The figure below is one approach to the exercise
posted here on December 10, 2016.
Some background from earlier posts —
Click the image below to enlarge it.
From posts now tagged “Memory-History-Geometry” —
“… even the dogs under the table
eat the children’s crumbs.” — Mark 7:28
From a 2015 post …
“… Kansas and Harvard officially met
as Kansas wrestled the unsuspecting Harvard
to the ground in a headlock.”
— Harvard Heart of Gold , by Dustin Aguilar,
quoted here on April 24, 2015
For the dogs under the table, a note from that same date —
See as well Tom Wolfe on manifestos
and “the creative spirit.”
Continuing the "Memory, History, Geometry" theme
from yesterday …
See Tetrahedral, Oblivion, and Tetrahedral Oblivion.
"Welcome home, Jack."
Update, later the same day —
The sons of Earl Browder enjoyed greater academic success later
in the twentieth century:
See Exercise in this journal.
Happy birthday to Pope Francis.
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
From this journal on Dec. 12, the date of the bishop's death —
"Ordinary life and daily work are paths to sanctity . . . ."
Close enough.
Two deaths on Tuesday, Dec. 13, 2016 —
In memory of game show figure Alan Thicke —
In memory of game theory author Thomas Schelling —
Barbara Rose in a Log24 search for Princeton + Art.
John Updike on Don DeLillo's thirteenth novel, Cosmopolis —
" DeLillo’s post-Christian search for 'an order at some deep level'
has brought him to global computerization:
'the zero-oneness of the world, the digital imperative . . . . ' "
— The New Yorker , issue dated March 31, 2003
On that date ….
Related remark —
" 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
Annals of Entertainment …
Earlier …
Even earlier (and more seriously) …
"It's been three long years" — Tony Orlando
The above link leads to Log24 posts that mention
the late British author Colin Wilson, whose obituary
appeared in The New York Times on this date in 2013.
A date which would perhaps be considered more relevant
by Wilson himself is that of his death, Dec. 5, 2013.
See this journal on that date.
Thirty-year medallion from
Alcoholics Anonymous —
Error Icon —
Context —
The title is from a post of last Thursday afternoon — Dec. 8, 2016.
An image from that post appeared here last year —
See also philosophy notes from Infinite Jest .
Some backstory —
"… were it not that I have bad dreams" — Hamlet
See references in this journal to
"Nightmare Alley" and "Damnation Morning."
Tony Stark's "little gray area" remark to Peter Parker
in the previous post suggests an elementary calculation:
Compare to a remark from Wikipedia:
"This is the total area of
the 88 modern constellations
in the sky."
— Wikipedia, Square degree
"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 Hudson of the title is the author of Kummer's Quartic Surface (1905).
The Rosenhain of the title is the author for whom Hudson's 4×4 diagrams
of "Rosenhain tetrads" are named. For the "complexity to simplicity" of
the title, see Roger Fry in the previous post.
Cézanne "showed how it was possible to pass
from the complexity of the appearance of things
to the geometrical simplicity which design demands."
— Roger Fry in the catalogue for the 1910 London
exhibition "Manet and the Post-Impressionists,"
according to …
See also A Roger Fry Reader
(edited by Christopher Reed,
University of Chicago Press, 1996).
Images from Burkard Polster's Geometrical Picture Book —
See as well in this journal the large Desargues configuration, with
15 points and 20 lines instead of 10 points and 10 lines as above.
Exercise: Can the large Desargues configuration be formed
by adding 5 points and 10 lines to the above Polster model
of the small configuration in such a way as to preserve
the small-configuration model's striking symmetry?
(Note: The related figure below from May 21, 2014, is not
necessarily very helpful. Try the Wolfram Demonstrations
model, which requires a free player download.)
Labeling the Tetrahedral Model (Click to enlarge) —
Related folk etymology (see point a above) —
Related literature —
The concept of "fire in the center" at The New Yorker ,
issue dated December 12, 2016, on pages 38-39 in the
poem by Marsha de la O titled "A Natural History of Light."
Cézanne's Greetings.
See Ballet Blanc in this journal.
For a darker perspective, click on the image below.
See also Cartier in The Hexagon of Opposition.
Happy birthday to Kirk Douglas.
"Bad news on the doorstep…." — American Pie
Update of 5:24 PM ET — A requiem chord —
|
Tom Stoppard, Jumpers —
“Heaven, how can I believe in Heaven?” “Just a lying rhyme for seven!” |
Perhaps.
The title is that of a presentation by Arnold Emch
at the 1928 International Congress of Mathematicians:
See also yesterday's "Emch as a Forerunner of S(5, 8, 24)."
Related material: Diamond Theory in 1937.
Further remarks: Christmas 2013 and the fact that
759 × 322,560 = the order of the large Mathieu group M24 .
For a concise historical summary of the interplay between
the geometry of an 8-set and that of a 16-set that is
involved in the the Miracle Octad Generator approach
to the large Mathieu group M24, see Section 2 of …
Alan R. Prince
A near projective plane of order 6 (pp. 97-105)
Innovations in Incidence Geometry
Volume 13 (Spring/Fall 2013).
This interplay, notably discussed by Conwell and
by Edge, involves spreads and Conwell’s heptads .
Update, morning of the following day (7:07 ET) — related material:
See also “56 spreads” in this journal.
Commentary —
|
"The close relationships between group theory and structural combinatorics go back well over a century. Given a combinatorial object, it is natural to consider its automorphism group. Conversely, given a group, there may be a nice object upon which it acts. If the group is given as a group of permutations of some set, it is natural to try to regard the elements of that set as the points of some structure which can be at least partially visualized. For example, in 1861 Mathieu… discovered five multiply transitive permutation groups. These were constructed as groups of permutations of 11, 12, 22, 23 or 24 points, by means of detailed calculations. In a little-known 1931 paper of Carmichael [5], they were first observed to be automorphism groups of exquisite finite geometries. This fact was rediscovered soon afterwards by Witt [11], who provided direct constructions for the groups and then the geometries. It is now more customary to construct first the designs, and then the groups…."
5. R. D. Carmichael, Tactical configurations of rank two,
11. E. Witt, Die 5-fach transitiven Gruppen von Mathieu,
— William M. Kantor, book review (pdf), |
"It was only the genius of Ramanujan
that could transmute the handicaps
of colonialism into a triumph."
— See more at:
http://www.3quarksdaily.com/3quarksdaily/2011/01/
the-use-and-misuse-of-srinivasa-ramanujan.html
Related material:
"The dramatic irony is tragically strong with this one."
— A line from …
|
‘Harry Potter’: Who Is BY KAYTI BURT AUGUST 1, 2016 |
Harry Potter with the lightning-bolt scar:
See also "Lumber Room" in this journal.
For "the Trojan family" —
Related material on the late Solomon W. Golomb —
"While at JPL, Sol had also been teaching some classes
at the nearby universities: Caltech, USC and UCLA. In
the fall of 1962, following some changes at JPL—and
perhaps because he wanted to spend more time with
his young children— he decided to become a full-time
professor. He got offers from all three schools. He
wanted to go somewhere where he could 'make
a difference'. He was told that at Caltech 'no one has
any influence if they don’t at least have a Nobel Prize',
while at UCLA 'the UC bureaucracy is such that no one
ever has any ability to affect anything'. The result was
that—despite its much-inferior reputation at the time—
Sol chose USC. He went there in the spring of 1963 as
a Professor of Electrical Engineering—and ended up
staying for 53 years." — Stephen Wolfram, 5/25/16
See also Priority (Nov. 25) and "What's in a Name" (Dec. 1).
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.
The New York Times 's online T Magazine yesterday —
"A version of this article appears in print on December 4, 2016, on page
M263 of T Magazine with the headline: The Year of Magical Thinking."
* Thanks to Emily Witt for inadvertently publicizing the
Miracle Octad Generator of R. T. Curtis, which
summarizes the 759 octads found in the large Witt design.
An image search today for
"Design Cube" + Cullinane:
Click to enlarge (5.3 MB) —
* For the title, see St. Andrew's Day.
http://m759.net/wordpress/?s="Correlation"
http://m759.net/wordpress/?tag=correlative
Related literary reference —
"The only way of expressing emotion in the form of art
is by finding an 'objective correlative'; in other words,
a set of objects, a situation, a chain of events which
shall be the formula of that particular emotion; such that
when the external facts, which must terminate in sensory
experience, are given, the emotion is immediately evoked.
If you examine any of Shakespeare’s more successful
tragedies, you will find this exact equivalence…."
— T. S. Eliot, "Hamlet and His Problems" (1919)
"Frye's largely imaginary eightfold roman
may have provided him a personal substitute—
or alternative— for both ideology and myth."
— P. 63 of 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
See also today's earlier post In Nuce .
From "Northrop Frye at Home and Abroad: His Ideas,"
by Jean O'Grady —
"Frye always denied the accusation that
he was trying to make everyone accept
his whole ‘system’ like a straightjacket;
he remarked to an interviewer that perhaps
he would ultimately be found less useful as a
systemizer than as a quarry for later thinkers,
'a kind of lumber-room for later generations…
a resource person for anyone to explore and
get ideas from.' "
From Wikipedia's Lumber Room article —
"The phrase 'lumber room' is found in British fiction
at least during the 19th century …. Probably one of
the most evocative references is the short story by
'Saki' (H. H. Munro) called 'The Lumber Room':
'Often and often Nicholas had pictured to himself
what the lumber-room might be like, that region
that was so carefully sealed from youthful eyes
and concerning which no questions were ever answered.
It came up to his expectations. In the first place it was large
and dimly lit, one high window opening on to the forbidden
garden being its only source of illumination. In the second
place it was a storehouse of unimagined treasures.' "
See also Two by Four in this journal.
|
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 — |
Click here to enlarge.
Update of 4:00 PM —
See also this journal on Sunday morning and
Bill Murray's "Razor's Edge."
Or: A Candle for Sunrise
Commentary —
“Looking carefully at Golay’s code is like staring into the sun.”
Or: Notes for the Metaphysical Club
Northrop Frye on Wallace Stevens:
"He… stands in contrast to the the dualistic
approach of Eliot, who so often speaks of poetry
as though it were an emotional and sensational
soul looking for a 'correlative' skeleton of
thought to be provided by a philosopher, a
Cartesian ghost trying to find a machine that
will fit."
Ralph Waldo Emerson on "vacant and vain" knowledge:
"The new position of the advancing man has all
the powers of the old, yet has them all new. It
carries in its bosom all the energies of the past,
yet is itself an exhalation of the morning. I cast
away in this new moment all my once hoarded
knowledge, as vacant and vain."
Harold Bloom on Emerson:
"Emerson may not have invented the American
Sublime, yet he took eternal possession of it."
Wallace Stevens on the American Sublime:
"And the sublime comes down
To the spirit itself,
The spirit and space,
The empty spirit
In vacant space."
A founding member of the Metaphysical Club:
See also the eightfold cube.
A passage quoted here Wednesday, Nov. 23 —
The exploding cigar and peanut-can snake of the previous post
suggest that the source of the above "series of surprises"
be made clear. It is not Stevens, but Emerson.
Related material from this journal —
Before the monograph "Diamond Theory" was distributed in 1976,
two (at least) notable figures were published that illustrate
symmetry properties of the 4×4 square:
Hudson in 1905 —
Golomb in 1967 —
It is also likely that some figures illustrating Walsh functions as
two-color square arrays were published prior to 1976.
Update of Dec. 7, 2016 —
The earlier 1950's diagrams of Veitch and Karnaugh used the
1's and 0's of Boole, not those of Galois.
See Bonanza and Magnificent Seven in this journal.
* Al Caiola, who reportedly died on November 9th.
This journal at 11:48 PM ET Sunday, Nov. 20, 2016 —
The New York Times online this evening* —
* On the New York Times Wire at 8:29 PM ET.
Cover: Night at the Brooklyn Bridge
From the American Mathematical Society (AMS) webpage today —
From the current AMS Notices —
Related material from a post of Aug. 6, 2014 —
(Here "five point sets" should be "five-point sets.")
From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens 54, 59-79 (1992):
“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”
The above symplectic structure* now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).
* The phrase as used here is a deliberate
abuse of language . For the real definition of
“symplectic structure,” see (for instance)
“Symplectic Geometry,” by Ana Cannas da Silva
(article written for Handbook of Differential
Geometry , Vol 2.) To establish that the above
figure is indeed symplectic , see the post
Zero System of July 31, 2014.
See "sacerdotal jargon" in this journal.
For those who prefer scientific jargon —
"… open its reading to
combinational possibilities
outside its larger narrative flow.
The particulars of attention,
whether subjective or objective,
are unshackled through form,
and offered as a relational matrix …."
— Kent Johnson in a 1993 essay
For some science that is not just jargon, see …
and, also from posts tagged Dirac and Geometry …
The above line complex also illustrates an outer automorphism
of the symmetric group S6. See last Thursday's post "Rotman and
the Outer Automorphism."
See also "Both Hands and an Ass Map"
in posts tagged "Academy Map."
From "Kafka: An End or a Beginning?"
by Morten Høi Jensen
in Los Angeles Review of Books ,
November 19, 2016 —
From a New York Times obit for a music producer who reportedly
died on Tuesday, November 15, 2016 —
"He also produced … the Starland Vocal Band’s No. 1 hit,
'Afternoon Delight' (1976), and conducted Rabbi Shlomo Carlebach,
and the orchestra that accompanied him, on his album
'Haneshama Lach' (1959)." — Daniel E. Slotnik
See as well …
and …
"The high-end diamond game is played
on a very small field by only a few players."
— Matthew Hart in Vanity Fair , Sept. 2016 issue
Alicia Vikander and Matt Damon in "Jason Bourne" (2016).
The linked-to trailer was uploaded on April 20, 2016.
For related entertainment, see posts of April 2016…
in particular, those related to the April 20 death of
"Diamonds Are Forever" director Guy Hamilton.
This post's title is that of a book by Marshall McLuhan,
Through the Vanishing Point: Space in Poetry and Painting .
From a post of 6 PM yesterday —
Click image to enlarge.
From the Web —
" The mystical school of thought came to be known as
Kabbalah , from the Hebrew root Qof-Beit-Lamed ,
meaning 'to receive, to accept.' The word is usually
translated as 'tradition.' " — Judaism 101
Gruber reportedly died yesterday — November 17, 2016.
This is a followup to Tuesday's post on the Nov. 15 American
Mathematical Society (AMS) obituary of Joseph J. Rotman.
Detail of a page in "Notes on Finite Geometry, 1978-1986,"
"An outer automorphism of S6 related to M24" —
Related work of Rotman —
"Outer Automorphisms of S6," by
Gerald Janusz and Joseph Rotman,
The American Mathematical Monthly ,
Vol. 89, No. 6 (Jun. – Jul., 1982), pp. 407-410
Some background —
"In a Nutshell: The Seed," Log24 post of Sept. 4, 2006:
Lines for a late cellist —
For a different sort of quartet,
see "Arrowy, Still Strings."
See also this journal ten years ago.
The obituary linked to by the American Mathematical Society today
is a brief funeral-home summary.
A more complete account of Rotman's life, on the occasion of his
retirement, appeared in an academic newsletter in the spring of 2004 —
(Click image to enlarge.)
See also Rotman in this journal.
The half-hour referred to here was from 12 PM ET
to 12:30 PM ET on Friday, April 4, 2014 …
12 PM at Log24 —
12:30 PM at Princeton —
The New York Times on an art lecturer who died on Nov. 9 —
She became a Vogue correspondent in postwar Paris
and worked for art magazines before starting her own,
the celebrated L’Oeil (The Eye).
See also Obituary Metaphysics from November 11th —
Three Log24 posts of April 5, 2014 —
… and, on that same date, three Facebook
posts from Clovis, CA.
See also the Log24 post of 7:13 AM ET
Saturday, November 12, 2016, which
contained only the following link —
(A post suggested by a Facebook page from Clovis, California)
See Elysian in this journal.
Related material — Shell Game in this journal.
Sewell is supposedly modeled on literary critic R. P. Blackmur.
For a quotation from Blackmur, see a post of June 1, 2006.
See "No Space or Time" in this journal and
the new trailer, starring Scarlett Johansson,
for "Ghost in the Shell."
Related philosophy — Search Log24 for "Trinity."
"… a place where there's no space or time …."
— Leon Russell, "A Song for You"
"And in the midst of the war is
the Place, outside space and time…."
The character who dies in the above scene was not
played by Robert Vaughn (also in the film), but by
Brad Dexter, who reportedly died on Dec. 12, 2002.
… Songwriter Leonard Cohen, who reportedly
died on November 7, 2016.
In memory of an art lecturer who reportedly died at 100
on Wednesday, November 9, 2016 —
"… an evening with Ms. Bernier was
a gateway to another realm."
— Robert D. McFadden,
New York Times online yesterday
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."
Click images for related material.
"After finishing high school in Miami,
Ms. Reno attended Cornell University,
graduating in 1960 with a degree in chemistry."
— The online New York Times today
An example that is blatantly not "just the facts," from a Cornell author
found via last midnight's link "Ghost Light" —
— David W. Henderson, Cornell University
On a renovation of Manhattan's Irish Repertory Theatre:
"Performances in the new space began on May 17, 2016."
This journal on May 17, 2016 —
Click the image below for a related story.
See also Cartesian Theatre, a post of April 19, 2004.
From The Cincinnati Kid , a 1963 novel
by Richard Jessup —
"Funeral services will be held Sunday at 2 p.m.
at Weil Funeral Home at 8350 Cornell Road….
Burial will follow the funeral service at the
United Jewish Cemetery in Walnut Hills."
"There'll be time enough for counting
when the dealing's done." — Kenny Rogers
Wikipedia— "The first Million Mask March occurred in 2013."
A check of the date of that march in this journal yields …
See as well, more generally, "Interpenetration" in this journal.
On a Thursday death in Cincinnati …
"At his death, Mr. Steiner was developing
a musical version of the movie 'Bull Durham.'
— William Grimes in tonight's online New York Times
Enjoy the show.
This post was suggested by …
A death last Sunday and a Harvard Crimson story today.
Related images —
From last Sunday …
From an author who reportedly died on Oct. 31 (Halloween) …
Adam Bernstein on the late singer Kay Starr:
"She also was widely considered a master of the blues,
drawing praise for her authenticity from Billie Holiday,
Dinah Washington, Lester Young and Basie singer
Jimmy Rushing, who once exclaimed that she had
'so much soul!' Along with Peggy Lee, she was one of
the few non-black vocalists who emphasized a blues
repertoire at the time. (Ms. Starr was three-quarters
American Indian and one-quarter Irish.)"
Commentary —
The Washington Post yesterday evening —
|
Kay Starr, ferociously expressive singer By Adam Bernstein November 3 at 8:01 PM Kay Starr, a ferociously expressive singer whose ability to infuse swing, pop and country songs with her own indelible, bluesy stamp made her one of the most admired recording artists of her generation, died Nov. 3 at her home in Los Angeles. She was 94. … |
Midrash —
Yesterday afternoon's post "Triple Cross" and …
(Continued … See the title in this journal, as well as Cube Bricks.)
Cube Bricks 1984 —
Related material —
Dirac and Geometry in this journal,
Kummer's Quartic Surface in this journal,
Nanavira Thera in this journal, and
The Razor's Edge and Nanavira Thera.
See as well Bill Murray's 1984 film "The Razor's Edge" …
Movie poster from 1984 —
"A thin line separates
love from hate,
success from failure,
life from death."
Three other dualities, from Nanavira Thera in 1959 —
"I find that there are, in every situation,
three independent dualities…."
(Click to enlarge.)
"So, how do we sift truth from belief? How do we write
our own histories, personally or culturally, and thereby
define ourselves? How do we penetrate years, centuries,
of historical distortion to find original truth? Tonight, this
will be our quest."
— Robert Langdon, symbologist, in "The Da Vinci Code."
"… in Spain. There they are robes worn by priests."
— Langdon, op. cit.
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