A more impressive Lucifer —
The late theoretical physicist John Archibald Wheeler,
author of the phrase "it from bit."
Related material —
"The Thing and I" (April 17, 2016) and an essay by
Julian Barbour, "Bit from It."
A more impressive Lucifer —
The late theoretical physicist John Archibald Wheeler,
author of the phrase "it from bit."
Related material —
"The Thing and I" (April 17, 2016) and an essay by
Julian Barbour, "Bit from It."
In memory of Claude Shannon, who would have turned 100 today.
See "The Matthias Defense" and citations of that page in this journal.
… Continues.
"OK Baby, let's go dancing."
— Amy Adams in "American Hustle"
Click image below for some backstory.
Happy birthday to Uma Thurman.
For those who prefer "Hamilton" to Hamilton
"You've got the look
You've got the hook
You sho' nuf do be cookin' in my book
Your face is jammin' …."
In memory of a culture jammer *—
* "Mr. Lyons … made a living partly by buying,
reconditioning and selling used cars." —
— Ben Ratliff in The New York Times this evening.
See also the previous post and, from Feb. 14 in
this journal, the phrase "more global than local."
Three notes on local symmetries
that induce global symmetries
From July 1, 2011 —
From November 5, 1981 —
From December 24, 1981 —
Peter Schjeldahl on Wallace Stevens in the current New Yorker —
"Stevens was born in 1879 in Reading, Pennsylvania,
the second of five children. His father, from humble
beginnings, was a successful lawyer, his mother a
former schoolteacher. Each night, she read a chapter
of the Bible to the children, who attended schools
attached to both Presbyterian and Lutheran churches,
where the music left an indelible impression on Stevens.
Both sides of the family were Pennsylvania Dutch,
an identity that meant little to him when he was young
but a great deal later on, perhaps to shore up a precarious
sense of identity."
See also this journal on Christmas Day, 2010 —
It's a start. For more advanced remarks from the same date, see Mere Geometry.
"… I would drop the keystone into my arch …."
— Charles Sanders Peirce, "On Phenomenology"
" 'But which is the stone that supports the bridge?' Kublai Khan asks."
— Italo Calvino, Invisible Cities, as quoted by B. Elan Dresher.
(B. Elan Dresher. Nordlyd 41.2 (2014): 165-181,
special issue on Features edited by Martin Krämer,
Sandra Ronai and Peter Svenonius. University of Tromsø –
The Arctic University of Norway.
http://septentrio.uit.no/index.php/nordlyd)
Peter Svenonius and Martin Krämer, introduction to the
Nordlyd double issue on Features —
"Interacting with these questions about the 'geometric'
relations among features is the algebraic structure
of the features."
For another such interaction, see the previous post.
This post may be viewed as a commentary on a remark in Wikipedia —
"All of these ideas speak to the crux of Plato's Problem…."
See also The Diamond Theorem at Tromsø and Mere Geometry.
An old version of the Wikipedia article "Group theory"
(pictured in the previous post) —
"More poetically …"
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
of mankind."
The seven seals from the previous post, with some context —
These models of projective points are drawn from the underlying
structure described (in the 4×4 case) as part of the proof of the
Cullinane diamond theorem .
Quine, Pursuit of Truth , Harvard
University Press, 1990, epigraphs:
For another quote from Sherwin-Williams,
see the April 21 post Purple Requiem.
The prominent display of an ad for Elixir Vitae in
today's 11:02 AM post suggests a review of that concept.
See also Raiders of the Lost Crucible in this journal.
Guy Hamilton, director of "Diamonds are Forever"
and "Goldfinger," reportedly died at 93 on Wednesday,
April 20, 2016. In his memory, here is a link to the
posts of All Souls' Day, 2015.
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.
See as well "The Stars My Destination" in this journal.
Material related to the previous post and to Alfred Bester's
1981 followup to The Stars My Destination titled The Deceivers —
The Lapis Philosophorum :
"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe." And from Bester's The Deceivers : Meta Physics "'… Think of a match. You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released. Friction does it. But when Meta excites and releases energy, it's like a stick of dynamite compared to a match. It's the chess legend for real.' 'I don't know it.' 'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah. The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what. The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.' 'That doesn't sound like much.'" Related material : |
The reference in the previous post to the work of Guitart and
The Road to Universal Logic suggests a fiction involving
the symmetric generation of the simple group of order 168.
See The Diamond Archetype and a fictional account of the road to Hell …
The cover illustration below has been adapted to
replace the flames of PyrE with the eightfold cube.
For related symmetric generation of a much larger group, see Solomon’s Cube.
From a Washington Post book review this evening —
"… some people find an almost spiritual, liminal state
called the Bright…."
And some people may see as an illustration of that fictional state
this scene from a video —
For more on the word "liminal," see October 20, 2015.
For a tale related to the above image, see Floating Dragon .
A recent post about the eightfold cube suggests a review of two
April 8, 2015, posts on what Northrop Frye called the ogdoad :
As noted on April 8, each 2×4 "brick" in the 1974 Miracle Octad Generator
of R. T. Curtis may be constructed by folding a 1×8 array from Turyn's
1967 construction of the Golay code.
Folding a 2×4 Curtis array yet again yields the 2x2x2 eightfold cube .
Those who prefer an entertainment approach to concepts of space
may enjoy a video (embedded yesterday in a story on theverge.com) —
"Ghost in the Shell: Identity in Space."
"When Death tells a story…"
— Cover of The Book Thief
"Finnegan's waterlogged epiphany"
— Phrase by John Lancaster in a Washington Post review of an
autobiography by William Finnegan, a book that today won a Pulitzer Prize.
The review is dated August 7, 2015. This journal on that date —
… is a novel by James Morrow reviewed in The New York Times
on March 23, 2008:
"Morrow’s inventiveness is beguiling, as are his delight
in Western philosophy and his concern for the sorry state
of the world. Yet there’s also something comic-bookish
about his novel…."
"Something comic-bookish"
in memory of Albert Einstein,
who reportedly died on this date
in 1955 —
(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 …
The New York Times philosophy column yesterday —
The Times's philosophy column "The Stone" is named after the legendary
"philosophers' stone." The column's name, and the title of its essay yesterday
"Is that even a thing?" suggest a review of the eightfold cube as "The object
most closely resembling a 'philosophers' stone' that I know of" (Page 51 of
the current issue of a Norwegian art quarterly, KUNSTforum.as).
The eightfold cube —
Definition of Epiphany
From James Joyce’s Stephen Hero , first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959). Three Times: … By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance: — Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin’s street furniture. Then all at once I see it and I know at once what it is: epiphany. — What? — Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty. — Yes? said Cranly absently. — No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action. — Yes … — You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a thing. You recognise its integrity. Isn’t that so? — And then? — That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing , a definitely constituted entity. You see? — Let us turn back, said Cranly. They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away. — Now for the third quality. For a long time I couldn’t make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas . After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one integral thing, then we recognise that it is an organised composite structure, a thing in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany. Having finished his argument Stephen walked on in silence. He felt Cranly’s hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend’s company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled: — It has not epiphanised yet, he said. |
Today is Kelli O'Hara's last Saturday matinee in "The King and I."
A show that some may prefer —
Related to the plot of Dante's film —
"…it would be quite a long walk
Swiftly Mrs. Who brought her hands… together.
"Now, you see," Mrs. Whatsit said,
– A Wrinkle in Time , Chapter 5, "The Tesseract" |
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"
A search in Log24 for Wallace Stevens's phrase
"the A B C of Being" suggests a related search, for
"Happy Birthday, Wallace Stevens." That search
in turn suggests a search for "Maori."
“Literature begins with geography.”
— Attributed to Robert Frost
On this date in 2005, mathematician Saunders Mac Lane died at 95.
Related material —
Max Planck quotations:
Mac Lane on Boolean algebra:
Mac Lane’s summary chart (note the absence of Galois geometry ):
I disagree with Mac Lane’s assertion that “the finite models of
Boolean algebra are dull.” See Boole vs. Galois in this journal.
"Those who see a model as a mere crutch
are like those who consider metaphor
a mere decoration or ornament."
This suggests a search for "Analogies between Analogies" —
“A mathematician is a person who can find analogies
between theorems; a better mathematician is one who
can see analogies between proofs and the best
mathematician can notice analogies between theories.
One can imagine that the ultimate mathematician is one
who can see analogies between analogies.”
— Stefan Banach, according to MacTutor.
From a review of a play by the late Anne Meara* —
"Meara, known primarily as an actress/comedian
(half of the team of Stiller & Meara, and mother of
Ben Stiller), is also an accomplished writer for the
stage; her After Play was much acclaimed….
This new, more ambitious piece starts off with a sly
send-up of awards dinners as the late benefactor of
a wealthy foundation–the comically pixilated scientist
Herschel Strange (Jerry Stiller)–is seen on videotape.
This tape sets a light tone that is hilariously
heightened when John Shea, as Arthur Garden,
accepts the award given in Strange's name."
Compare and contrast —
I of course prefer the Galois I Ching .
* See the May 25, 2015, post The Secret Life of the Public Mind.
Anne Jackson's obituary in yesterday's online New York Times
mentioned her appearance in "Down the Garden Paths,"
a play by Anne Meara.
Some may prefer to picture Jackson and her late husband,
Eli Wallach, on a garden path pictured here in a post of
January 17, 2003, "The Walk to Paradise Garden."
For the above title, see today's 1 PM post Black List.
A search for "Max Black" in this journal yields some images
from a post of August 30, 2006 . . .
"Jackson has identified the seventh symbol." |
The "Jackson" above is played by the young James Spader,
who in an older version currently stars in "The Blacklist."
"… the memorable models of science are 'speculative instruments,' — Max Black in Models and Metaphors , Cornell U. Press, 1962 |
The American Mathematical Society today got around to
publishing an obituary for Solomon Marcus, a Bucharest
mathematician who died on St. Patrick's Day, March 17.
See as well this journal on March 22.
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."
"Try the grey stuff, it's delicious
Don't believe me? Ask the dishes"
— Disney's "Beauty and the Beast"
Related material —
Friday, April 1, 2016 Filed under: Uncategorized — m759 @ 12:00 AM See also the previous post and the usual suspects. |
Happy birthday to Saoirse Ronan.
The previous post, Charlatans 101, was on a book whose author
is associated rather closely with an Alabama institution called
"Samford University" (not to be confused with Stanford University).
A photo from Samford —
Related material for non-charlatans, not from Samford —
See as well A Wrinkle in Terms in this journal.
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.
A remark by New Yorker editor David Remnick
at Princeton on June 3, 2013 —
The new New Yorker online this evening —
" 'If we look at the word "eulogy," it comes from
the ancient Greek word eulogia , and eulogia
simply means "praise." ' The desire to be present
at one’s own funeral is nothing new. In an era of
near-constant mutual affirmation—pause here to
check the number of likes on your most recent selfie—
why let a little thing like death stand in the way? "
From Sunday evening's In Memoriam post —
The "from Princeton" remark in the previous post came from
Princeton, but originated with a retired professor in Rochester,
NY, one Joseph Neisendorfer.
Another remark by Neisendorfer, from his weblog —
Those familiar with the chapter on Galois in the
Eric Temple Bell classic Men of Mathematics
will know that the words quoted above by
Neisendorfer are definitely not those of Albert Einstein.
The previous post contained a remark from Princeton
on the January 1, 2016, death of a mathematician.
"There's a certain Princeton style that focuses on
precision, centrality and simplicity."
See also …
For a different sort of style, see Death on New Year's Day.
"Principles before personalities" — AA saying
Principles
From an April 8 Princeton obituary of a mathematician —
" Moore embodied a 'Princeton style' that made him
a challenging and influential presence in the careers
of his students, said Joseph Neisendorfer, a professor
of mathematics at the University of Rochester who
received his Ph.D. in mathematics from Princeton in
1972. Because of Moore's style, his students would
write theses that 'almost without exception' were
significant advances in mathematics, Neisendorfer said.
'There's a certain Princeton style that focuses on
precision, centrality and simplicity. He was a superb
mathematician and he exercised a lot of influence
by imparting his style to his students,' Neisendorfer said.
'He epitomized the Princeton style.' "
Personalities
Gospel of the Nobodies
“Chaos is order yet undeciphered.”
— The novel The Double , by José Saramago,
on which the film "Enemy" was based
Some background for the 2012 Douglas Glover
"Attack of the Copula Spiders" book
mentioned in Sunday's Synchronicity Check —
The saying of poet Mary Karr that
"there is a body on the cross in my church,"
together with the crosses of the previous post,
suggests a synchronicity check of the
date discussed in that post —
“Be serious, because
The stone may have contempt
For too-familiar hands”
— Adrienne Rich in “The Diamond Cutters” (1955)
Blackboard Jungle , 1955 —
The book quoted in the previous post, Attack of the Copula Spiders,
was reportedly published on March 27, 2012.
For the Church of Synchronology —
The above icon may be viewed as a simplified version
of the image described in the April 8 post Space Cross.
"But now, as a kind of reality check,
let’s look at James Joyce’s 'The Dead.' "
— Attack of the Copula Spiders
… And at day five of April 2016 —
(Today is day ten . See the previous post.)
"Driving the car is Beat Personified Johnny Five. . . ."
— What Does the Protagonist Want? website
* See Getcha in this journal.
I watched the 2015 film "Mojave" this morning. Some related remarks:
"Mojave" screenwriter William Monahan won an Oscar for "The Departed."
The opening of a book by another Hollywood author, now departed —
The Latecomers
"Nicholas Concert, a minister without particular portfolio
or flock, and once, long ago, a priest of the Roman faith,
awoke in a troubled dawn. It was the new day sensed
rather than perceptible to him in the interior blackness of
the detached truck camper. It was cold. He was tempted
to huddle in his sleeping bag awhile longer, until the sun
would rise out of the Mojave, climb the ridge and fill the
isolated desert valley. He had not slept well. His night had
been frantic with apparitions, sounds, fragments of dialogue.
It had been a long night, a terrible night, one that Concert
had thought would never end or, at its worst, that it had ended
and he had died during its passing and this was his eternal hell,
to be transfixed in this night forever, kept from his tomorrow as
Moses, flawed, had been kept from his. …"
"Mr. Conrad was relentless and rigorous in expanding
the parameters of the fields in which he worked."
See also Spielfeld in this journal, as well as Conrad Moonshine.
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 …
Consider the space AG(4,2) invoked . See last night's Space Cross.
For George Orwell
Illustration from a book on mathematics —
This illustrates the Galois space AG(4,2).
For some related spaces, see a note from 1984.
"There is such a thing as a space cross."
— Saying adapted from a young-adult novel
"Arthur's favorite scripture was Romans 8."
— Legacy.com on a death of March 28, 2016
Cf. Karl Barth on Romans .
As was previously noted here, the construction of the Miracle Octad Generator
of R. T. Curtis in 1974 may have involved his "folding" the 1×8 octads constructed
in 1967 by Turyn into 2×4 form.
This results in a way of picturing a well-known correspondence (Conwell, 1910)
between partitions of an 8-set and lines of the projective 3-space PG(3,2).
For some background related to the "ogdoads" of the previous post, see
A Seventh Seal (Sept. 15, 2014).
"Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye's formal interest lay in
the 'schematosis' and fearful symmetries of his own presentations."
— From p. 61 of James C. Nohrnberg's "The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye,"
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterly, January 2001)
See also Two by Four in this journal.
The previous post is about two Princeton-related deaths
on March 12, 2016. See Log24 posts on that date.
From the American Mathematical Society today —
Verena Huber-Dyson (1923-2016) Huber-Dyson, who worked in group theory and logic, died March 12 at the age of 92. She was born to Swiss parents in Naples and grew up in Athens but moved with her family to Switzerland in 1940 because of the war. Huber-Dyson received her PhD from the University of Zurich in 1947 and moved to the U.S. in 1948 for a post-doctoral fellowship at the Institute for Advanced Study. She held positions at many universities around the world and taught courses on the foundation of mathematics as a philosophy professor at the University of Calgary from 1973 to 1988. Her son, George Dyson, said that her last words were, "This will all go smoothly. Let's get going." She was an AMS member since 1949. Read more about her life. |
See also Huber-Dyson in this journal.
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 —
"Will the circle be unbroken?" — Funeral hymn
"Like a forgotten dream" — Merle Haggard
"Like Shakespeare, Ingrid Bergman was born and died
on the same date… In her case, August 29."
"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."
The Washington Post pictures an event from
the evening of Sunday, November 1, 2015:
All Saints' Day —
See as well Ay Que Bonito .
An April 4 Boston Globe story by Kevin Cullen
suggests a review of …
The spring play this March at Princeton's McCarter Theatre Center
was Agatha Christie's "The Mousetrap."
In related news —
See as well, in this journal, a post from the date pictured above,
that of the Disneyland Diamond Celebration on May 22, 2015 —
From the April 2 obituary of a counterculture figure —
"Ms. Crystal was born Jacqueline Diamond
on Dec. 21, 1947, in Manhattan and grew up
in Mamaroneck, N.Y. Her father, Jack, owned
J. Diamond Furs. Her mother, the former Rita
Dunn, was a fur model who, after marrying,
stayed home to raise her children."
— William Grimes in The New York Times
"Jack o' Diamonds is a hard card to play."
From Log24 on the reported date of Ms. Crystal's death —
Images from a post titled For Stephen King —
Related images —
"Pray for the grace of accuracy" — Robert Lowell
The previous post was about the death of a figure
from the world of entertainment.
I prefer the work of a figure with the same last name
but from a different world —
"Spiel ist nicht Spielerei." — Friedrich Fröbel
"If you would be a poet, create works capable of
answering the challenge of apocalyptic times,
even if this meaning sounds apocalyptic."
"It's a trap!"
— Ferlinghetti's friend Erik Bauersfeld,
who reportedly died yesterday at 93
* See also, in this journal, Galois Cube and Deathtrap.
(A sequel to today's earlier posts Cube for Berlin and Midnight for Paris.)
See London in this journal.
That search yields …
“The more intellectual, less physical,
the spell of contemplation
the more complex must be the object,
the more close and elaborate
must be the comparison
the mind has to keep making
between the whole and the parts,
the parts and the whole.”
— The Journals and Papers of Gerard Manley Hopkins ,
ed. by Humphry House (London: Oxford University Press, 1959),
as quoted by Philip A. Ballinger in The Poem as Sacrament
(From the post The Inscape of 24, April 24, 2014. The 14 blocks in
the design S(3, 4, 8) of today's previous post are analogous to the 759
blocks in the design S(5, 8, 24).)
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.)
Illustration for Florence King's 1989 review of The Eight , a novel
by Katherine Neville that features prominently the date April 4.
A check on the source of the Wittgenstein quotations
in the previous post yields …
Sounds like Verhexung to me. See also Plotnitsky in this journal.
The previous post suggests a review of Wittgenstein's
Verhexung remark in context.
Backstory: Verhexung and Ein Kampf .
Prequel: The Verhexung quote above is from Wittgenstein's section 109
in Philosophical Investigations . The search result shown links to a page
containing part of the preceding Wittgenstein section —
For another look at "crystalline purity" and language, see the previous
two posts, Logic and Fruit Loom.
Wallace Stevens, “Country Words” —
“What is it that my feeling seeks?
I know from all the things it touched
And left beside and left behind.
It wants the diamond pivot bright.”
"This area is called Silicon Valley and it was not always
called Silicon Valley. When I grew up here from seven
years old on, it was called Santa Clara Valley and as far
as you could see it was fruit trees — one of the greatest
fruit-producing areas in the world."
— Steve Wozniak at mashable.com today
See also Just Desserts and The Looming.
See also Stone Logical Dimensions …
“Lord Arglay had a suspicion that the Stone
would be purely logical. Yes, he thought,
but what, in that sense, were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
… at The Restaurant Quarré in Berlin,
with a view of the Brandenburg Gate:
See also versions of the title more suited to 2 AM .
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 —
Publisher's description of a book about everything —
"When the whole is greater than the sum of the parts—
indeed, so great that the sum far transcends the parts
and represents something utterly new and different—
we call that phenomenon emergence."
— Oxford University Press
Titles for Harlan Kane, from the date that
the above book's author reportedly died —
Continued from Easter Sunday 2016 —
256×256 pixels, enlarged from 16×16
Related reporting from this evening's New York Times —
Clicking the above favicon will yield the cited Federation webpage.
See also the previous post and the usual suspects.
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