Tuesday, February 28, 2017

Easy E for Cullinan*

Filed under: General — m759 @ 7:59 PM

See the "symbol of Apollo" in the previous post
as well as posts tagged on050730, and
Conrad H. Roth on "The E at Delphi."

* The now-famous Oscars accountant


Filed under: General — m759 @ 11:32 AM

Monday, February 27, 2017

Against Logic

Filed under: General — m759 @ 11:16 PM

The title is that of an essay by Rebecca Goldstein
in Tikkun  (Nov.-Dec. 1997).  An excerpt:

"… And so it was that I became an analytic philosopher.
If my story ended there, it would make sense.
But against logic, I also became a writer of fiction.
My hopeless passion for fiction had seemed to me,
in the days when I hung exclusively with philosophers,
a rather shameful little aberration. Plato had planned to
rid his utopia of the epic poets, who were the novelists
of his day. Fiction writers are enchanters, those who
spread their dreams abroad; and Plato— whom I still revere—
thoroughly disapproved of enchantment."

See also the previous post.

Logic for Jews

Filed under: General — Tags: — m759 @ 9:07 PM


Adam Gopnik in The New Yorker  today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —

"The implicit dread logic is plain."

Related material —

Transformers in this journal and

“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

See also

The above figure is from Ian Stewart's 1996 revision of a 1941 classic, 
What Is Mathematics? , by Richard Courant and Herbert Robbins.

One wonders how the confused slave boy of Plato's Meno  would react
to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Best Picture

Filed under: General — m759 @ 2:40 PM

From 'The Accountant,' a painting clip with Anna Kendrick

'Preparation,' a Log24 post of April 1, 2013

Tricky Business*

Filed under: General — m759 @ 12:45 AM

* For the title, see Sunday morning.

Sunday, February 26, 2017

Turn, Turn, Turn

Filed under: General — m759 @ 8:25 PM

In memory of a reported long-ago date

Poetic Order

Filed under: General,Geometry — Tags: — m759 @ 1:06 PM

Transformations acting on Solomon's Cube
furnish a model of poetic order.

Some backstory for Hollywood —

Hollywood analogue to Solomon's Cube in 'Transformers'

Transformers Meet Transformations

Filed under: General — m759 @ 10:30 AM

"Transformations , Anne Sexton’s 1971 collection of poems, is a portal."

— "A Poisonous Antidote," by Nick Ripatrazone, at themillions.com
      at noon on October 22, 2015

"You see, opening dimensional portals is a tricky business."

— The librarian in "Buffy the Vampire Slayer," season 1, episode 2

See also Transformers in this journal.


"Objective Quality" in this journal on the date of the above review,
October 22, 2015, at 2:26 AM ET.

Saturday, February 25, 2017

Crazy Stupid Love

Filed under: General — m759 @ 7:11 PM

Or:  Deep  Link

Thanks to The New York Times  for the "Love" title above —
the subtitle of today's Maureen Dowd column.

Dowd quotes a memorable phrase by another writer,
Lloyd Grove —

“King Lear meets Rodney Dangerfield.”

I prefer Rodney Crowell.

Click on Crowell for another old link, to remarks on
the poet Anne Sexton.

Ryman Religion

Filed under: General — m759 @ 6:29 PM

"Two Out of Three Ain't Bad" — Bat Out of Hell  album, Oct. 1977

Impact Statement

Filed under: General — m759 @ 5:29 PM

See also Kostant in this  journal and a link in a 
Log24 post Friday on another mathematical death —

Hollywood Easter Egg (Groundhog Day, 2017).

Groundhog Day was the day Kostant reportedly died.


Filed under: General — m759 @ 9:45 AM

"The deepest strain in a religion is
the particular and particularistic doctrine
it asserts at its heart,
in the company of such pronouncements as
‘Thou shalt have no other Gods before me.’
Take the deepest strain of religion away…
and what remains are the surface pieties — 
abstractions without substantive bite — 
to which everyone will assent
because they are empty, insipid, and safe."

— Stanley Fish, quoted here on July 3, 2007
The opening date of the film "Transformers."

The opening pronouncement of "Transformers" —

"Before time began, there was the Cube."

Those who prefer Fish's abstractions  may consult 
the previous post.

Friday, February 24, 2017

Abstract Configurations on Good Friday

Filed under: General,Geometry — m759 @ 9:16 PM

An arXiv article from Good Friday, 2003, by Igor Dolgachev,
a student of the late Igor Shafarevich (see previous post) —

See also my Dec. 29, 1986, query on Duality and Symmetry.

Getting It Right

Filed under: General — m759 @ 2:28 PM

From a webpage linked to here in the post 
"Outside the Box" (June 10, 2012).

"… the good news is that there are companies that do
get it right in the Russian market, even on the first try."

—  Chris Crowl, director of operations at TD International,
in a speech of 27 May 2010, "Russia: Getting It Right
the First Time." The quote is from a webpage that is
no longer online.

The above figure, Russian mathematician Igor Shafarevich,
reportedly died on Feb. 19, 2017. (See remarks in a Feb. 22 post
by Peter Woit at Not Even Wrong .)

An old post revisited here on Feb. 19, 2017, Shafarevich's
reported date of death

Related material —

Hollywood Easter Egg (Groundhog Day, 2017).

For Your Consideration

Filed under: General — Tags: , — m759 @ 12:25 AM

Hollywood, from the Alto Nido Apartments
to Sunset Boulevard —

From Alto Nido Apts. to Sunset Boulevard: Aerial view including Los Angeles Film School

See also the Jan. 31 post "Sunset Passion."

Thursday, February 23, 2017

Too Clever by Half

Filed under: General — m759 @ 9:48 PM

"What Yokoyama does in Six Four  evokes — improbably —
the fastidious ethical parsings of a novel by Henry James,
all qualms and calibrations, and while that might not sound
like a good idea, he makes it work. He writes, fortunately,
in plain, declarative prose (ably translated by Jonathan Lloyd-Davies),
and because Mikami is such an ordinary man the mental gymnastics
he puts himself through are moving and sometimes deeply funny.
A Jamesian police procedural — 'The Wings of the Perp,' maybe?
Not exactly. But this novel is a real, out-of-the-blue original.*
I’ve never read anything like it."

 — Terrence Rafferty in the online New York Times 
      on Tuesday, Feb. 21, 2017

Illustration from this journal on that date


See also the previous post, "Six Four."

Update of 10 PM ET Feb. 23, 2017 —

A pathetic asterisk for, and by, Rafferty —

* A passage from Rafferty's essay
in The New York Times  on July 27, 2003:

"…  the message is clearscreenwriters are pathetic.
You can hear, clearly, the voice of Joe Gillis,
describing himself from beyond his watery grave:
'Nobody important, really. Just a movie writer with
a couple of B pictures to his credit. The poor dope
.' "

See as well  this  journal on July 27, 2003.

Six Four

Filed under: General — m759 @ 9:00 PM

Key sentence meets key title …

The title, Six Four , of the book under review is more interesting than
either of the headlines assigned by the Times to the review itself.

For another mystery related to the numbers six and four, see
this  journal on Feb. 21.

Bullshit Studies

Filed under: General — Tags: , — m759 @ 1:21 PM


" The origin of new ways of doing things may often be
a disciplinary crisis. The definition of such a crisis
provided by Barry Mazur in Mykonos (2005) applies
equally well to literary creation. '[A crisis occurs] when
some established overarching framework, theoretical
vocabulary or procedure of thought is perceived as
inadequate in an essential way, or not meaning
what we think it means.' "

— Circles Disturbed :
The Interplay of Mathematics and Narrative

Edited by Apostolos Doxiadis & Barry Mazur
Princeton University Press, 2012. See
Chapter 14, Section 5.1, by Uri Margolin.

See also "overarching" in this journal.

Midnight Special

Filed under: General — m759 @ 12:00 AM

Click to enlarge:

See also, in this  journal, "Go Set a Structure,"
"Interior/Exterior," and "Midnight Special."


Wednesday, February 22, 2017


Filed under: General — m759 @ 11:00 PM

A memorable phrase —

"the transcendental horizon of the ‘I’."

For some backstory, see a Google search for

Marion + transcendental + horizon.

For a perhaps more intelligible horizon, see

Line at Infinity  in this journal.

A Dead Ringer

Filed under: General — m759 @ 1:00 PM

"According to Thelemic legend, in 1918 Aleister Crowley
came into contact with a interdimensional entity
named Lam, who by the way is a dead ringer for
the popular conception of the 'alien grey '
depicted on the cover of Whitley Strieber's Communion ."

Related material —

"Robert Langdon stood mesmerized at the glass portal,
absorbing the power of the landscape below him."


From 'Buffy the Vampire Slayer,' season 1, episode 2

"Ting-a-ling." — Kurt Vonnegut Jr.

Riddle for the Mall of America*

Filed under: General — m759 @ 11:16 AM

* See the film "The End of the Tour."

Tuesday, February 21, 2017

Arrow Economics

Filed under: General — m759 @ 11:29 PM

Broken Symmetries  in  Diamond Space 

Goldstein’s Asterisk

Filed under: General — m759 @ 10:30 PM

"… a pathetic asterisk of condescension" — Steven Goldstein

See also the Vonnegut asterisk in this journal.

Zen and the Art

Filed under: General — m759 @ 12:12 PM

From today's print version of the New York Times —

“He eliminates anything that’s not essential
from the face of this little rabbit until it’s really
reduced to the absolute minimum,”
Mr. Dibbits said. “And he does the same for
the text of his children’s books. He uses a
language that’s not simple or stupid, but he
reduces to the bare essentials.”

About his own work, Mr. Bruna once said,
“I spend a long time making my drawings
as simple as possible, throwing lots away,
before I reach that moment of recognition.”
He added, “I leave plenty of space for children’s

The result is a series of “Zen-like” tales,
Ms. Vogt said, “and that’s also part of the
universal appeal.”

The passage above is from an obituary for an artist who
reportedly died on Feb. 16.

See also, in this journal, "How deep the rabbit hole goes."

Tetradion …

Filed under: General,Geometry — m759 @ 10:09 AM

Also known as quaternion —

"Diagram of an 8 leaf gathering: Quaternion (8 folio or leaf gathering).
A quaternion is composed of 4 bifolios. Conjugate folios form a bifolio
at either end of a gathering or quire. So in the diagram above folios
1 and 8 which form a bifolio are conjugate folios."

— http://employees.oneonta.edu/farberas/arth/arth214_folder/workshop.htm

The source:

SUNY Oneonta

ARTH 214
History of Northern Renaissance Art
Spring, 2013

Dr. Allen Farber, Associate Professor

Tuesday, February 26: From Workshop to Chamber:
The Paris Book Industry of the Early Fifteenth Century

"Images for class" folder 


An image from Publication, a Log24 post on the above date, 

Feb. 26, 2013 —

Monday, February 20, 2017


Filed under: General — Tags: — m759 @ 10:31 PM

Wiktionary —

тетра́дь   (tetrádʹ)  f  inan 
(genitive  тетра́ди
nominative plural  тетра́ди
genitive plural  тетра́дей)


Borrowing from Ancient Greek τετράδιον  ‎(tetrádion, 
“quaternion of parchment”), from τετράς  ‎(tetrás),


  1.  exercise book, notebook

See also Tetrad in this journal.

Mathematics and Narrative

Filed under: General,Geometry — Tags: , — m759 @ 2:40 PM

Mathematics —

Hudson's parametrization of the
4×4 square, published in 1905:

A later parametrization, from this date in 1986:


A note from later in 1986 shows the equivalence of these
two parametrizations:

Narrative —

Posts tagged Memory-History-Geometry.

The mathematically challenged may prefer the narrative of the
Creation Matrix from the religion of the Transformers:

"According to religious legend, the core of the Matrix
was created from Solomus, the god of wisdom,
trapped in the form of a crystal by Mortilus, the god
of death. Following the defeat of Mortilus, Solomus
managed to transform his crystal prison into the Matrix—
a conduit for the energies of Primus, who had himself
transformed into the life-giving computer Vector Sigma."

At 3:33*

Filed under: General — Tags: — m759 @ 3:33 AM

* A reference to a line in a poem in a novel
by Katherine Neville, The Eight  (1988)

Sunday, February 19, 2017


Filed under: General — Tags: — m759 @ 7:14 PM

"La morte è avvenuta alle 22.30 di ieri sera nella sua abitazione."
— http://www.repubblica.it/cultura/2016/02/20/news/

See also the previous post, "Radical."


Filed under: General,Geometry — m759 @ 6:17 PM

Book from 1969 by the late Michael Novak

Science demonstrator in Boston today —

See as well Galois Imaginary in this journal.

So I called up the Captain, "Please bring me my wine"
He said, "We haven't had that spirit here since 1969"

Ships That Pass in the Night

Filed under: General — m759 @ 11:00 AM

… Namely,  Scholarship  and  Showmanship  (previous post)

"The suffix '-schaft '  (cognate with the English '-ship ')
can be added to nouns…."

— http://www.dartmouth.edu/~deutsch/

For instance —

"… I’d rely on the old sociological distinction between gemeinschaft  and gesellschaft . All across the world, we have masses of voters who live in a world of gemeinschaft : where relationships are personal, organic and fused by particular affections. These people define their loyalty to community, faith and nation in personal, in-the-gut sort of ways.

But we have a leadership class and an experience of globalization that is from the world of gesellschaft : where systems are impersonal, rule based, abstract, indirect and formal."

— David Brooks, New York Times  columnist, Jan. 20, 2017

The Lost Well

Filed under: General — m759 @ 9:45 AM

Eight years ago yesterday —

Saturday, February 18, 2017

Not Strange Enough?

Filed under: General,Geometry — m759 @ 7:59 PM

Peter Woit today discusses a book by one Zeeya Merali:

Some earlier remarks by Merali:

Zeeya Merali in Nature  on 28 August 2013

"… a small band of researchers who think that
the usual ideas are not yet strange enough.
If nothing else, they say, neither of the two great
pillars of modern physics — general relativity,
which describes gravity as a curvature of space
and time, and quantum mechanics, which governs
the atomic realm — gives any account for
the existence of space and time.

. . . .

'All our experiences tell us we shouldn't have two
dramatically different conceptions of reality —
there must be one huge overarching theory,' says
Abhay Ashtekar, a physicist at Pennsylvania State
University in University Park."

See as well Overarching and Doctor Strange in this  journal.

Solid Symmetry (continued)

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

See Hanks + Cube in this journal For instance

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

See Cube Symbology.

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Da hats ein Eck 

Fluid Requiem

Filed under: General — m759 @ 11:45 AM

Remarks on fluidity and lucrative ventures in
yesterday evening's post Transformers suggest
a reading in memory of a Catholic philosopher
who reportedly died yesterday at 83 —

Psalm 22:  "I am poured out like water . . . ."


Filed under: General — m759 @ 11:00 AM

The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.


Filed under: General,Geometry — Tags: — m759 @ 3:00 AM

The Log24 version  (Nov. 9, 2005, and later posts) —



Escher's 'Verbum'

Escher's Verbum

Solomon's Cube

Solomon's Cube

I Ching hexagrams as parts of 4x4x4 cube

Geometry of the I Ching

The Warner Brothers version

The Paramount version

See also related material in the previous post, Transformers.

Friday, February 17, 2017


Filed under: General — m759 @ 9:00 PM

Accentuating the positive —

"Among Mr. Grey’s accomplishments is
the enormously lucrative “Transformers” franchise;
a new installment is scheduled for this summer."

See as well (Click to enlarge. . .



Filed under: General — m759 @ 7:00 PM

Steve Martin on his character Ray Porter 
in the novella Shopgirl  —


"He said, 'I wrote a piece of code
 that they just can’t seem to do without.'
 He was a symbolic logician. That was his career…."

"In short, he seeks to objectify crucial areas . . . ."

Or crucify objective areas.

Kostant Is Dead

Filed under: General,Geometry — Tags: — m759 @ 1:10 PM

"Bertram Kostant, professor emeritus of mathematics at MIT,
died at the Hebrew Senior Rehabilitation Center in Roslindale,
Massachusetts, on Thursday, Feb. 2, at the age of 88."

MIT News, story dated Feb. 16, 2017

See also a search for Kostant in this journal.

Regarding the discussions of symmetries and "facets" found in
that search —


A word about E(8). In my opinion, and shared by others,
E(8) is the most magnificent ‘object’ in all of mathematics.
It is like a diamond with thousands of facets. Each facet
offering a different view of its unbelievable intricate internal


In the Steiner system S(5, 8, 24) each octad might be
regarded as a "facet," with the order of the system's
automorphism group, the Mathieu group M24 , obtained
by multiplying the number of such facets, 759, by the
order of the octad stabilizer group, 322,560. 


Platonic solids' symmetry groups   

The Unreliable Reader

Filed under: General — m759 @ 12:21 PM

Continued from "Religion at Harvard,"  May 7, 2010 —

The Unreliable Narrator meets The Unreliable Reader
Aaron Diaz at Dresden Codak

"The warnings come after  the spells." — Doctor Strange

Fake News: The Definition

Filed under: General — m759 @ 11:15 AM

See also, on Feb. 8 in this journal, Damning.

Fear and Loathing at The New Yorker

Filed under: General — m759 @ 9:45 AM

See also Gopnik in this journal.

Heptads and Heptapods

Filed under: General,Geometry — m759 @ 12:00 AM

In the recent science fiction film "Arrival," Amy Adams portrays
a linguist, Louise Banks, who must learn to translate the language of
aliens ("Heptapods") who have just arrived in their spaceships.

The point of this tale seems to have something to do with Banks
learning, along with the aliens' language, their skill of seeing into
the future.

Louise Banks wannabes might enjoy the works of one
Metod Saniga, who thinks that finite geometry might have
something to do with perceptions of time.

See Metod Saniga, “Algebraic Geometry: A Tool for Resolving
the Enigma of Time?”, in R. Buccheri, V. Di Gesù and M. Saniga (eds.), 
Studies on the Structure of Time: From Physics to Psycho(patho)logy,
Kluwer Academic / Plenum Publishers, New York, 2000, pp. 137–166.
Available online at www.ta3.sk/~msaniga/pub/ftp/mathpsych.pdf .

Although I share an interest in finite geometry with Saniga —
see, for instance, his remarks on Conwell heptads in the previous post
and my own remarks in yesterday's post "Schoolgirls and Heptads" —
I do not endorse his temporal speculations.

Thursday, February 16, 2017

Nested Projective Structures

Filed under: General,Geometry — m759 @ 11:00 PM

Two views of nested sequences of projective structures —

From this journal in April 2013:

From the arXiv in September 2014

Saniga's reference [6] is to a paper submitted to the arXiv in May 2014. 

My own note of April 30, 2013, concludes with an historical reference
that indicates the mathematics underlying both my own and Saniga's
remarks —

The exercises at the end of Ch. II in Veblen and Young's 
Projective Geometry, Vol. I  (Ginn, 1910). For instance:

Against Bewitchment

Filed under: General — m759 @ 9:00 PM

(Continued from February 5, 2016)

Related material — the Feb. 5 death
of the above music figure David Axelrod.

See "Against Bewitchment" in this journal
on that date.

"Talkin' 'bout strange " — Lou Rawls
(See posts from the date of Rawls's death.)

Crimson Divinity

Filed under: General — m759 @ 12:12 PM

See also the Harvard University Press
webpage for Colors of the Mind —

Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book…  aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.

. . . .

Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s

Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.

Schoolgirls and Heptads

Filed under: General,Geometry — m759 @ 11:32 AM

A Feb. 12 note in the "talk" section of the Wikipedia article
"Kirkman's schoolgirl problem" —

The illustration above was replaced by a new section in the article,
titled "Galois geometry."

The new section improves the article by giving it greater depth.  
For related material, see Conwell Heptads in this journal
(or, more generally, Conwell) and a 1985 note citing Conwell's work.

Wednesday, February 15, 2017

Companion to Dante*

Filed under: General — m759 @ 10:00 PM

Commentary on Inferno ,  Canto XVI,  line 84 —

* " when it pleases you to say 'I was' " —

See also a 1992 poem by Thomas Lux.

Warp and Woof

Filed under: General,Geometry — m759 @ 3:00 PM

Space —

Space structure —

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….”

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

The above symplectic  figure appears in remarks on
the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

Space shuttle —

Related ethnic remarks —

As opposed to Michael  Larsen —

Funny, you don't look  Danish.

For Your Consideration

Filed under: General — m759 @ 2:02 PM

Related material —

"The warnings come after  the spells.”
— Doctor Stephen Strange

Tuesday, February 14, 2017

Bee Season Continued

Filed under: General — m759 @ 11:55 PM

“Spells are used for breaking enchantments as well as for inducing them.”

— C. S. Lewis, quoted here during November 2005.

A review of that month was suggested by the following search

Related to 'Bee Season' posts — 'Sefer Yetzirah'+ 'Cube' search result

which itself was suggested by an obituary in tonight’s online
New York Times  and by this morning’s post “Rhyme.”


Filed under: General,Geometry — m759 @ 11:00 AM

For the late poet Thomas Lux ,
who reportedly died on February 5 
(See posts tagged Bewitchment) —

"A darker riddle with no answer looms . . . .
For those who linger on among the tombs"

John Hollander, from a poem in A Draft of Light

Those who enjoy dark riddles with no answers
may search the Web for "Sefer Yetzirah" + Cube.

I prefer a purely mathematical approach to the cube.

Monday, February 13, 2017

Soundtracked Meets Sidetracked

Filed under: General — Tags: — m759 @ 9:07 PM

'Currently back in 1983' Tweet from Feb. 1, 2017

I was sidetracked by this peculiar Tweet after a search for
fictions titled "The Weaver's Tale." 

A version of the tale that I liked had led to the author's Twitter account
and the above remarks, dated 1 Feb. 2017.

That Tweet date led in turn to Log24 posts now tagged Heinlein Lottery.


“The Echo in Plato’s Cave” Continues.

Filed under: General — m759 @ 1:00 PM

The previous post, "Colorful Tales," on the Nov. 28, 2016, death
of one Angus Fletcher, together with the remarks indexed above,
suggest a review from 

The archives of The New York Times  —

Literature as a Way of Life

By Harold Bloom
357 pp. Yale University Press. $32.50.

Sam Tanenhaus is the editor of the Book Review.

A version of this review appeared in print
on May 22, 2011, on Page BR1 of the 
Sunday Book Review with the headline:
'An Uncommon Reader.'"

"By this time, Bloom had burrowed into a cave,
its lamplit forms and shapes merging into
an occult mythos scarcely intelligible
even to other scholars. 'Bloom had an idea,' 
Christopher Ricks said; 'now the idea has him.' 
Cynthia Ozick, meanwhile, called him an 'idol-maker.' 
In contrast to Cleanth Brooks . . . ."

An illustration from "The Echo in Plato's Cave" linked to
in the previous post


Judy Davis in the Marabar Caves

Cynthia Ozick on Bloom —

See also Dharwadker in the previous post and on the Higgs boson.

Sunday, February 12, 2017

Colorful Tales

Filed under: General — m759 @ 1:23 PM

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination  and Colors of the Mind

From the Harvard webpage for Colors of the Mind

Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book…  aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.

. . . .

Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s

Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.

A 1992 review by Vinay Dharwadker of Colors of the Mind —

See also the above word "dianoia" in The Echo in Plato's Cave.
Some context 

This post was suggested by a memorial piece today in
the Los Angeles Review of Books

A Florilegium for Angus Fletcher

By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood

Fletcher reportedly died on November 28, 2016.

"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."

— Harold Bloom in today's Los Angeles florilegium

For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.

Some backstory:  Dharwadker in this journal.

Religious Art for Sunday

Filed under: General,Geometry — m759 @ 11:02 AM

Euclidean  square and triangle

Galois  square and triangle

For some backstory, see the "preface" of the 
previous post and Soifer in this journal.

Saturday, February 11, 2017

Ultima Thule

Filed under: General — m759 @ 9:30 PM

"Skip the preface, and it's in the bag!"

— Character in a short story by Nabokov,
"Ultima Thule," in The New Yorker  of April 7, 1973

Recreational Logic

Filed under: General — m759 @ 2:40 PM

Smullyan reportedly died on Monday, February 6, 2017. 

This journal on that date

Sixteenth-century alchemist in a novel by Balzac —

"If we eliminate God from this world, sire,
what remains? Man! Let us examine our domain."

The God Identity

Filed under: General — Tags: , — m759 @ 1:00 PM

The previous post suggests a related concept, in which
"I Am that I Am" is replaced by "I am as  I am." —

The Quantum Identity

Filed under: General — m759 @ 12:45 PM

The title was suggested by the previous post and by
the novels of Harlan Kane.

Artistic Signifier

Filed under: General — m759 @ 1:58 AM

RSS feed screenshot of 1:53 AM ET today —

'Step aside, beauty and truth... Art's new  alpha and omega is identity.'

Norwegian Identity

Filed under: General — m759 @ 1:30 AM

"Siri Hustvedt is an award-winning and versatile American
writer and essayist. She earned her PhD in Literature at
Columbia University in 1986. She often points to her
Norwegian family background in her works, and she is
known as one of the foremost interpreters of Norwegian-
American identity in English literature."

— University of Oslo,
     "Siri Hustvedt: Honorary doctor 2014"

IMAGE- 'Siri Hustvedt Interview: Fakes and Fiction'

See also Hustvedt in this journal.

Friday, February 10, 2017

In Memoriam

Filed under: General — Tags: — m759 @ 1:22 PM

Harald S. Naess, a professor retired from the University of
Wisconsin-Madison, where he was the local authority on Norway,
reportedly died Sunday in Kristiansand, Norway, where he grew up.
He was 91. His academic specialty was the works and letters of
Knut Hamsun.

See posts from the date of Naess's death now tagged Bewitchment.

See also a Log24 post that mentions Kristiansand.

The Times’s Stone

Filed under: General — m759 @ 12:00 AM

See also the previous post.

Thursday, February 9, 2017

The Stone

Filed under: General — m759 @ 11:00 PM

See also other news on that date.

Conspiracy Theory

Filed under: General — m759 @ 10:45 PM

See also Jeremiah Denton in Wikipedia.

Those for whom entertainment is God
may enjoy a film based on a book by Denton, 
"When Hell Was in Session," starring
Hal Holbrook and Eva Marie Saint.

Denton reportedly died on March 28, 2014.
See a Log24 post from that date, "Blazing Thule."

"You've got to pick up every stitch." — Donovan


Filed under: General — m759 @ 2:24 PM

(A sequel to the previous post, Damning.)

The New York Times  at 11:44 AM today —

Barbara Gelb, an author and journalist who, with her husband, Arthur Gelb, produced the first full-scale biography of the playwright Eugene O’Neill, then followed it decades later with two volumes that reconsidered his life, died on Thursday [Feb. 9, 2017] at her home in Manhattan. She was 91.

Her death was confirmed by her son, Peter, general manager of the Metropolitan Opera.

For much of their long careers — Mr. Gelb was the culture editor and then managing editor of The New York Times — the Gelbs were consumed by O’Neill, who was regarded by many critics as the greatest American playwright. 

. . . .

Wednesday, February 8, 2017


Filed under: General — m759 @ 9:42 PM

BuzzFeed, Tuesday, January 10, 2017, on "the damning letter"—

From the Jan. 10 BuzzFeed story

At the time of the hearing, Judiciary Committee Chairman Strom Thurmond never put the letter into the congressional record, and its contents remained largely unknown. In the only line that was made public at the time — published in June 1986 by Knight Ridder reporter Aaron Epstein — King made clear her opposition to Sessions’ nomination.

“For a century, the racial practices that characterized our region were established and enforced by men who, like Mr. Sessions, protested that they, too, were not personally hostile to blacks,” King’s letter said, according to Epstein’s dispatch.

A searchable text of the alleged 1986 letter, along with the
alleged attached statement, is now available at

A search of the letter and statement at that webpage yields
no instances of the phrases "racial practices," "established and enforced,"
or "personally hostile."

Hence the word "alleged" above.

Update of 1:44 PM ET on Feb. 9, 2017:

A relevant Wikipedia article —
Questioned document examination.

Rhymes with Prize

Filed under: General,Geometry — m759 @ 3:01 PM

On the triangle in the excerpt above —

"A golden triangle can be split into
a golden triangle and a golden gnomon.
The same is true for a golden gnomon.
A golden gnomon and a golden triangle
with their equal sides matching each other
in length are also referred to as the obtuse
and acute Robinson triangles.

These isosceles triangles can be used to
produce Penrose tilings."

— Adapted from Wikipedia (Wikipedia's word
"bisected" is replaced above by the word "split.")

The previous post dealt with women and lies.

Related material — Quilt Prize in this journal.

Complicated Stories

Filed under: General — m759 @ 1:00 PM

Dore Ashton's Picasso on Art

"We all know that Art is not truth.
Art is a lie that makes us realize truth,
at least the truth that is given us
to understand." — Pablo Picasso

Tuesday, February 7, 2017


Filed under: General — m759 @ 7:48 PM

From a poem by Bécquer translated by Robert Lowell —

Some other love will sound his fireword for you
and wake your heart, perhaps, from its cool sleep

Physicist Marjorie D. Corcoran in a photo from her Rice University
home page. Corcoran reportedly died on Friday, Feb. 3, 2017.

This post was suggested by the date in the photo: 2003/07/27.

Authority Figure

Filed under: General — m759 @ 3:09 PM

Accepting for Professor Corey Thomas Pynchon.

Not a Group Member

Filed under: General — m759 @ 1:30 PM

The previous post included an image of a group
of eleven women in the cover photo for the current
Vanity Fair  Hollywood Issue.

To be fair and balanced, here is a twelfth, rather different,
feminine figure

Related philosophy by Rebecca Newberger Goldstein in
remarks published July 12, 2016, on Plato and mathematical beauty —

"Thinking in a narrow and amoral way about our own self-interest
is, for Plato, almost the definition of irrationality. Our self-centeredness
makes us not only stupid but nasty."

"I'm with Nasty."

Monday, February 6, 2017

And Now, the Entire Company!

Filed under: General — m759 @ 11:26 PM

"You may say that I'm a dreamer . . . ."


Filed under: General — Tags: , — m759 @ 2:10 PM

Some notes related to recent posts

"Rilke's insistent quest for a purity associated with primitive origins
took a Russian turning, but could also be seen as an extension of
traditions developed in Europe in the modern era. When Balzac
takes a metaphysical look at modern life, he exclaims: 'There is a
primitive principle! . . . .' "

— The late Dore Ashton,
     "Art Critic Who Embraced and Inhabited Modernism"

Sixteenth-century alchemist in a novel by Balzac —

"If we eliminate God from this world, sire,
what remains? Man! Let us examine our domain.
The material world is made up of elements;
thos elements are resolved into a single one
which is endowed with motion.
The number THREE is the formula of creation:
matter, motion, product!" *
. . . .

"There is a primitive principle!
Let us grasp it at the point where it acts upon itself,
where it is a unit, where it is really a principle,
not a creature, a cause, not an effect —
we shall see it by itself, formless, ready to assume
all the forms which we see it assume in life.  
When we are face to face with this atom, 
when we have surprised motion at its
starting-point, we shall know its laws . . . ."

* "… la Matière, le Mouvement, le Produit!"

Twenty-first century writer on physics —

"Besides the concept of Newtonian force,
the concept of momentum, as defined by
the multiplication of mass m and velocity v,
i.e., mv, is also one of the key concepts in
Newtonian mechanics. Historically, the
concept of momentum can be regarded as
an outgrowth of the impetus concept of the
Middle Ages. But momentum is in fact quite
different from impetus which has no
quantitative definition. In comparison,
momentum is a quantitatively precise and
well-defined mechanical concept."

—  http://www.thecatalyst.org/physics/chapter-two.html.
      No author is named, but a "curriculum vitae" link at
      the bottom of the webpage leads to Kai X. Miao.

"C’était la création elle-même,
qui se servait de la forme de Balzac
pour faire son apparition . . . ."

Auguste Rodin , by Rainer Maria Rilke,
translated from the German by Catherine Caron,
Editions La Part Commune , 2001

See also a version in English, and Rilke's original German

 Aber langsam wuchs Rodin's Vision von Form zu Form. Und endlich sah er ihn. Er sah eine breite, ausschreitende Gestalt, die an des Mantels Fall alle ihre Schwere verlor. Auf den starken Nacken stemmte sich das Haar, und in das Haar zurückgelehnt lag ein Gesicht, schauend, im Rausche des Schauens, schäumend von Schaffen: das Gesicht eines Elementes. Das war Balzac in der Fruchtbarkeit seines Überflusses, der Gründer von Generationen, der Verschwender von Schicksalen. Das war der Mann, dessen Augen keiner Dinge bedurften; wäre die Welt leer gewesen: seine Blicke hätten sie eingerichtet. Das war der, der durch sagenhafte Silberminen reich werden wollte und glücklich durch eine Fremde. Das war das Schaffen selbst, das sich der Form Balzac's bediente, um zu erscheinen; des Schaffens Überhebung, Hochmut, Taumel und Trunkenheit. Der Kopf, der zurückgeworfen war, lebte auf dem Gipfel dieser Gestalt wie jene Kugeln, die auf den Strahlen von Fontänen tanzen. Alle Schwere war leicht geworden, stieg und fiel.

 So hatte Rodin in einem Augenblick ungeheuerer Zusammenfassung und tragischer Übertreibung seinen Balzac gesehen, und so machte er ihn. Die Vision verging nicht; sie verwandelte sich. . . . .

Related material:  Momentum  in this journal.

Sunday, February 5, 2017

Against Bewitchment

Filed under: General — m759 @ 7:55 PM

A footnote in memory of a preservationist

Title page of a thesis on language by Miles Spencer Kimball from 1984

The previous post's quotation from the Kimball thesis contains
a reference (numbered 23) to the source of Wittgenstein's 
"savages" remarkPhilosophical Investigations , § 194.

Kimball's  remarks quoted in the previous post are from
page 121 of his thesis, under the heading "Wittgenstein's
Battle Against Bewitchment by Language."

From a cinematic example of such bewitchment —

Ein Kampf

Filed under: General — Tags: — m759 @ 1:00 PM

This is from a master's thesis of 1984.

For the source, see "Ein Kampf" in this journal.

An image from the Saturday Night Live  version —

Primitive Principle

Filed under: General,Geometry — Tags: , , — m759 @ 12:20 PM

"Rilke's insistent quest for a purity associated with primitive origins
took a Russian turning, but could also be seen as an extension of
traditions developed in Europe in the modern era. When Balzac
takes a metaphysical look at modern life, he exclaims: 'There is a
primitive principle! . . . .' "

— The late Dore Ashton,
     "Art Critic Who Embraced and Inhabited Modernism"

Putting aside the wild inaccuracy of Ashton's remarks,
the words "modernism" and "turning" suggest a review of

Saturday, February 4, 2017

Time Loop

Filed under: General — m759 @ 10:09 PM

"On a Saturday night" — Johnny Thunder, 1962

"Only a peculiar can enter a time loop." — Tim Burton film, 2016

Highly qualified —

The Rothko Conundrum

Filed under: General — Tags: , — m759 @ 8:48 PM

Photo:  J. Griffis Smith

By Molly Glentzer, Houston Chronicle , February 3, 2016

“At night, over Rothko Chapel’s reflecting pond, ‘Broken Obelisk’
looks particularly dramatic.

The great American sculptor Barnett Newman once said his
monumental sculpture ‘Broken Obelisk’ was intended to transform
ideas about life and tragedy into a glimpse of the ‘sublime.’ ”

. . . 

See as well Rothko
in this journal.

Houston Problem

Filed under: General — Tags: , — m759 @ 3:33 PM

"A noted Rice University professor died Friday morning
when a Metro light rail train hit her near Hermann Park.

Marjorie Corcoran was bicycling toward the campus
about 8:30 a.m. when she was struck on the southbound
tracks at 6300 Fannin near Sunset, according to Metro officials."

The Houston Chronicle  yesterday

Houston is on Central Standard Time; 8:30 a.m. there
is 9:30 a.m. Eastern Standard Time (the time used here).

Log24 at that time yesterday

Corcoran's Rice University page
has some brief remarks 
on fundamental symmetries.

Character in a novel by Balzac

" la Matière, le Mouvement, le Produit!"

♫ Are You Going to Vanity Fair?

Filed under: General — Tags: , — m759 @ 2:00 PM
"In those days, the occult sciences were 
cultivated with ardor well calculated to surprise the 
incredulous minds of our own sovereignly analytical 
age; perhaps they may detect in this historical 
sketch the germ of the positive sciences, widely 
studied in the nineteenth century, but without the 
poetic grandeur which was ascribed to them by the 
audacious investigators of the sixteenth century; 
who, instead of devoting their energy to industry, 
magnified art and made thought fruitful. The 
patronage universally accorded to art by the sov- 
ereigns of that time was justified, too, by the mar- 
vellous creations of inventors who started in quest 
of the philosopher's stone and reached amazing re- 
sults." — Balzac, Catherine de' Medici 

Honoré de Balzac, Sur Catherine de Médicis :

— Hé! bien, sire, en ôtant Dieu de ce monde, que reste-t-il?
L’homme! Examinons alors notre domaine?
Le monde matériel est composé d’éléments, ces éléments
ont eux-mêmes des principes. Ces principes se résolvent 
en un seul qui est doué de mouvement. Le nombre TROIS est
la formule de la création: la Matière, le Mouvement, le Produit!

— La preuve? Halte-là, s’écria le roi.

Illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress 
(New York, The Century Co., 1912)


Filed under: General,Geometry — m759 @ 2:12 AM

See also "Universal" in this  journal.

Friday, February 3, 2017

A Fable of Art Criticism

Filed under: General — Tags: , — m759 @ 6:42 PM

Part I —

Part II —

Part III —

"Let us examine our domain." — Character in a Balzac novel

Ashton reportedly died on Monday, Jan. 30, 2017.
See some more-scholarly remarks by Ernst Cassirer
on "the domain of perception" quoted here on that date.

Hard Kernel

Filed under: General — m759 @ 11:13 AM

Kamuf, 'Remains to be Seen,' Los Angeles Review of Books

Hermeneutics —

The above quote occurs in a search called up by clicking on the image
of Amy Adams in the noon post on Groundhog Day (yesterday).

For a "universal message" see the final post of Groundhog Day.
For an "unintelligible secret," see today's previous post.

See also kernel  in this journal.

Raiders of the Lost Chalice

Filed under: General — Tags: — m759 @ 9:30 AM

Personally, I prefer
the religious symbolism
of Hudson Hawk .

Thursday, February 2, 2017

Hollywood Easter Egg

Filed under: General — Tags: — m759 @ 9:33 PM

From yesterday's post Hollywood Arrival

Yesterday's events at 6407 Sunset Blvd. in Hollywood,
together with the logic of number and time from recent
posts based on a Heinlein short story, suggest that the
character played by Adams is a sort of 'fifth element'
needed to save the world. 

In other words, the strange logic of recent posts ties the
California lottery number  6407 to the date  April 12, 2015, 
and a check of that date in this journal yields posts tagged
Orthodox Easter 2015 that relate to the 'fifth element.' "

A related image from Arrival  (at 1:37:18) —

A related passage of scientific prose —

"Paramount discoveries are still being made…."

Or at least distributed.

An Object for New Haven

Filed under: General — m759 @ 1:44 PM

The title was suggested by a Wallace Stevens poem.

See "The Thing and I" in this journal. See also

Words and Objects according to Whorf

Page 240 of Language, Thought, and Reality , MIT, 1956,
     in the article "Languages and Logic," reprinted from
    Technol. Rev. , 43: 250-252, 266, 268, 272 (April 1941)

Y* is for Yale

Filed under: General — Tags: — m759 @ 1:00 PM

See "Sapir" in this journal as well as a Yale University page on Whorf:

* For a different view of "Y," see the previous post.

Putting the Y in Vanity

Filed under: General — Tags: , — m759 @ 12:00 PM

Amy Adams on the cover of the 
Vanity Fair  Hollywood issue, 2017

Line spoken to Adams's
character in Arrival

You approach language
like a mathematician.

Speak, Memory

Filed under: General — m759 @ 11:05 AM

This post was suggested by today's National Prayer Breakfast,
the 1990 film Total Recall , and a post of July 20, 2015.

Detail from that post —

Wednesday, February 1, 2017

Free Speech Movement*

Filed under: General — m759 @ 11:01 PM

* See also the title phrase in Wikipedia.


Filed under: General — m759 @ 10:34 PM

Search results suggested by the previous post :

See also Wechsler in this journal.

But Wait, There’s …

Filed under: General — m759 @ 9:57 PM

Shifts and Pivots

Filed under: General — m759 @ 8:13 PM

In a New Yorker  "Cultural Comment" column today,
Richard Brody describes a 2004 novel that he says

"… dramatizes the American character as
vast, manifold, and inchoate;
it can use its prodigious and uninhibited energy
for good or for evil, and it shifts
under the sudden force of unforeseeable events.
The shifts and pivots of the American nation
at large are also those of each individual American.
The grand political stage and the intimate life
are inseparable; identity itself is inextricable
from the currents of history. The novel’s
mighty psychological weight rests upon
a terrifyingly delicate balance of circumstances
that depend on whims of chance." 

I prefer the shifts and pivots in earlier fictions; for example,
those of Robert A. Heinlein, who died in 1988.

Some backstory :  Glory Road  in this journal.

Faust and the Media

Filed under: General — m759 @ 2:00 PM

Announcement of a Harvard event:

"The Future of News: Journalism in a Post-Truth Era,"
 Tuesday, January 31, 4 – 6 pm., Sanders Theatre,
 Harvard University, Cambridge, Mass."

The event as reported by The Harvard Crimson

Related material — This  journal at 12:31 PM ET Tuesday —
"The Devil's Arithmetic," a post with title taken from a 1988
fiction by Jane Yolen.

From the Jan. 28 post Cranking It Up —

"We are rooted in yoga and love the magic
that happens when that practice is
cranked up to eleven." — The late Trevor Tice

Hollywood Arrival

Filed under: General — Tags: , — m759 @ 12:00 PM

In the new film Arrival , Amy Adams plays a linguist
who must interpret the language used by aliens whose
spaceships hover at 12 points around the globe.

Yesterday's events at 6407 Sunset Blvd. in Hollywood,
together with the logic of number and time from recent
posts based on a Heinlein short story, suggest that the
character played by Adams is a sort of "fifth element"
needed to save the world. 

In other words, the strange logic of recent posts ties the
California lottery number  6407 to the date  April 12, 2015, 
and a check of that date in this journal yields posts tagged
Orthodox Easter 2015 that relate to the "fifth element."

Midrash by Ted Chiang from the story on which Arrival  was based  —

After the breakthrough with Fermat's Principle, discussions of scientific concepts became more fruitful. It wasn't as if all of heptapod physics was suddenly rendered transparent, but progress was suddenly steady. According to Gary, the heptapods' formulation of physics was indeed topsy-turvy relative to ours. Physical attributes that humans defined using integral calculus were seen as fundamental by the heptapods. As an example, Gary described an attribute that, in physics jargon, bore the deceptively simple name “action,” which represented “the difference between kinetic and potential energy, integrated over time,” whatever that meant. Calculus for us; elementary to them.

Conversely, to define attributes that humans thought of as fundamental, like velocity, the heptapods employed mathematics that were, Gary assured me, “highly weird.” The physicists were ultimately able to prove the equivalence of heptapod mathematics and human mathematics; even though their approaches were almost the reverse of one another, both were systems of describing the same physical universe.

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