(Continued from 9:23 PM ET yesterday)
For the rube himself, see the previous post.
"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.
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.
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…."
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
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 .
Compare and contrast Peirce's seven systems of metaphysics with
the seven projective points in a post of March 1, 2010 —
From my commentary on Carter's question —
Quine, Pursuit of Truth , Harvard
University Press, 1990, epigraphs:
For another quote from Sherwin-Williams,
see the April 21 post Purple Requiem.
See also Raiders of the Lost Crucible 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 :
"'… 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 :
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.
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 —
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."
"Finnegan's waterlogged epiphany"
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…."
in memory of Albert Einstein,
who reportedly died on this date
in 1955 —
"… Mathematics may be art, but to the general public
it is a black art, more akin to magic and mystery."
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).
… 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.
— 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"
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"
“Literature begins with geography.”
— Attributed to Robert Frost
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.
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.
"Jackson has identified the seventh symbol."
"… the memorable models of science are 'speculative instruments,'
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.
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
Happy birthday to Saoirse Ronan.
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 —
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.
"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
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.' "
Gospel of the Nobodies
“Chaos is order yet undeciphered.”
— The novel The Double , by José Saramago,
on which the film "Enemy" was based
“Be serious, because
The stone may have contempt
For too-familiar hands”
Blackboard Jungle , 1955 —
For the Church of Synchronology —
"But now, as a kind of reality check,
let’s look at James Joyce’s 'The Dead.' "
… 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 —
"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. …"
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