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. …
Friday, December 9, 2016
… As opposed to —
A Nov. 9 panel from the Mahindra Humanities Center at Harvard
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.
Thursday, December 8, 2016
"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!”
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 .
Wednesday, December 7, 2016
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 …
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.
"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 , they were first observed to be automorphism groups of exquisite finite geometries. This fact was rediscovered soon afterwards by Witt , 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),
Tuesday, December 6, 2016
"It was only the genius of Ramanujan
that could transmute the handicaps
of colonialism into a triumph."
Monday, December 5, 2016
Update of 10:45 PM ET the same day —
See posts now tagged Sublime. Happy birthday, General Custer.
Sunday, December 4, 2016
Interpenetration of Opposites
See also "Interpenetration" in this journal.
Saturday, December 3, 2016
"The dramatic irony is tragically strong with this one."
— A line from …
BY KAYTI BURT AUGUST 1, 2016
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
Friday, December 2, 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."|
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."
An image search today for
"Design Cube" + Cullinane:
Click to enlarge (5.3 MB) —
* For the title, see St. Andrew's Day.
Thursday, December 1, 2016
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…."
Wednesday, November 30, 2016
"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 —
Tuesday, November 29, 2016
Monday, November 28, 2016
Click here to enlarge.
Update of 4:00 PM —
Or: A Candle for Sunrise
“Looking carefully at Golay’s code is like staring into the sun.”
Sunday, November 27, 2016
Or: Notes for the Metaphysical Club
"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
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.
Saturday, November 26, 2016
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.
Friday, November 25, 2016
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.
Thursday, November 24, 2016
* Al Caiola, who reportedly died on November 9th.
Wednesday, November 23, 2016
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.
Tuesday, November 22, 2016
See "sacerdotal jargon" in this journal.
For those who prefer scientific jargon —
"… open its reading to
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."
Monday, November 21, 2016
Detail of a note from 7/11, 1986
Backstory: Notes on Groups and Geometry, 1978-1986.
See also "Both Hands and an Ass Map"
in posts tagged "Academy Map."
Sunday, November 20, 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 …
Saturday, November 19, 2016
"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
For related entertainment, see posts of April 2016…
in particular, those related to the April 20 death of
"Diamonds Are Forever" director Guy Hamilton.
Friday, November 18, 2016
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.
Thursday, 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:
Wednesday, November 16, 2016
Lines for a late cellist —
For a different sort of quartet,
see "Arrowy, Still Strings."
See also this journal ten years ago.
Tuesday, November 15, 2016
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 —
Monday, November 14, 2016
(A post suggested by a Facebook page from Clovis, California)
See Elysian in this journal.
Related material — Shell Game in this journal.
See also Solomon Marcus in this journal.
"Look out, kid, they keep it all hid." — Bob Dylan
Sunday, November 13, 2016
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…."
Saturday, November 12, 2016
Friday, November 11, 2016
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
Wednesday, November 9, 2016
Another opening, another show.
"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."
Monday, November 7, 2016
"After finishing high school in Miami,
Ms. Reno attended Cornell University,
graduating in 1960 with a degree in chemistry."
Sunday, November 6, 2016
"Performances in the new space began 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
Saturday, November 5, 2016
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.
Friday, November 4, 2016
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 …
Related images —
From last Sunday …
From an author who reportedly died on Oct. 31 (Halloween) …
"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.)"
The Washington Post yesterday evening —
By Adam Bernstein November 3 at 8:01 PM
Yesterday afternoon's post "Triple Cross" and …
Thursday, November 3, 2016
Cube Bricks 1984 —
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.)
Monday, October 31, 2016
Entertainment suggested by TV news tonight …
See as well some related humor.
"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."
"… in Spain. There they are robes worn by priests."
— Langdon, op. cit.
See also the previous post.
Sunday, October 30, 2016
Saturday, October 29, 2016
And tomorrow's New York Times
Scene from "Invasion of the Body Snatchers" included in
"The Living Dead," a 1995 BBC TV series by Adam Curtis —
"Several times, Curtis and I circled back to
the notion of the 'hyperobject' — that which
is too big in time and space to comprehend."
See as well the BBC TV series in the previous post, "Boo."
A scene from the 2014 BBC TV series “Intruders”
(Season 1, Episode 1, at 9:22 of 45 min.)
Friday, October 28, 2016
"Protection of digital content from being tapped by intruders is a crucial task in the present generation of Internet world. In this paper, we proposed an implementation of new visual secret sharing scheme for gray level images using diamond theorem correlation. A secret image has broken into 4 × 4 non overlapped blocks and patterns of diamond theorem are applied sequentially to ensure the secure image transmission. Separate diamond patterns are utilized to share the blocks of both odd and even sectors. Finally, the numerical results show that a novel secret shares are generated by using diamond theorem correlations. Histogram representations demonstrate the novelty of the proposed visual secret sharing scheme."
— "New visual secret sharing scheme for gray-level images using diamond theorem correlation pattern structure," by V. Harish, N. Rajesh Kumar, and N. R. Raajan.
Published in: 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT).
Related material — Posts tagged Diamond Theorem Correlation.
Thursday, October 27, 2016
Or: Pentagram Meets Counting-Pattern, Continued
Arts & Letters Daily today links to a Chronicle of Higher Education
piece on philosophy with an illustration by the late Paul Laffoley …
This suggests a review of Laffoley's work. In particular —
Wednesday, October 26, 2016
In memory of Jack T. Chick, 1924-2016.
Related material —
See also Log24 on the date of Chick's death.
Tuesday, October 25, 2016
Monday, October 24, 2016
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.
Sunday, October 23, 2016
From mathematician Izabella Laba today —
From Harry T. Antrim’s 1967 thesis on Eliot —
“That words can be made to reach across the void
left by the disappearance of God (and hence of all
Absolutes) and thereby reestablish some basis of
relation with forms existing outside the subjective
and ego-centered self has been one of the chief
concerns of the first half of the twentieth century.”
… And then there is the Snow White void —
A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —
The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).
“The man who lives in contact with what he believes to be a living Church
is a man always expecting to meet Plato and Shakespeare to-morrow
— G. K. Chesterton
Or Sunday dinner.
|Not to mention Euclid and Picasso.|
Saturday, October 22, 2016
From "The Magis way: Notes on the publishing culture,"
by Giampiero Bosoni, at http://www.magisdesign.com/magis-world/ —
"… perhaps it is interesting to reflect further on the relationship between a design object and a literary work, by reading (in whatever interpretative key you choose) the illuminating definition given by the great semiologist Roland Barthes of the act of writing and of the literary value of a text. 'Writing,' Barthes tells us, 'is historically an action that involves constant contradiction, based on dual expectations. One aspect of writing is essentially commercial, a means of control and segregation, steeped in the most materialistic aspect of society. The other is an act of pleasure, connected to the deepest urges of the body and to the subtlest and most successful products of art. This is how the written text is woven. All I have done is to arrange and reveal the threads. Now each can add his own warp to the weft.' 
Magis’ long and highly advanced experience has given evidence, further confirmed by this latest publishing catalogue, of an ever-growing awareness of this necessary interweaving between warp and weft, between the culture of craftsmanship and that of industry, between design culture and business culture, between form and technique, between symbolic codes and practical functions, between poetry and everyday life."
— Giampiero Bosoni
 Barthes R., Variations sur l’écriture (1972), Editions du Seuil, Paris 1994, published in the second volume of the Oeuvres complètes 1966-1975 (freely translated from the Italian translation, Variazioni sulla scrittura seguite da Il piacere del testo , Ossola C. (editor) Einaudi, Turin 1999).
See as well "Interweaving" in this journal.
"Design is how it works." — Steve Jobs
Friday, October 21, 2016
Thursday, October 20, 2016
Wednesday, October 19, 2016
A Meditation on Two Dates
The dates are October 14, 2016, the release date of
the new film "The Accountant" —
"… clearer, more economical and formal, more liturgical."
— David Remnick on lyrics of Leonard Cohen
vs. those of Bob Dylan, quoted here on Oct. 14
— and May 12, 2016, the publication date of
a YouTube trailer for "The Accountant."
Also quoted in the May 12 post —
See as well the Ape with Skull (Affe mit Schädel) statue in
the Oct. 17 post Memorial Encounter. The version of the statue
pictured there omits the inscription "ERITIS SICUT DEUS"
in a book at the statue's base. There are related remarks on
Mephistopheles and Faust at a different weblog.
Tuesday, October 18, 2016
The term "parametrization," as discussed in Wikipedia,
seems useful for describing labelings that are not, at least
at first glance, of a vector-space nature.
Examples: The labelings of a 4×4 array by a blank space
plus the 15 two-subsets of a six-set (Hudson, 1905) or by a
blank plus the 5 elements and the 10 two-subsets of a five-set
(derived in 2014 from a 1906 page by Whitehead), or by
a blank plus the 15 line diagrams of the diamond theorem.
Thus "parametrization" is apparently more general than
the word "coodinatization" used by Hermann Weyl —
“This is the relativity problem: to fix objectively
a class of equivalent coordinatizations and to
ascertain the group of transformations S
mediating between them.”
Note, however, that Weyl's definition of "coordinatization"
is not limited to vector-space coordinates. He describes it
as simply a mapping to a set of reproducible symbols .
(But Weyl does imply that these symbols should, like vector-space
coordinates, admit a group of transformations among themselves
that can be used to describe transformations of the point-space