer
deliver this riff . . . . "
Yes, they may.
A smaller number for Marissa's meditations:
Six has been known since antiquity as the first "perfect" number.
Why it was so called is of little interest to anyone but historians
of number theory (a discipline that is not, as Wikipedia notes,
to be confused with numerology .)
What part geometry , on the other hand, played in Marissa's education,
I do not know.
Here, for what it's worth, is a figure from a review of posts in this journal
on the key role played by the number six in geometry —
For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.
The above passage suggests a meditation on this morning's
New York Times * —
"When shall we three meet again?" — William Shakespeare
“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin
Continued from Saturday, May 7, 2016 .
From an obituary in yesterday evening's online New York Times —
"I was writing plays, one-acters, about musicians
who were speakers of the idiom I loved most:
black American male speech, full of curse words,"
he wrote in an autobiographical essay. . . .
The obituary is for a poet who reportedly died on Saturday, May 7.
This journal on that day ("By Diction Possessed") recalled the death
(on Valentine's Day 2015) of an English actor who was the voice of
the Ring in two of the "Lord of the Rings" films —
Backstory from Wikipedia — See Black Speech —
"The only example of 'pure' Black Speech is
the inscription upon the One Ring . . .
One Ring to rule them all,
One Ring to find them,
One Ring to bring them all
And in the darkness bind them. "
Earlier posts have dealt with Solomon Marcus and Solomon Golomb,
both of whom died this year — Marcus on Saint Patrick's Day, and
Golomb on Orthodox Easter Sunday. This suggests a review of
Solomon LeWitt, who died on Catholic Easter Sunday, 2007.
A quote from LeWitt indicates the depth of the word "conceptual"
in his approach to "conceptual art."
|
From Sol LeWitt: A Retrospective , edited by Gary Garrels, Yale University Press, 2000, p. 376:
THE SQUARE AND THE CUBE "The best that can be said for either the square or the cube is that they are relatively uninteresting in themselves. Being basic representations of two- and three-dimensional form, they lack the expressive force of other more interesting forms and shapes. They are standard and universally recognized, no initiation being required of the viewer; it is immediately evident that a square is a square and a cube a cube. Released from the necessity of being significant in themselves, they can be better used as grammatical devices from which the work may proceed." "Reprinted from Lucy R. Lippard et al ., “Homage to the Square,” Art in America 55, No. 4 (July-August 1967): 54. (LeWitt’s contribution was originally untitled.)" |
See also the Cullinane models of some small Galois spaces —
„Ich begriff plötzlich, daß in der Sprache oder doch
mindestens im Geist des Glasperlenspiels tatsächlich
alles allbedeutend sei, daß jedes Symbol und jede
Kombination von Symbolen nicht hierhin oder dorthin,
nicht zu einzelnen Beispielen, Experimenten und
Beweisen führe, sondern ins Zentrum, ins Geheimnis
und Innerste der Welt, in das Urwissen. Jeder Übergang
von Dur zu Moll in einer Sonate, jede Wandlung eines
Mythos oder eines Kultes, jede klassische, künstlerische
Formulierung sei, so erkannte ich im Blitz jenes
Augenblicks, bei echter meditativer Betrachtung,
nichts andres als ein unmittelbarer Weg ins Innere
des Weltgeheimnisses, wo im Hin und Wider zwischen
Ein- und Ausatmen, zwischen Himmel und Erde,
zwischen Yin und Yang sich ewig das Heilige vollzieht.“
— Hermann Hesse, Das Glasperlenspiel .
Berlin: Suhrkamp Taschenbuch Verlag, 2012, p. 172,
as quoted in a weblog.
"Only connect." — Howards End
Mr. Howard reportedly died on Valentine's Day, 2015.
Random thoughts suggested by the reference in the
previous post to Aegean Park Press and to stencils —
"Stencil’s entire existence is focused on the hunt for V.,
a classic novelistic quest-without-resolution (in fact, V.
might be fiction’s greatest example of a MacGuffin). V.
may be a person, or may be a place, though it could
also be neither: Pynchon calls it, at one point,
'a remarkably scattered concept' and, at another,
'the ultimate Plot Which Has No Name.' "
— Alexander Nazaryan in The New Yorker ,
article dated March 29, 2013
How about a date ?
From this journal on Good Friday, March 29, 2013 —
A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —
The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .
Some may view the above web page as illustrating the
Glasperlenspiel passage quoted here in Summa Mythologica —
“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”
A less poetic meditation on the above web page* —
"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."
Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955: "…three different readings
become possible: left to right, top to bottom, front
to back."
* For the underlying mathematics, see a June 21, 1983, research note.
Detail of illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress
(New York, The Century Co., 1912)
Yesterday's posts Legend and Purple Requiem suggest a review
of John Bunyan. A search for "Vanity Fair" + "Temple of Art" yields…
The above Vanity Fair article was linked to here previously.
(Continued, in memory of the late meteorologist William Gray,
from August 10, 2010, and from April 16, 2016.)
For some backstory, see Huàn, the Flood and Impact Award.
"… Mathematics may be art, but to the general public
it is a black art, more akin to magic and mystery."
— Sir Michael Atiyah, "The Art of Mathematics"
in the AMS Notices , January 2010, quoted in
Log24 on April 4, 2016.
Related material: Gray Space and …
In memory of a Toledo Presbyterian who reportedly
died at 96 on April 11, 2016 — Log24 on that day.
A post reproduced here on April 11 —
See also some lyrics from the following day:
"Try the grey stuff, it's delicious
Don't believe me? Ask the dishes"
— Disney's "Beauty and the Beast"
In memory of a producer — Black Trinity.
See also a phrase from an image* in today's earlier post
For Non -Charlatans:
"Let us make a small example. . . ."
* Page 149 of "Groups and Symmetries," by F. Oggier
& A. M. Bruckstein. "These notes were designed to fit
the syllabus of the course 'Groups and Symmetries',
taught at Nanyang Technological University in autumn
2012, and 2013."
Thanks to Chris Matthews, who last night recommended
the book quoted below —
“I dislike the charlatan class, even if it is they who pay me,”
he said as we drove to my house. “To whom do you refer?”
I asked. He tapped his cigarette out of the cracked window
and looked at me with a sardonic smile: “The sort who
subscribe to Vanity Fair .”
— Taunton, Larry Alex (2016-04-12).
The Faith of Christopher Hitchens: The Restless Soul
of the World's Most Notorious Atheist (p. 115).
Thomas Nelson. Kindle Edition.
See also Orson Welles in this journal.
Vanity Fair illustrated —
Detail of illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress
(New York, The Century Co., 1912)
See also …
Seymour Lazar, Flamboyant Entertainment Lawyer, Dies at 88
The New York Times this evening has an obituary for Seymour Lazar,
"Seymour the Head in Supermoney , George Goodman’s 1972 account
of the global financial game, written under the pen name Adam Smith."
From that obituary —
"It was in Cuernavaca that Mr. Goodman, quite skeptical of the Lazar lore
he had heard so much of, met the man behind the myth. 'Seymour was
real,' he wrote…."
As is the Hungarian algorithm.
Mr. Lazar reportedly died on March 30. This journal on that date —
"Then-Secretary of State Hillary Rodham Clinton
checked her Blackberry inside a C-17 military plane
upon her departure from Malta bound for Tripoli, Libya,
in October 2011. (Kevin Lamarque/AP)"
— Washington Post, 11:13 AM today
See as well …
“It was only in retrospect
that the silliness became profound."
Foreword by Sir Michael Atiyah —
"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . .
… Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.
In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."
— Sir Michael Atiyah, "The Art of Mathematics"
in the AMS Notices , January 2010
Judy Bass, Los Angeles Times , March 12, 1989 —
"Like Rubik's Cube, The Eight demands to be pondered."
As does a figure from 1984, Cullinane's Cube —
For natural group actions on the Cullinane cube,
see "The Eightfold Cube" and
"A Simple Reflection Group of Order 168."
See also the recent post Cube Bricks 1984 —
Related remark from the literature —
Note that only the static structure is described by Felsner, not the
168 group actions discussed by Cullinane. For remarks on such
group actions in the literature, see "Cube Space, 1984-2003."
(From Anatomy of a Cube, Sept. 18, 2011.)
Continued from the April 1 posts
Apple Gate and Wonders of the Invisible World
Background music: "Like a rose under the April snow…." — Streisand
The Emergence of Harlan Kane continues from yesterday —
The revisiting, below, of an image shown here in part
on Spy Wednesday, 2016, was suggested in part by
a New York Times obituary today for a Nobel-prize
winning Hungarian novelist.
Note the references on the map to
"Devil's Gate" and "Pathfinder."
See also the following from a review of The Pathseeker , a novel
by the Nobel laureate (Imre Kertész), who reportedly died today —
|
… The commissioner is in fact not in search of a path, but rather of traces of the past (more literally the Hungarian title means ‘trace seeker’). His first shock comes at his realization that the site of his sufferings has been converted into a museum, complete with tourists “diligently carrying off the significance of things, crumb by crumb, wearing away a bit of the unspoken importance” (59). He meets not only tourists, however. He also comes across paradoxically “unknown acquaintances who were just as much haunted by a compulsion to revisit,” including a veiled woman who slowly repeats to him the inventory of those she lost: “my father, my younger brother, my fiancé” (79). The commissioner informs her that he has come “to try to redress that injustice” (80). When she asks how, he suddenly finds the words he had sought, “as if he could see them written down: ‘So that I should bear witness to everything I have seen’” (80). The act of bearing witness, however, proves elusive. In the museum he is compelled to wonder, “What could this collection of junk, so cleverly, indeed all too cleverly disguised as dusty museum material, prove to him, or to anyone else for that matter,” and adds the chilling observation, “Its objects could be brought to life only by being utilized” (71). As he touches the rust-eaten barbed wire fence he thinks, “A person might almost feel in the mood to stop and dutifully muse on this image of decay – were he not aware, of course, that this was precisely the goal; that the play of ephemerality was merely a bait for things” (66). It is this play of ephemerality, the possibility that the past will be consigned to the past, against which the commissioner struggles, yet his struggle is frustrated precisely by the lack of resistance, the indifference of the objects he has come to confront. “What should he cling on to for proof?” he wonders. “What was he to fight with, if they were depriving him of every object of the struggle? Against what was he to try and resist, if nothing was resisting?” (68) He had come with the purpose of “advertis[ing] his superiority, celebrat[ing] the triumph of his existence in front of these mute and powerless things. His groundless disappointment was fed merely by the fact that this festive invitation had received no response. The objects were holding their peace” (109). In point of fact The Pathseeker makes no specific mention either of the Holocaust or of the concentration camps, yet the admittedly cryptic references to places leave no doubt that this is its subject. Above the gate at the camp the commissioner’s wife reads the phrase, “Jedem das Seine,” to each his due, and one recalls the sign above the entrance to the camp at Buchenwald. Further references to Goethe as well as the Brabag factory, where Kertész himself worked as a prisoner, confirm this. Why this subterfuge on the part of the author? Why a third-person narrative with an unnamed protagonist when so many biographical links tie the author to the story? One cannot help but wonder if Kertész sought specifically to avoid binding his story to particulars in order to maintain the ultimately metaphysical nature of the quest. Like many of Kertész’s works,The Pathseeker is not about the trauma of the Holocaust itself so much as the trauma of survival. The self may survive but the triumph of that survival is chimerical. Translator Tim Wilkinson made the bold decision, in translating the title of the work, not to resort to the obvious. Rather than simply translate Nyomkereső , an allusion to the Hungarian translation of James Fenimore Cooper’s The Pathfinder , back into English, he preserves an element of the unfamiliar in his title. This tendency marks many of the passages of the English translation, in which Wilkinson has opted to preserve the winding and often frustratingly serpentine nature of many of the sentences of the original instead of rewriting them in sleek, familiar English. . . . — Thomas Cooper |
"Sleek, familiar English" —
"Those were the good old days!" — Applegate in "Damn Yankees"
(See previous post.)
For the title, see a post of Dec. 20, 2015.
See also "Damn Yankees."
"When Mr. Amoroso made the announcement about Yahoo!’s
new CEO, he said, The Board of Directors unanimously agreed
that Marissa’s unparalleled track record in technology, design,
and product execution makes her the right leader for Yahoo!
at this time of enormous opportunity.” — John Mattone yesterday
See as well Something in the Way She Moves, which links to
Master Class. Another amoroso story: Oja Kodar and Picasso
in Orson Welles's last completed film.
The New York Times this evening on the late Rita Gam:
"After generally being typecast in supporting roles
in two dozen films for what Life described as
'her sultry face and insinuating voice,' she recalled
in 1992, 'I looked into the black pit at 40 and
wondered, what do I do for an encore?' "
See also Sidney Lumet in this journal as well as
"Some cartoon graveyards are better than others."
A search for "Wordsworth" in this journal yields
an image from "The Edge of Eternity," a post of
Sunday, Christmas Eve, 2006 …
“Just a lying rhyme for seven!”
— Playwright Tom Stoppard on Heaven
|
" 'Heaven lies about us in our infancy!' wrote William Wordsworth, one of Geoffrey Hartman’s beloved Romantics…. For Hartman, in 2010 proclaimed by his Yale colleague Paul Fry to be 'arguably the finest Wordsworth critic who has ever written,' those lines from 'Ode on Intimations of Immortality from Recollections of Early Childhood' must have been especially bittersweet. His own childhood had been cut short; born in Frankfurt in 1929…."
— "Remembering Geoffrey Hartman — |
From the 1984 New Orleans film Tightrope—
This post was suggested by the late Yale literary critic
Geoffrey Hartman, who reportedly died on March 14.
" 'Interpretation is like a football game,' Professor Hartman
wrote in 'The Voice of the Shuttle,' a 1969 essay."
— A 2016 obituary by Margalit Fox
In memory of the late architect Patrick Hodgkinson
Harvey Court at Gonville & Caius College, Cambridge
For the architect, see yesterday's post "Brick-Perfect."
See as well a meditation on the numbers 9 and 13
in the post "Space" on day 13 of May, 2015.
Patrick Hodgkinson, a British architect, reportedly died at 85 on
February 21, 2016. From his March 4 obituary in the Telegraph —
|
Before Brunswick, came Harvey Court for Gonville and Caius College, Cambridge. Colin St John Wilson, exLCC, his senior in the Martin studio, had done a scheme with four freestanding ranges in concrete. Hodgkinson radically transformed this at short notice into the final version presented to the College, a tight, connected square finished in local brick with a stepped section and impressive close-spaced brick columns on the exterior faces where the section overhung. Never afflicted by modesty, Hodgkinson called it “designed to a brick-perfect, three-dimensional grid clear of ugly moments: the builders enjoyed making it”. It was attributed to Martin, Wilson and Hodgkinson jointly, but Hodgkinson felt that his contribution was under-appreciated, and again with the Law Library at Oxford, normally credited to Martin and Wilson. The theory of compact medium-rise courtyard forms derived from the Harvey Court design became central to Martin’s research programme at Cambridge in the 1960s; Hodgkinson felt that he deserved more credit for this too. |
One possible answer —
|
BBC "Intruders" transcript
From https://groups.google.com/forum/
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539 |
* See Veritas (March 7, 2016).
New York lottery today —
This evening's NY lottery results, interpreted as a phone number, yield …
See also posts tagged The Poet's Pineapple …
"The momentary footings of a climb
Up the pineapple, a table Alp and yet
An Alp…."
— Wallace Stevens, "Someone Puts a Pineapple Together"
(Lines from p. 252 of Partisan Review Vol. XIV No. 3,
May-June 1947)
Related aesthetics —
"Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . .
… Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.
In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier."
— Sir Michael Atiyah, "The Art of Mathematics"
in the AMS Notices , January 2010
A rose on a Harvard University Press book cover (2014) —
A Log24 post's "lotus" (2004) —
A business mandorla (2016) —
"In the planes that tilt hard revelations on
The eye, a geometric glitter, tiltings …."
— Wallace Stevens, "Someone Puts a Pineapple Together" (1947)
From a New York Times obituary today —
"The Rev. Fernando Cardenal, a son of privilege
who embraced Latin America’s poor as a revolutionary
priest and brazenly defied Pope John Paul II’s order to
quit Nicaragua’s leftist cabinet in the 1980s, died on
Saturday in Managua. He was 82."
Photo caption from the same obituary —
"Fernando Cardenal in 1990. As education minister of
Nicaragua under the Sandinistas in the 1980s, he
oversaw a sweeping campaign credited with reducing
illiteracy to 13 percent from 51 percent."
This alleged literacy improvement makes him sound like
a Protestant revolutionary.
For a Catholic view of literacy, see The Gutenberg Galaxy .
See also the post Being Interpreted (Aug. 14, 2015) —
A post for Tom Hanks and Dan Brown
Yahoo! President and CEO Marissa Mayer delivers a keynote
during the Yahoo Mobile Developers Conference on February 18,
2016, at Nob Hill Masonic Center in San Francisco, California.
Credit: Stephen Lam
"Have you ever thought about
the properties of numbers?"
— "The Maiden" in Shaw's
Back to Methuselah , quoted in
the Fritz Leiber Changewar story
“No Great Magic” (1963), Part V
"Le silence éternel de ces espaces infinis m'effraie." — Pascal
(Quoted here in The Search for Finite Space on Mon., Feb. 8, 2016.)
|
Accolades poured in from across the science world, as experts hailed a discovery that will help mankind better understand the universe. "This expands hugely the way we can observe the cosmos, and the kinds of physics and astrophysics we can do," said professor Sheila Rowan, Director of the University of Glasgow's Institute for Gravitational Research. Abhay Ashtekar, director of the Institute for Gravitation and the Cosmos at Penn State University, described the discovery as "breathtaking" and said it "will stand out among the major achievements of the 21st-century science." "We can now listen to the universe rather than just look at it," said Professor B S Sathyaprakash of Cardiff University. "This window turns on the soundtrack for the universe." |
Click the above image for a web page on the question
"Why was New Haven divided into nine squares?".
… Professionally, at least …
Click image to enlarge.
See also the previous post, Lechner's End.
For a more up-to-date look at harmonic analysis
and switching functions (i.e., Boolean functions),
see Ryan O'Donnell, Analysis of Boolean Functions ,
Cambridge U. Press, 2014. Page 40 gives an
informative overview of the history of this field.
It is an odd fact that the close relationship between some
small Galois spaces and small Boolean spaces has gone
unremarked by mathematicians.
A Google search today for “Galois spaces” + “Boolean spaces”
yielded, apart from merely terminological sources, only some
introductory material I have put on the Web myself.
Some more sophisticated searches, however led to a few
documents from the years 1971 – 1981 …
“Harmonic Analysis of Switching Functions” ,
by Robert J. Lechner, Ch. 5 in A. Mukhopadhyay, editor,
Recent Developments in Switching Theory , Academic Press, 1971.
“Galois Switching Functions and Their Applications,”
by B. Benjauthrit and I. S. Reed,
JPL Deep Space Network Progress Report 42-27 , 1975
D.K. Pradhan, “A Theory of Galois Switching Functions,”
IEEE Trans. Computers , vol. 27, no. 3, pp. 239-249, Mar. 1978
“Switching functions constructed by Galois extension fields,”
by Iwaro Takahashi, Information and Control ,
Volume 48, Issue 2, pp. 95–108, February 1981
An illustration from the Lechner paper above —
“There is such a thing as harmonic analysis of switching functions.”
— Saying adapted from a young-adult novel
"In 2012, Lucas sold his company
and his homegrown mythology —
I think we call it I.P. now — to Disney."
— Bryan Curtis, "The George Awakens"
See Fields of Force and recent posts.
From PR Newswire in July 2011 —
Campus Crusade for Christ Adopts New Name: Cru
60-year-old Int’l Ministry Aims to Increase
Relevance and Global Effectiveness
Related material:
Related material:
The previous post (Bright Symbol) and
a post from Wednesday,
December 23, 2015, that links to posts
on Boolean algebra vs. Galois geometry.
“An analogy between mathematics and religion is apposite.”
— Harvard Magazine review by Avner Ash of
Mathematics without Apologies
(Princeton University Press, January 18, 2015)
An excerpt from http://yarchive.net/med/middle_ages.html —
From: ((Steven B. Harris)) Subject: Re: Problems with sci.med.aids FAQ (section 7) Part II Date: 09 Jun 1995 In <173AD1188AS85.AVIRAMA@UNIVSCVM.CSD.SCAROLINA.EDU> AVIRAMA@UNIVSCVM.CSD.SCAROLINA.EDU (Amittai F. Aviram) writes to David Mertz: >Ahem.... With all due respect, it seems to me to make no sense >to criticize a scientist or medical doctor for "a childish >little schoolboy positivism." Well, I think he was referring to the Vienna School, where the schoolboys shout childish things like "Your mother still believes in Compte!" and "Well, at least my mother has values and isn't a logical empiricist like YOUR old man!" Woody Allen went there, but says he was expelled during a philosophy test for looking into the soul of the kid next to him.
Midrash —
"There's a concert hall in Vienna
Where your mouth had a thousand reviews"
— Leonard Cohen lyric, "Take This Waltz"
Synchronicity check:
A December 7th New York Times column:
A current exhibition by Joseph Kosuth in Oslo:
From the two texts by Mondrian at the right hand of Kosuth —
"The positive and negative states of being bring about action."
"Through its pure relationships, purely abstract art
can approach the expression of the universal …."
These texts may be viewed as glosses on the following image —
Click image for related posts.
"… if your requirement for success is to be like Steve Jobs,
good luck to you."
— "Transformation at Yahoo Foiled by Marissa Mayer’s
Inability to Bet the Farm," New York Times online yesterday
"Design is how it works." — Steve Jobs
Related material: Posts tagged Ambassadors.
This post's title was suggested by the previous post
and by today's news of a notable sale of a one-copy
record album, "Once Upon a Time in Shaolin."
See as well posts from Tuesday, March 11, 2014,
the day Emma Watson unveiled a new trailer —
Scientific American photo caption —
"Monday, November 2, marks the 200-year anniversary
of the birth of the man who put True/False, 0/1, and
AND/OR and NOT on the map."
See Hardegree's Symbolic Logic on "and/or" and its purported use
"to avoid ambiguity in legal contracts." His book is NOT recommended.
See also Bryan Garner in the ABA Journal on "and/or" in legal usage,
as well as a post in this journal, The Witch of And/Or.
The following slides are from lectures on “Advanced Boolean Algebra” —
The small Boolean spaces above correspond exactly to some small
Galois spaces. These two names indicate approaches to the spaces
via Boolean algebra and via Galois geometry .
A reading from Atiyah that seems relevant to this sort of algebra
and this sort of geometry —
” ‘All you need to do is give me your soul: give up geometry
and you will have this marvellous machine.’ (Nowadays you
can think of it as a computer!) “
Related material — The article “Diamond Theory” in the journal
Computer Graphics and Art , Vol. 2 No. 1, February 1977. That
article, despite the word “computer” in the journal’s title, was
much less about Boolean algebra than about Galois geometry .
For later remarks on diamond theory, see finitegeometry.org/sc.
According to René Guitart in May 2008 —
"In fact, in concrete terms, the Mathematical Pulsation is
nothing else but the thing that everyone does when doing
mathematics, even the most elementary ones. It is a very
special gesture in understanding ('geste de pensée'), well
known by each mathematician. The mind have to go to
and fro between to antinomical postures: to have the
situation under control, to leave the door open. To master
and to fix (a clear unique meaning) or to neglect and to
change (toward other possible meanings). Because of the
similarity of the pulsation of inspiration and expiration in
breath with the pulsation of closing and opening phases
in mathematical thinking, at the end of [Guitart (2003/a)]
I suggested to consider the famous book 'Zen in the Art
of Archery' [Herrigel (1997)] as a true treatise in didactic
of mathematics: just you have to replace everywhere the
words 'archery' by 'mathematical proof'."
Related material: Heisenberg on Beauty and the previous post.
Update of 6:20 AM Oct. 19, 2015 —
„Ich begriff plötzlich, daß in der Sprache oder doch
mindestens im Geist des Glasperlenspiels tatsächlich
alles allbedeutend sei, daß jedes Symbol und jede
Kombination von Symbolen nicht hierhin oder dorthin,
nicht zu einzelnen Beispielen, Experimenten und
Beweisen führe, sondern ins Zentrum, ins Geheimnis
und Innerste der Welt, in das Urwissen. Jeder Übergang
von Dur zu Moll in einer Sonate, jede Wandlung eines
Mythos oder eines Kultes, jede klassische, künstlerische
Formulierung sei, so erkannte ich im Blitz jenes
Augenblicks, bei echter meditativer Betrachtung,
nichts andres als ein unmittelbarer Weg ins Innere
des Weltgeheimnisses, wo im Hin und Wider zwischen
Ein- und Ausatmen, zwischen Himmel und Erde,
zwischen Yin und Yang sich ewig das Heilige vollzieht.“
— Hermann Hesse, Das Glasperlenspiel.
Berlin: Suhrkamp Taschenbuch Verlag, 2012. p. 172,
as quoted in a weblog.
For a version in English, see Summa Mythologica (Nov. 3, 2009).
“I need a photo opportunity, I want a shot at redemption.
Don’t want to end up a cartoon in a cartoon graveyard.”
— Paul Simon
A portion of the above photo appeared on the cover of
a German edition of a book by the winner of the 2015 Nobel
Prize in Literature, Svetlana Alexievich. The German title,
Der Krieg hat kein weibliches Gesicht , is closer to the Russian
original than is the title of an English translation, War's Unwomanly Face .
Further book and photo information —
|
Saturday, March 14, 2015
Introduction to Yau
|
A note on the somewhat distant relation —
See also Kummer in this journal.
From an essay by Mark Edmundson,
University Professor at the University of Virginia,
who was granted a Ph.D. by Yale in 1985 —
|
The American Scholar The Roman Catholic Church may forgive us our sins—but can it be forgiven for its own?
By Mark Edmundson “Aren’t you a Catholic?” People often ask me that question in a gotcha tone. It’s as though they’re saying: I see through you. You pretend to be an intellectual, a more or less secular guy who can maybe lay claim to some sophistication. You want to pass as someone (here’s the rub) who has grown up and is not a child anymore. But I see through all that, the questioner implies. I can tell that you live under the old dispensation. You’re a creature not of light and intellect, light and truth, but of guilt and fear. Light and truth, lux et veritas , was the motto of the university where I went to graduate school. It signifies the power of enlightened intellect to remake the world—or at least to transform and elevate the individual. Religions don’t generally have mottoes, and it is probably not a good idea when they do. But if the Roman Catholic Church had a motto, it surely would not be light and truth. I spent 12 years, give or take, in the faith, the most influential years of my life. And I was surely a Catholic. But what if anything remains of that immersion? What value does it have here and now? |
An example of vincible ignorance:
Edmundson's remarks above, in light of …
In memory of the late Claus Adolf Moser,
Baron Moser, who reportedly died at 92
on Friday, September 4, 2015.
Moser, a statistician, later became an arts
administrator as well. (He was chairman of the
Royal Opera House, 1974-1987).
Arts for Moser:
From the current New Yorker (Sept. 7, 2015) —
From this journal last year —
But Is It Art? and Diamond Star
(Feb. 1 and Jan. 31, 2014):
"Thinking Outside the Square:
Support for Landscape and Portrait
Formats on Instagram"
Related material from March 18, 2015 —
Play Is Not Playing Around
|
— "The Noble Rider and the Sound of Words"
For some backstory, click or touch the dark passage above.
See also Monolith (August 23, 2014).
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