Good question. See also this journal on the above date —
Images from Log24 yesterday . . .
And from The New Yorker yesterday . . .
See also RIP: The Peace of Pi —
From BUtterfield 8 (1960) —
From the 7/20/2017 post "Divided Attention" —
Another phrase for divided attention is "bulk apperception."
"My words say split, but my words they lie" — Bruce Springsteen
See a search for "Split" in this journal.
Click for the pages below at Internet Archive.
Enveloping algebras also appeared later in the work on "crystal bases"
of Masaki Kashiwara. It seems highly unlikely that his work on enveloping
algebras, or indeed any part of his work on crystal bases, has any relation
to my own earlier notes.
A 1995 page by Kashiwara —
Kashiwara was honored with a Kyoto prize in 2018:
Kashiwara's 2018 Kyoto Prize diploma —
Image from a post of November 13, 2006.
See as well Schoolgirl Tetrahedron.
Related lyrics from Bruce Springsteen and
the Pointer Sisters —
Well, Romeo and Juliet, Samson and Delilah
Baby you can bet a love they couldn't deny
My words say split, but my words they lie
Cause when we kiss, ooh, fire
{Bridge}
Oh fire
Kisses like fire…
Burn me up with fire
I like what you're doin now, fire
Touchin' me, fire
Touchin' me, burnin me, fire
Take me home
arXiv.org > quant-ph > arXiv:1905.06914 Quantum Physics Placing Kirkman's Schoolgirls and Quantum Spin Pairs on the Fano Plane: A Rainbow of Four Primary Colors, A Harmony of Fifteen Tones J. P. Marceaux, A. R. P. Rau (Submitted on 14 May 2019) A recreational problem from nearly two centuries ago has featured prominently in recent times in the mathematics of designs, codes, and signal processing. The number 15 that is central to the problem coincidentally features in areas of physics, especially in today's field of quantum information, as the number of basic operators of two quantum spins ("qubits"). This affords a 1:1 correspondence that we exploit to use the well-known Pauli spin or Lie-Clifford algebra of those fifteen operators to provide specific constructions as posed in the recreational problem. An algorithm is set up that, working with four basic objects, generates alternative solutions or designs. The choice of four base colors or four basic chords can thus lead to color diagrams or acoustic patterns that correspond to realizations of each design. The Fano Plane of finite projective geometry involving seven points and lines and the tetrahedral three-dimensional simplex of 15 points are key objects that feature in this study. Comments:16 pages, 10 figures Subjects:Quantum Physics (quant-ph) Cite as:arXiv:1905.06914 [quant-ph] (or arXiv:1905.06914v1 [quant-ph] for this version) Submission history
From: A. R. P. Rau [view email] |
See also other posts tagged Tetrahedron vs. Square.
See also other posts tagged Tetrahedron vs. Square, and a related
Log24 search for "Schoolgirl + Space."
See also Visual Structure (May 22, 2014)
and Snakes on a Plane posts.
The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —
See also . . .
The Quantum Tesseract Theorem Revisited
"The secret is that the super-mathematician expresses by the anticommutation
of his operators the property which the geometer conceives as perpendicularity
of displacements. That is why on p. 269 we singled out a pentad of anticommuting
operators, foreseeing that they would have an immediate application in describing
the property of perpendicular directions without using the traditional picture of space.
They express the property of perpendicularity without the picture of perpendicularity.
Thus far we have touched only the fringe of the structure of our set of sixteen E-operators.
Only by entering deeply into the theory of electrons could I show the whole structure
coming into evidence."
A related illustration, from posts tagged Dirac and Geometry —
Compare and contrast Eddington's use of the word "perpendicular"
with a later use of the word by Saniga and Planat.
From Pi Day 2017 —
"Don't want to end up a cartoon in a cartoon graveyard."
“God’s plan for man in this world is Adam and Eve,
not Adam and Steve.”
— The late William E. Dannemeyer, who reportedly
died at 89 on July 9, 2019.
Hollywood offers a second opinion —
— The garden of Eden. The birthplace of Adam and Eve and Steve. — Steve? Who's Steve? — Steve is the original supermodel. The first of the purebloods.
Curse of the Fire Temple
"Power outages hit parts of Manhattan
plunging subways, Broadway, into darkness"
Related material — Tetrahedron vs. Square and Cézanne's Greetings.
Compare and contrast:
A figure from St. Patrick's Day 2004 that might represent a domed roof …
Inscribed Carpenter's Square:
In Latin, NORMA
… and a cinematic "Fire Temple" from 2019 —
See as well the previous post.
"The area is home to many artists and people who work in
the media, including many journalists, writers and professionals
working in film and television." — Wikipedia
Tusen takk to My Square Lady —
The title is from a New York Times correction in the previous post.
Piano roll for "I am sixteen going on seventeen" —
Backstory: Posts tagged Root Circle.
June 14 . . .
Later . . .
Earlier . . .
http://cristal.inria.fr/~weis/info/commandline.html
See also Stiff.
… τοῦ γὰρ ἀεὶ ὄντος ἡ γεωμετρικὴ γνῶσίς ἐστιν.
… for geometry is the knowledge of the eternally existent.
See also the previous post — "Artifice of Eternity" —
and the June 23, 2010, post "Group Theory and Philosophy."
… and Schoolgirl Space
"This poem contrasts the prosaic and sensual world of the here and now
with the transcendent and timeless world of beauty in art, and the first line,
'That is no country for old men,' refers to an artless world of impermanence
and sensual pleasure."
— "Yeats' 'Sailing to Byzantium' and McCarthy's No Country for Old Men :
Art and Artifice in the New Novel,"
Steven Frye in The Cormac McCarthy Journal ,
Vol. 5, No. 1 (Spring 2005), pp. 14-20.
See also Schoolgirl Space in this journal.
* See, for instance, Lewis Hyde on the word "artifice" and . . .
"Elmore Rual 'Rip' Torn Jr. (February 6, 1931 – July 9, 2019)
was an American actor, voice artist … Torn was born in
Temple, Texas,
on February 6, 1931, the son of Elmore Rual "Tiger" Torn Sr. and
Thelma Mary Torn (née Spacek)."
For the Church of Synchronology —
The above photo was reportedly taken on March 10, 2011.
An image from this journal on that date —
Found in translation — See "Ex Fano " in this journal
and the Fano post "In Nomine Patris."
Cube Bricks 1984 —
From "Tomorrowland" (2015) —
From John Baez (2018) —
See also this morning's post Perception of Space
and yesterday's Exploring Schoolgirl Space.
The three previous posts have now been tagged . . .
Tetrahedron vs. Square and Triangle vs. Cube.
Related material —
Tetrahedron vs. Square:
Labeling the Tetrahedral Model (Click to enlarge) —
Triangle vs. Cube:
… and, from the date of the above John Baez remark —
“I am always the figure in someone else’s dream. I would really rather
sometimes make my own figures and make my own dreams.”
— John Malkovich at squarespace.com, January 10, 2017
Also on that date . . .
See also "Quantum Tesseract Theorem" and "The Crosswicks Curse."
Anonymous remarks on the schoolgirl problem at Wikipedia —
"This solution has a geometric interpretation in connection with
Galois geometry and PG(3,2). Take a tetrahedron and label its
vertices as 0001, 0010, 0100 and 1000. Label its six edge centers
as the XOR of the vertices of that edge. Label the four face centers
as the XOR of the three vertices of that face, and the body center
gets the label 1111. Then the 35 triads of the XOR solution correspond
exactly to the 35 lines of PG(3,2). Each day corresponds to a spread
and each week to a packing."
See also Polster + Tetrahedron in this journal.
There is a different "geometric interpretation in connection with
Galois geometry and PG(3,2)" that uses a square model rather
than a tetrahedral model. The square model of PG(3,2) last
appeared in the schoolgirl-problem article on Feb. 11, 2017, just
before a revision that removed it.
Merlin : Our journey together began many years ago …
"… he never lost touch with the days he lived in a double wide
and used a blow dryer to thaw his winter pipes…."
Mythos
Logos
The six square patterns which, applied as above to the faces of a cube,
form "diamond" and "whirl" patterns, appear also in the logo of a coal-
mining company —
Related material —
The New York Times on an arranger/composer who reportedly
died at 100 on Monday:
"By the 1950s he was the musical arranger for
'The Milton Berle Show' (originally 'Texaco Star Theater'),
NBC’s hit hourlong variety-comedy series."
Related Log24 posts —
Notes towards a Dark Tower (Aug. 2, 2016) and Maine to Mexico.
"János Bolyai was a nineteenth-century mathematician who
set the stage for the field of non-Euclidean geometry."
— Transylvania Now , October 26, 2018
From Coxeter and the Relativity Problem —
Desiring the exhilarations of changes:
The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being,
The ruddy temper, the hammer
Of red and blue, the hard sound—
Steel against intimation—the sharp flash,
The vital, arrogant, fatal, dominant X.
The previous post suggests a line for James McAvoy —
"Pardon me boy, is this the Transylvania Station?"
See as well "Out of Nothing" in this journal.
"Lost is that camp, and wasted all its fire;
And he who wrought that spell?"
— Bret Harte, "Dickens in Camp"
“Finality is death. Perfection is finality. Nothing is perfect.
There are lumps in it, said the Philosopher.”
― James Stephens, The Crock of Gold
These quotations were suggested by Google News today —
For the origin of the name "Bret Stephens," see his
Wall Street Journal essay from June 26, 2009.
See also this journal on that date.
And now, General, time presses; and America is in a hurry.
Have you realized that though you may occupy towns and win battles,
you cannot conquer a nation? — The Devil's Disciple
A figure related to Dürer's "magic" square posted during Devil's Night —
The above title is that of a facetious British essay linked to in the previous post.
It suggests a review . . .
“. . . some point in a high corner of the room . . . .”
— Point Omega
Duncan reportedly died on June 29. See Log24 on that date.
An illustration from the previous post may be interpreted
as an attempt to unbokeh an inscape —
The 15 lines above are Euclidean lines based on pairs within a six-set.
For examples of Galois lines so based, see Six-Set Geometry:
Metaphysical conceit | literature | Britannica.com
|
This post's title refers to a metaphysical conceit
in the previous post, Desperately Seeking Clarity.
Related material —
The source of the above mystical octahedron —
See also Jung's Imago Dei in this journal.
"Let us consider the crux of Hopkins' sensibility…"
Seeking claritas :
From a "cube tales" post of June 21 —
The number "six" in the second tale above counts faces of the cube,
as shown in a post of June 23 —
". . . Then the universe exploded into existence . . . ."
The phrase "ontological secret" is from 1927 —
" Beauty is thus 'a flashing of intelligence…
on a matter intelligibly arranged' or, as Maritain
adds in the 1927 edition of Art and Scholasticism ,
it is 'the ontological secret that [things] bear within
them[selves], their spiritual being, their operating
mystery.' "
— John G. Trapani, Jr., "'Radiance': The Metaphysical Foundations
of Maritain's Aesthetics," pp. 11-19 in Beauty, Art, and the Polis ,
ed. by Alice Ramos, publ. by American Maritain Association, 2000.
This 1927 phrase may be the source of McLuhan's 1944
"ontological secret" —
From a search in this journal for "Object of Beauty" —
“She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test.”
— Steve Martin, An Object of Beauty
In memory of Susan Bernard , who reportedly died on June 21, 2019* —
Image from the 2016 post A Paris Review . . .
* See as well this journal on June 21,
"Cube Tales for Solstice Day."
Yesterday's post The Benson Epiphany suggests a review of another
retired UC Davis mathematics professor who also died in May…
John Robert Chuchel —
UC Davis mathematics students may consult the following page:
A check of this journal on the date of Chuchel's reported death
yields posts now tagged Hallows for UC Davis.
* See Ex Fano Apollinis (June 24).
"John Horton Conway is a cross between
Archimedes, Mick Jagger and Salvador Dalí."
— The Guardian paraphrasing Siobhan Roberts,
John Horton Conway and his Leech lattice doodle
in The Guardian . Photo: Hollandse Hoogte/Eyevine.
. . . .
"In junior school, one of Conway’s teachers had nicknamed him 'Mary'.
He was a delicate, effeminate creature. Being Mary made his life
absolute hell until he moved on to secondary school, at Liverpool’s
Holt High School for Boys. Soon after term began, the headmaster
called each boy into his office and asked what he planned to do with
his life. John said he wanted to read mathematics at Cambridge.
Instead of 'Mary' he became known as 'The Prof'. These nicknames
confirmed Conway as a terribly introverted adolescent, painfully aware
of his own suffering." — Siobhan Roberts, loc. cit.
From the previous post —
See as well this journal on the above Guardian date —
"Leibniz … could also be called the first digerati."
— The Guardian , May 10, 2013
"Digerati" is a term modeled after "literati" —
Example —
See also this journal on the above
Guardian date: 10 May 2013.
See also Hard Candy.
For affine group actions, see Ex Fano Appollinis (June 24)
and Solomon's Cube.
For one approach to Mathieu group actions on a 24-cube subset
of the 4x4x4 cube, see . . .
For a different sort of Mathieu cube, see Aitchison.
Vinnie Mancuso, in an article now dated December 25, 2018 —
Not so useless —
The caption in fine print below says
"Download Blender and install it.
I won't show you how to do that
because I don't want to insult your
intelligence…."
Q —
"What kind of person
bokehs an inscape?"
A —
Robert Gorham Davis:
McLuhan's " 'mosaic' mode of presentation …
rules out discriminations, qualifications,
close reasoning, the structuring of
articulated wholes."
— Robert Gorham Davis on Marshall McLuhan.
See also Articulation in this journal.
The Small quotation is from a page describing his transcription
for string quartet of Bach's Goldberg Variations:
https://manontroppomusic.wordpress.com/goldberg-variations/.
* See too other Log24 occurrences of "da capo."
From a New Yorker theatre review posted at 5 AM ET today —
“A Strange Loop” takes its title from a concept pioneered by
Douglas Hofstadter, the cognitive-science professor who
wrote the book “Gödel, Escher, Bach: An Eternal Golden Braid”
and, later, the more focussed study “I Am a Strange Loop”;
both were premised upon the impossibly complex, hopelessly
circular means by which each of us composes a self, an “I.”
See as well "Strange Loop" and "Loop de Loop" in this journal.
In memory of John Clarkeson, Harvard ’64, who “read broadly and inquisitively,
and was always on the lookout for a good tale….” Clarkeson reportedly died
on May 28, 2019.
Some Harvard-related material from that date: The Hogwash Papers.
Vinnie Mancuso, in an article now dated December 25, 2018 —
Related art —
Click image for further details.
See also other posts now tagged For Zankel Hall.
(Note the phrase "geometric complexities" in those posts.)
The phrase "various other activities" in the previous post, and a poem
by Yeats, suggest an image that appeared here in miniature on June 7:
See as well some related artistic images from January 4, 2007.
"When they all finally reach their destination —
a deserted field in the Florida Panhandle…."
" When asked about the film's similarities to the 2015 Disney movie
Tomorrowland , which also posits a futuristic world that exists in an
alternative dimension, Nichols sighed. 'I was a little bummed, I guess,'
he said of when he first learned about the project. . . . 'Our die was cast.
Sometimes this kind of collective unconscious that we're all dabbling in,
sometimes you're not the first one out of the gate.' "
See 7/11, 2006.
Related material — Dabblers in the Collective Unconscious.
For fans of the story theory of truth:
A "tale as old as time . . ."
— Song lyric, Beauty and the Beast
Nicholas Hoult as X-Men "Beast" Hank McCoy —
See also the previous post, "Equals Tolkien?"
Related material: The real McCoy —
"The loveliness of Paris seems somehow sadly gay." — Song lyric
Stewart also starred in "Equals" (2016). From a synopsis —
"Stewart plays Nia, a writer who works at a company that extols
the virtues of space exploration in a post-apocalyptic society.
She falls in love with the film's main character, Silas (Nicholas Hoult),
an illustrator . . . ."
Space art in The Paris Review —
For a different sort of space exploration, see Eightfold 1984.
From a date described by Peter Woit in his post
“Not So Spooky Action at a Distance” (June 11) —
See also The Lost Well.
* “As a Chinese jar….” — Four Quartets
Powered by WordPress