Wednesday, June 15, 2016

The Garden of Allah

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM

Continues .

From "The Back Page," Notices of the American Mathematical Society ,
June-July 2016 —

Related material:  Page 1 of Screenland , April 1923 —

Saturday, January 14, 2012

Derrida at Villanova

Filed under: Uncategorized — Tags: — m759 @ 8:00 PM

"As Derrida said at Villanova,
"We wait for something we would not like to wait for.
That is another name for death."

— Brian D. Ingraffia, "Is the Postmodern Post-Secular?,"
p. 50 in Postmodern Philosophy and Christian Thought ,
ed. by Merold Westphal, Indiana University Press, 1999, pp. 44-68

See also Derrida at Villanova in this journal.

The link to Ingraffia's remarks was suggested by
this evening's New York Times  obituaries—


Tuesday, February 13, 2018

A Titan of the Field

Filed under: Uncategorized — Tags: — m759 @ 9:45 AM

On the late Cambridge astronomer Donald Lynden-Bell —

"As an academic at a time when students listened and lecturers lectured, he had the disconcerting habit of instead picking on a random undergraduate and testing them on the topic. One former student, now a professor, remembered how he would 'ask on-the-spot questions while announcing that his daughter would solve these problems at the breakfast table'.

He got away with it because he was genuinely interested in the work of his colleagues and students, and came to be viewed with great affection by them. He also got away with it because he was well established as a titan of the field."

The London Times  on Feb. 8, 2018, at 5 PM (British time)

Related material —

Two Log24 posts from yesteday, Art Wars and The Void.

See as well the field GF(9)


and the 3×3 grid as a symbol of Apollo
    (an Olympian rather than a Titan) —


Monday, February 12, 2018

The Void

Filed under: Uncategorized — Tags: — m759 @ 11:46 AM

In memory of Professor Donald Lynden-Bell,
Emeritus Professor of Astrophysics at the University of Cambridge

Lynden-Bell with colleagues at Meteor Crater, Arizona, reportedly in 1960 —

Lynden-Bell was one of the subjects of the 2015 film "Star Men."

Related material —

"After peering into the void from a perch 
outside the visitor center, young Henry, 9, 
said he liked the rugged landscape. 
'It’s a good place to film a space movie,' he said.

Funny he should mention that — 
the crater was the setting for the climactic scenes 
of the 1984 sci-fi film 'Starman,' with Jeff Bridges 
and Karen Allen arriving for a rendezvous with 
an alien mother ship."

Henry Fountain in The New York Times , Jan. 22, 2009

Lynden-Bell reportedly died at 82 on Feb. 5, 2018 (British time).

See as well this  journal on that date.

Art Wars

Filed under: Uncategorized — Tags: — m759 @ 8:55 AM

'In the end the space itself is the star'— Gia Kourlas

See also Krauss Cross.

Friday, February 2, 2018

For Plato’s Cave

Filed under: Uncategorized — Tags: , — m759 @ 12:06 PM

"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large fire burns behind
the prisoners, and as people pass this fire their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."

— From the Occupy Space gallery in Ireland

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

Sunday, January 14, 2018


Filed under: Uncategorized — Tags: — m759 @ 4:00 AM

Ken Yuszkus, Salem News  staff photo

SALEM — The former MIT professor from Hamilton
accused of trying to swindle his son’s widow and children
out of nearly $5 million pleaded not guilty to the charges
on Friday in Salem Superior Court. 

John Donovan Sr., 75, was clutching a set of rosary beads
as he entered his plea before Judge Timothy Feeley

Donovan was indicted last month by an Essex County grand jury
on 13 counts, including larceny, forgery and witness intimidation. 

. . . .

— Julie Manganis, Salem News  staff writer, Jan. 13, 2018

See also other posts tagged Systems Programming.

Sunday, January 7, 2018


Filed under: Uncategorized — Tags: — m759 @ 11:00 AM

Peter Zhang and Eric McLuhan on Interality

Space Program

Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

Or:  Interality Illustrated

See also Seven Seals.

Saturday, January 6, 2018

Report from Red Mountain

Filed under: Uncategorized — Tags: — m759 @ 4:00 PM

Tom Wolfe in The Painted Word  (1975):

"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde  understood, they
were not only theories but … hot news,
straight from the studios, from the scene."

Harold Rosenberg in The New Yorker  (click to enlarge)

See also Interality  and the Eightfold Cube .

Friday, January 5, 2018

Types of Ambiguity

Filed under: Uncategorized — Tags: , — m759 @ 2:56 AM

From "The Principle of Sufficient Reason," by George David Birkhoff
in "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940 —

From the same lecture —

Up to the present point my aim has been to consider a variety of applications of the Principle of Sufficient Reason, without attempting any precise formulation of the Principle itself. With these applications in mind I will venture to formulate the Principle and a related Heuristic Conjecture in quasi-mathematical form as follows:

PRINCIPLE OF SUFFICIENT REASON. If there appears in any theory T a set of ambiguously  determined ( i e . symmetrically entering) variables, then these variables can themselves be determined only to the extent allowed by the corresponding group G. Consequently any problem concerning these variables which has a uniquely determined solution, must itself be formulated so as to be unchanged by the operations of the group G ( i e . must involve the variables symmetrically).

HEURISTIC CONJECTURE. The final form of any scientific theory T is: (1) based on a few simple postulates; and (2) contains an extensive ambiguity, associated symmetry, and underlying group G, in such wise that, if the language and laws of the theory of groups be taken for granted, the whole theory T appears as nearly self-evident in virtue of the above Principle.

The Principle of Sufficient Reason and the Heuristic Conjecture, as just formulated, have the advantage of not involving excessively subjective ideas, while at the same time retaining the essential kernel of the matter.

In my opinion it is essentially this principle and this conjecture which are destined always to operate as the basic criteria for the scientist in extending our knowledge and understanding of the world.

It is also my belief that, in so far as there is anything definite in the realm of Metaphysics, it will consist in further applications of the same general type. This general conclusion may be given the following suggestive symbolic form:

Image-- Birkhoff diagram relating Galois's theory of ambiguity to metaphysics

While the skillful metaphysical use of the Principle must always be regarded as of dubious logical status, nevertheless I believe it will remain the most important weapon of the philosopher.

Related remarks by a founding member of the Metaphysical Club:

See also the previous post, "Seven Types of Interality."

Seven Types of Interality*

Filed under: Uncategorized — Tags: , — m759 @ 1:00 AM

* See the term interality  in this journal.
For many synonyms, see 
"The Human Seriousness of Interality,"
by Peter Zhang, Grand Valley State University,
China Media Research  11(2), 2015, 93-103.

Thursday, January 4, 2018

Perspectives from a Chinese Jar

Filed under: Uncategorized — Tags: , — m759 @ 4:40 PM

" . . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— T. S. Eliot, Four Quartets

"The Grand Valley spirit never dies."

— Adapted from the Tao Te Ching

Saturday, December 30, 2017

A Dream

Filed under: Uncategorized — Tags: — m759 @ 11:26 AM

Say You, Say Me

Lionel Richie
. . . .

"I had a dream,
     I had an awesome dream
People in the park
     playing games in the dark
And what they played
     was a masquerade
And from behind walls of doubt
     a voice was crying out"
. . . .

 "Something else was behind this . . .
  because it makes no sense.”

— The author reviewed in today's previous post,
as quoted yesterday in The Boston Globe

Say you, say me, say  IT . . .

A comment on Sean Kelly's Christmas Morning column on "aliveness"
in the New York Times  philosophy series The Stone  —

About IT

Filed under: Uncategorized — Tags: — m759 @ 12:06 AM

Goodreads review of 'Systems Programming,' a book by John J. Donovan

Background: See Wrinkle  in this journal and a post,
Field of Manifestation, from the above 2015 date.

See as well the Goodreads page below.

The six books reviewed by this user were written or
co-written by the author in the review shown above.
Each review gave the highest rating, five stars.

Wednesday, December 13, 2017


Filed under: Uncategorized — Tags: , — m759 @ 2:04 AM

"The philosopher Jerry Fodor was important for the same reason
you’ve probably never heard of him: he was unimpressed,
to put it politely, by the intellectual trends of the day."

—  Stephen Metcalf in The New Yorker , Dec. 12, 2017

See also "The French Invasion," a Dec. 11 Quarterly Conversation
essay about Derrida in Baltimore in 1966, and the Dec. 10 posts
in this  journal tagged Interlacing Derrida. (The deplorable Derrida
trend is apparently still alive in Buffalo.)

According to Metcalf, Fodor's "occasional review-essays in the L.R.B. 
were masterpieces of a plainspoken and withering sarcasm. To Steven
Pinker’s suggestion that we read fiction because ' it supplies us with a
mental catalogue of the fatal conundrums we might face someday,' for
instance, Fodor replied, ' What if it turns out that, having just used the ring
that I got by kidnapping a dwarf to pay off the giants who built me my
new castle, I should discover that it is the very ring that I need in order to
continue to be immortal and rule the world? ' "

In the Fodor-Pinker dispute, my sympathies are with Pinker.

Related material — Google Sutra (the previous Log24 post) and earlier posts
found in a Log24 search for Ring + Bear + Jung —

Four Colours and Waiting for Logos.

Sunday, December 10, 2017


Filed under: Geometry — Tags: , — m759 @ 8:45 PM

Google search result for Plato + Statesman + interlacing + interweaving

See also Symplectic in this journal.

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). See also
related remarks on the notion of  linear  (or line ) complex
in the finite projective space PG(3,2) —

Anticommuting Dirac matrices as spreads of projective lines

Ron Shaw on the 15 lines of the classical generalized quadrangle W(2), a general linear complex in PG(3,2)


Filed under: Uncategorized — Tags: — m759 @ 4:10 PM

See also The Derrida Reader: Writing Performances, edited by
Julian Wolfreys (U. of Nebraska Press, 1998), pages 112-113,
discussed here in the previous two posts, and this  journal on
1/12-1/13. Related material: Polytropos .


Filed under: Uncategorized — Tags: — m759 @ 2:55 PM

Derrida quote from the previous post

See also Black + Algebra + Metaphor.

Interlacing, Interweaving

Filed under: Uncategorized — Tags: — m759 @ 2:00 PM

The above title should be sung to the following tune

"Right through hell
 there is a path…."
 — Malcolm Lowry,
Under the Volcano

Saturday, November 11, 2017

For Your Consideration

Filed under: Uncategorized — Tags: — m759 @ 11:00 PM

From today's online Wall Street Journal

A synchronology check of the above 2015 Taylor Swift date —

The above remarks suggest Swift as a possible presidential candidate:

From The Harvard Crimson  on Halloween



Filed under: Uncategorized — Tags: — m759 @ 3:00 PM

Related material —

Michael Sudduth in this journal and an October 28, 2017,
Facebook post by Sudduth.

Friday, October 20, 2017

Punch Lines

Filed under: Uncategorized — Tags: — m759 @ 10:06 PM

From a post last month

"You're gonna need a bigger boat."
Roy Scheider in "Jaws"

"We're gonna need more holy water."
— "Season of the Witch" 

… and for Tom HanksDan Brown, and Francine Prose —

"You're gonna need more typewriters!"

Heart of the Monkey God

Filed under: Uncategorized — Tags: — m759 @ 9:42 PM

In Memoriam

"Renowned Canadian theologian Gregory Baum, 94,
author of the first draft of the Second Vatican Council's
'Nostra Aetate,' died Oct. 18 in a Montreal hospital."

National Catholic Reporter , Oct. 20, 2017

October 18 was St. Luke's Day

From the Log24 post "Prose" on that date

"Mister Monkey . . . . is also Hanuman, the Hindu monkey god . . . ."
— Cathleeen Schine in an online October 17 NY Times  review.

From the novel under review —

"Only the heart of the monkey god is large enough
to contain the hearts and souls of all the monkeys,
all the humans, the gods, every shining thread
that connects them."

— Francine Prose, Mister Monkey: A Novel  (p. 263).
     HarperCollins. Kindle Edition. 

See as well all posts now tagged Prose Monkey.

Thursday, October 19, 2017

Prose (continued from yesterday)

Filed under: Uncategorized — Tags: — m759 @ 12:20 PM

"While Prose's adult works have touched on various subjects,
her fiction for children, which she began writing in earnest
in the mid-1990s, all has a basis in Jewish folklore."

»  Read more.

Aficionados of what Dan Brown has called "symbology"
can read about the above right-chevrons symbol in
Fast Forward, a post of November 21, 2010.

And Howe

Filed under: Uncategorized — Tags: — m759 @ 11:01 AM

The Harvard Crimson , Feb. 28, 2017

Cambridge City Councillors formally requested that the Cambridge
Historical Commission consider designating the Abbott Building in
Harvard Square as a historical landmark at its weekly meeting Monday.
. . . .

“There are only a few gems that give the really Square character.”
Councillor Dennis J. Carlone said. “And in the heart of the square,
it’s this building.”

See as well the cover of
The Monkey Grammarian ,
a book by Octavio Paz —

A related NPR book review yesterday

"Like Curious George , another vaguely imperialist children's classic —
which Prose refers to frequently — the simian hero of Mister Monkey 
gets into trouble in his new urban environment." 

Wednesday, October 18, 2017


Filed under: Uncategorized — Tags: — m759 @ 11:01 PM

New York Times  review  of a new novel by Francine Prose —

"Mister Monkey . . . . is also Hanuman, the Hindu monkey god . . . ."
— Cathleeen Schine in in the above October 17 review.

A related book

See as well The Monkey Grammarian  in this  journal.

Sunday, October 15, 2017

The Strength at the Centre

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

The title, a phrase from a poem by Wallace Stevens,
was suggested by the previous post, "Center."

See posts tagged May 19 Gestalt in particular, 
May 19, 2007 — "Point of View."

Saturday, October 14, 2017


Filed under: Geometry — Tags: , — m759 @ 2:20 PM

Rosalind Krauss in 1978

"To get inside the systems of this work,
whether LeWitt's or Judd's or Morris's,
is precisely to enter
a world without a center,
a world of substitutions and transpositions
nowhere legitimated by the revelations
of a transcendental subject. This is the strength
of this work, its seriousness, and its claim to modernity." 


"The center of
the quaternion group,
Q8 = {1, −1, i, −i, j, −j, k, −k} ,
is {1, −1}."

Illustration from a post of Feb. 3,  2011


In Principio:

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

Red October  continues …

See also Molloy in this  journal.

Related art  theory —

Geometry of the 4×4 Square 

Friday, October 13, 2017

Sicut Erat

Filed under: Uncategorized — Tags: — m759 @ 9:26 PM

Smith College in 2011 on some music by Dan Brown's brother —

"Using the conventions of a traditional five-movement
Roman Catholic Mass to revere Darwin’s body of work,
Gregory Brown, Smith’s assistant director of choral
activities and a composer of choral music, is
collaborating with Craig Phillips, an early music specialist
and member of the classical a cappella male quartet
New York Polyphony, to create the piece Missa Charles Darwin . 
Brown is building the work in three large-scale sections and
scoring it for a male vocal quartet, which will be performed by
New York Polyphony."


Dan Brown has said his brother's Missa  helped suggest his new novel Origin .

Material from Smith College related to a performance of
Missa Charles Darwin  at the college on Feb. 4, 2011 —

Dan Brown, in the following passage, claims that an eight-ray star with arrowheads
at the rays' ends is "the mathematical symbol for entropy."  Brown may have first
encountered this symbol at a questionable "Sacred Science" website.  Wikipedia
discusses some even less  respectable uses of the symbol.

My own version of the above symbol (from the pure mathematics of group actions
on a 3×3 square) appeared here the day before  the Friday, Feb. 4, 2011,
Smith College Darwin Mass . . .

See posts now tagged The Next Thing.

Speak, Memra

Filed under: Geometry — Tags: — m759 @ 11:59 AM

The above was suggested by a Log24 review of October 13, 2002,
which in turn suggested a Log24 search for Carousel that yielded
(from Bloomsday Lottery) —

See as well Asimov's "prime radiant," and an illustration
of the number 13 as a radiant prime

"The Prime Radiant can be adjusted to your mind,
and all corrections and additions can be made
through mental rapport. There will be nothing to
indicate that the correction or addition is yours.
In all the history of the Plan there has been no
personalization. It is rather a creation of all of us 
together. Do you understand?"  

"Yes, Speaker!"

— Isaac Asimov, 
    Second Foundation , Ch. 8: Seldon's Plan

"Before time began, there was the Cube."
— Optimus Prime

See also Transformers in this journal.

Tuesday, October 10, 2017

Another 35-Year Wait

Filed under: Geometry — Tags: — m759 @ 9:00 PM

The title refers to today's earlier post "The 35-Year Wait."

A check of my activities 35 years ago this fall, in the autumn
of 1982, yields a formula I prefer to the nonsensical, but famous,
"canonical formula" of Claude Lévi-Strauss.

The Lévi-Strauss formula

My "inscape" formula, from a note of Sept. 22, 1982 —

S = f ( f ( X ) ) .

Some mathematics from last year related to the 1982 formula —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also Inscape in this  journal and posts tagged Dirac and Geometry.

Thursday, September 28, 2017


Filed under: Uncategorized — Tags: — m759 @ 4:01 PM

From the New York Times Wire  last night —

"Mr. Hefner styled himself as an emblem
of the sexual revolution."

From a Log24 post on September 23 —

A different emblem related to other remarks in the above Sept. 23 post

On the wall— A Galois-geometry 'inscape'

(On the wall — a Galois-geometry inscape .)

The Last Word

Filed under: Uncategorized — Tags: , — m759 @ 6:00 AM

Remarks suggested by the previous post

From Jeremy Biles, "Introduction: The Sacred Monster," in
Ecce Monstrum: Georges Bataille and the Sacrifice of Form

(Fordham University Press, 2007, page 3) —

Bataille’s insistent conjunction of the monstrous and the sacred is the subject of this book. Regarded by many as one of the most important thinkers of our time, and acknowledged as an important influence by such intellectuals as Michel Foucault, Julia Kristeva, Maurice Blanchot, and Jacques Derrida, Bataille produced a corpus of wide-ranging writings bearing the monstrous marks of the affective and intellectual contradictions he also sought to produce in his readers. In the following chapters, I will specify some of the ways in which Bataille evokes monstrosity to elicit in himself and his audience an experience of simultaneous anguish and joy—an experience that he calls sacred. In particular, Bataille is fascinated with the ‘‘left-hand’’ sacred. In contradistinction to its lucent and form-conferring ‘‘right-hand’’ counterpart, the left-hand sacred is obscure and formless—not transcendent, pure, and beneficent, but dangerous, filthy, and morbid. This sinister, deadly aspect of the sacred is at once embodied in, and communicated by, the monster. As we will see, it is in beholding the monster that one might experience the combination of ecstasy and horror that characterizes Bataille ’s notion of the sacred.

The dual etymology of ‘‘monster’’ reveals that aspect of the sacred that enticed Bataille. According to one vein of etymological study, the Latin monstrum  derives from monstrare  (to show or display). The monster is that which appears before our eyes as a sign of sorts; it is a demonstration. But another tradition emphasizes a more ominous point. Deriving from monere  (to warn), the monster is a divine omen, a portent; it heralds something that yet remains unexpected, unforeseeable—as a sudden reversal of fortune. In the writings of Bataille, the monster functions as a monstrance, putting on display the sinister aspect of the sacred that Bataille sees as the key to a ‘‘sovereign’’ existence. But in doing so the monster presents us with a portent of something that we cannot precisely foresee, but something that, Bataille claims, can be paradoxically experienced in moments of simultaneous anguish and ecstasy: death.

See as well

(Order of news items transposed for aesthetic effect.)

Wednesday, September 27, 2017


Filed under: Uncategorized — Tags: , — m759 @ 6:11 AM

    See also a related Log24 post.

Saturday, September 23, 2017

The Turn of the Frame

Filed under: Uncategorized — Tags: — m759 @ 2:19 AM

"With respect to the story's content, the frame thus acts
both as an inclusion of the exterior and as an exclusion
of the interior: it is a perturbation of the outside at the
very core of the story's inside, and as such, it is a blurring
of the very difference between inside and outside."

— Shoshana Felman on a Henry James story, p. 123 in
"Turning the Screw of Interpretation,"
Yale French Studies  No. 55/56 (1977), pp. 94-207.
Published by Yale University Press.

See also the previous post and The Galois Tesseract.

Saturday, September 16, 2017

The Zero Monstrance

Filed under: Uncategorized — Tags: , — m759 @ 6:00 AM

From "The Metaphysics of Entities," a post of Sept. 20, 2014 —

Anthony Lane in The New Yorker  on a 2013 film —

"The hero of 'The Zero Theorem' is a computer genius
called Qohen Leth (Christoph Waltz)…. He is the sole
resident of a derelict church, where, on a crucifix in front
of the altar, the head of Christ has been replaced by a
security camera. No prayers are ever said, and none are

Related dialogue from a 2008 film

Another view of the Zero Theorem derelict church —

Tuesday, September 12, 2017


Filed under: Uncategorized — Tags: — m759 @ 12:18 PM

"Truth and clarity remained his paramount goals…"

— Benedict Nightingale in today's online New York TImes  on an
English theatre director, founder of the Royal Shakespeare Company,
who reportedly died yesterday at 86.

See also Paramount in this  journal.

Monday, September 11, 2017

New Depth

Filed under: Uncategorized — Tags: — m759 @ 9:48 PM

A sentence from the New York Times Wire  discussed in the previous post

NYT Wire on Len Wein: 'Through characters like Wolverine and Swamp Thing, he helped bring a new depth to his art form.'

"Through characters like Wolverine and Swamp Thing,
he helped bring a new depth to his art form."

For Wolverine and Swamp Thing in posts related to a different
art form — geometry — see …

Wednesday, September 6, 2017

National Comedy

Filed under: Uncategorized — Tags: — m759 @ 3:20 PM

From a search in this journal for "More Holy Water" —

A post of January 7, 2011, has the following:

"Infinite Jest… now stands as the principal contender
for what serious literature can aspire to
in the late twentieth and early twenty-first centuries."

— All Things Shining, a work of pop philosophy
published January 4th


"You're gonna need a bigger boat."
Roy Scheider in "Jaws"

"We're gonna need more holy water."
— "Season of the Witch" 

Thursday, August 3, 2017

Glitter at the Dark Tower

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

"The centre of transformations that
Transform for transformation's self,

In a glitter that is a life, a gold
That is a being, a will, a fate."

— Wallace Stevens, "Human Arrangement"

From "The Dark Tower," a post of July 9, 2016 —

See also a search for Glitter in this journal.

Poetic Theology at the New York Times

Filed under: Uncategorized — Tags: — m759 @ 12:19 PM

Or:  Trinity Test Site

From the New York Times Book Review  of
next Sunday, August 6, 2017 —

"In a more conventional narrative sequence,
even a sequence of poems,
this interpenetration would acquire
sequence and evolution." [Link added.]

The concept under review is that of the Holy Trinity.

See also, in this  journal, Cube Trinity.

For a simpler Trinity model, see the three-point line  

Monday, June 26, 2017

Upgrading to Six

Filed under: Uncategorized — Tags: , — m759 @ 9:00 PM

This post was suggested by the previous post — Four Dots —
and by the phrase "smallest perfect" in this journal.

Related material (click to enlarge) —

Detail —

From the work of Eddington cited in 1974 by von Franz —

See also Dirac and Geometry and Kummer in this journal.

Updates from the morning of June 27 —

Ron Shaw on Eddington's triads "associated in conjugate pairs" —

For more about hyperbolic  and isotropic  lines in PG(3,2),
see posts tagged Diamond Theorem Correlation.

For Shaw, in memoriam — See Contrapuntal Interweaving and The Fugue.

Thursday, May 25, 2017

Presidential Address of November 19, 1976

Filed under: Uncategorized — Tags: — m759 @ 2:14 PM

Deep Problems in the Faculty Lounge

Filed under: Uncategorized — Tags: — m759 @ 7:14 AM

The Story of Six Continues

Filed under: Uncategorized — Tags: — m759 @ 6:00 AM

A post of March 22, 2017, was titled "The Story of Six."

Related material from that date —

"I meant… a larger map." — Number Six in "The Prisoner"

Friday, May 19, 2017

From Algebra to Geometry

Filed under: Uncategorized — Tags: — m759 @ 10:45 PM

Heptapod Fluency at Yale

Filed under: Uncategorized — Tags: — m759 @ 2:34 PM

". . . riverrun, past Eve and Adam's . . . ."

Cover Girl

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

See also the previous post.

In the Service of Narrative

Filed under: Uncategorized — Tags: — m759 @ 12:40 PM

Quoted here on St. Stephen's Day, 2008

Wayne C. Booth’s lifelong
 study of the art of rhetoric
 illuminated the means
 by which authors seduce,
 cajole and lie to their readers
 in the service of narrative.”

— New York Times, Oct. 11, 2005

Booth was a native of American Fork, Utah.

Monday, May 15, 2017

For Penelope Reed Doob…

Filed under: Uncategorized — Tags: — m759 @ 2:40 PM

who reportedly died on March 11 —

Posts now tagged Labyrinth for Penelope.

See also the previous post and this journal on the above date.

Friday, April 28, 2017

As In :: A Sin

Filed under: Uncategorized — Tags: — m759 @ 1:09 PM

For the Church of Simultaneous Devices

Related art —

Wednesday, April 26, 2017

A Tale Unfolded

Filed under: Uncategorized — Tags: , — m759 @ 2:00 AM

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

Note that Hudson's 1905 "unfolding" of even and odd puts even on top of
the square array, but my own 2013 unfolding above puts even at its left.

Saturday, April 15, 2017

A Cinematographer Departs

Filed under: Uncategorized — Tags: — m759 @ 2:04 AM

In memory of cinematographer Michael Ballhaus, who reportedly
died at 81 in Berlin on Tuesday evening, April 11, the first full day 
of Passover, 2017.

From a New York Times  description of his work —

"The sinuous shot, which shows people parting  
like the Red Sea. . . ." — Margalit Fox tonight

From Log24 on the reported date of Ballhaus's death:

Tuesday, April 11, 2017

Partitioning the Crimson Abyss

Filed under: Uncategorized — Tags: — m759 @ 6:00 PM

For the title, see Crimson + Abyss in this journal.

"Ready when you are, C. B."

Hexagram 63, "After Completion"

Wednesday, April 5, 2017

Dem Bones

Filed under: Uncategorized — Tags: , — m759 @ 12:15 PM

A note at the end of an article on architecture historian
Christopher Gray in the current online New Yorker  —

This article appears in other versions
of the April 10, 2017, issue, with
the headline “Dem Bones.”

"Defeated, you will rise to your feet as is said of Dry Bones .
These bones will rise again." — Agnes Martin, 1973

Accounting for Taste —

Faye Dunaway and Warren Beatty at the Oscars:

Ben Affleck, star of "The Accountant," at the Oscars:

See also Prisoner + Bones in this  journal.

Tuesday, April 4, 2017

Plan 9 Continues

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

"Plan 9 deals with the resurrection of the dead."

— Bill Murray in "Ed Wood"

For The Church of Plan 9

(The plan , as well as the elevation ,
of the above structure is a 3×3 grid.)

Making Science Come Alive

Filed under: Uncategorized — Tags: — m759 @ 8:42 PM

From a post on March 13, 2017

Shafarevich was not the only one with a legacy . . .

See also posts in this  journal
now tagged The Gray Legacy.

Wednesday, March 29, 2017

The Crimson Abyss

Filed under: Uncategorized — Tags: , — m759 @ 3:19 PM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson , March 29


IMAGE- 'Affine Groups on Small Binary Spaces,' illustration


Logo design for Stack Exchange Math by Jin Yang

Recent posts now tagged Crimson Abyss suggest
the above logo be viewed in light of a certain page 29

"… as if into a crimson abyss …." —

Update of 9 PM ET March 29, 2017:

Prospero's Children  was first published by HarperCollins,
London, in 1999. A statement by the publisher provides
an instance of the famous "much-needed gap." —

"This is English fantasy at its finest. Prospero’s Children 
steps into the gap that exists between The Lion, the Witch
and the Wardrobe
  and Clive Barker’s Weaveworld , and
is destined to become a modern classic."

Related imagery

See also "Hexagram 64 in Context" (Log24, March 16, 2017).

Design Abyss

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

Hexagram 29,
The Abyss (Water)

This post was suggested by an August 6, 2010, post by the designer
(in summer or fall, 2010) of the Stack Exchange math logo (see
the previous Log24 post, Art Space Illustrated) —

http://www.8164.org/☵☲/  .

In that post, the designer quotes the Wilhelm/Baynes I Ching  to explain
his choice of Hexagram 63, Water Over Fire, as a personal icon —

"When water in a kettle hangs over fire, the two elements
stand in relation and thus generate energy (cf. the
production of steam). But the resulting tension demands
caution. If the water boils over, the fire is extinguished
and its energy is lost. If the heat is too great, the water
evaporates into the air. These elements here brought in
to relation and thus generating energy are by nature
hostile to each other. Only the most extreme caution
can prevent damage."

See also this  journal on Walpurgisnacht (April 30), 2010 —


Hexagram 29:



Hexagram 30:

"Hates California,
it's cold and it's damp.

Image--'The Fire,' by Katherine Neville

A thought from another German-speaking philosopher

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

See also The Crimson 's abyss in today's 4:35 AM post Art Space, Continued.

Art Space Illustrated

Filed under: Uncategorized — Tags: , — m759 @ 10:45 AM

Another view of the previous post's art space  —

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

More generally, see Solomon's Cube in Log24.

See also a remark from Stack Exchange in yesterday's post Backstory,
and the Stack Exchange math logo below, which recalls the above 
cube arrangement from "Affine groups on small binary spaces" (1984).

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Art Space, Continued

Filed under: Uncategorized — Tags: , — m759 @ 4:35 AM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson  today

From Log24 posts tagged Art Space

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader, and
Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Sunday, March 26, 2017

Seagram Studies

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

From a search in this journal for Seagram + Tradition

Related art:  Saturday afternoon's Twin Pillars of Symmetry.

Four-Year* Date

Filed under: Uncategorized — Tags: — m759 @ 11:00 AM

"Eigenvalues. Fixed points. Stable equilibria.
Mathematicians like things that stay put.
And if they can't stay put, the objects of study
should at least repeat themselves on a regular basis. . . ."

Barry Cipra, "A Moveable Feast," SIAM News , Jan. 14, 2006

Tuesday, March 18, 2014

Class of 64 continues…

Uncategorized — m759 @ 12:00 PM 

Mathematician Norbert Wiener reportedly
died on this date in 1964.

“Mathematics is too arduous and uninviting a field
to appeal to those to whom it does not give great rewards.
These rewards are of exactly the same character as
those of the artist. To see a difficult uncompromising material
take living shape and meaning is to be Pygmalion,
whether the material is stone or hard, stonelike logic."
. . . .

Wednesday, March 18, 2015

Play Is Not Playing Around

Uncategorized — m759 @ 1:00 PM

(A saying of Friedrich Fröbel)

. . . .

Friday, March 18, 2016

Southwestern Noir

Uncategorized — m759 @ 2:56 PM 

Kyle Smith on April 15, 2015, in the New York Post —

"The ludicrous action thriller 'Beyond the Reach'
fails to achieve the Southwestern noir potency
of 'No Country for Old Men,' but there’s no denying
it brings to mind another Southwestern classic
about malicious pursuit: the Road Runner cartoons."
. . . .

Saturday, March 18, 2017

Back to the Past

Uncategorized — Tags:  — m759 @ 7:35 PM 

"Old men ought to be explorers" — T. S. Eliot

. . . .

* For a full  four years, see also March 18, 2013.

Saturday, March 25, 2017

Twin Pillars of Symmetry

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

The phrase "twin pillars" in a New York Times  Fashion & Style
article today suggests a look at another pair of pillars —

This pair, from the realm of memory, history, and geometry disparaged
by the late painter Mark Rothko, might be viewed by Rothko
as  "parodies of ideas (which are ghosts)." (See the previous post.)

For a relationship between a 3-dimensional simplex and the {4, 3, 3},
see my note from May 21, 2014, on the tetrahedron and the tesseract.

Like Decorations in a Cartoon Graveyard

Filed under: Uncategorized — Tags: — m759 @ 4:00 AM

Continued from April 11, 2016, and from

A tribute to Rothko suggested by the previous post

For the idea  of Rothko's obstacles, see Hexagram 39 in this journal.

Wednesday, March 22, 2017

The Story of Six

Filed under: Uncategorized — Tags: , — m759 @ 8:01 PM

On a psychotherapist who died at 86 on Monday

"He studied mathematics and statistics at the Courant Institute,
a part of New York University — he would later write   a
mathematical fable, Numberland  (1987)."

The New York Times  online this evening


From Publishers Weekly

This wry parable by a psychotherapist contains one basic message: though death is inevitable, each moment in life is to be cherished. In the orderly but sterile kingdom of Numberland, digits live together harmoniously under a rigid president called The Professor. Their stable society is held intact by the firm conviction that they are immortal: When has a number ever died? This placid universe is plunged into chaos when the inquisitive hero SIX crosses over into the human world and converses with a young mathematician. This supposedly impossible transition convinces the ruling hierarchy that if SIX can talk to a mortal, then the rest of the numbers are, after all, mortal. The digits conclude that any effort or achievement is pointless in the face of inevitable death, and the cipher society breaks down completely. The solution? Banish SIX to the farthest corners of kingdom. Weinberg (The Heart of Psychotherapy ) uses his fable to gently satirize the military, academics, politicians and, above all, psychiatrists. But his tale is basically inspirational; a triumphant SIX miraculously returns from exile and quells the turmoil by showing his fellow digits that knowledge of one's mortality should enrich all other experiences and that death ultimately provides a frame for the magnificent picture that is life. 

Copyright 1987 Reed Business Information, Inc.

See also The Prisoner in this journal.

Saturday, March 18, 2017

Back to the Past

Filed under: Uncategorized — Tags: — m759 @ 7:35 PM

"Old men ought to be explorers" — T. S. Eliot

"All on a Saturday night" — Johnny Thunder, 1962

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Update of 8:25 PM ET on March 18 —

"Analysis." — Dr. Robert Ford in "Westworld"

"Master theorist and conceptual genius."

— Jon Pareles, front page, online New York Times   tonight

News Search

Filed under: Uncategorized — Tags: — m759 @ 12:30 PM

See also, in this journal, "Before the Devil Knows You're Dead."


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

A search for Gamers in this journal yields

The image “http://www.log24.com/log/pix06A/061019-Tombstones.jpg” cannot be displayed, because it contains errors.

This is not unrelated to the title of a 2008 
book by Jeremy Gray:

Plato's Ghost:
The Modernist Transformation
of Mathematics

Friday, March 17, 2017

To Coin a Phrase

Filed under: Uncategorized — Tags: — m759 @ 9:26 PM

(A sequel to the previous post, Narrative for Westworld)

"That corpse you planted last year . . . ." — T. S.  Eliot

Circle and Square at the Court of King Minos

Harmonic analysis based on the circle involves the
circular  functions.  Dyadic  harmonic analysis involves

For some related history, see (for instance) E. M. Stein
on square functions in a 1982 AMS Bulletin  article.

Narrative for Westworld

Filed under: Uncategorized — Tags: — m759 @ 12:12 PM

“That corpse you planted
          last year in your garden,
  Has it begun to sprout?
          Will it bloom this year?  
  Or has the sudden frost
          disturbed its bed?”

— T. S. Eliot, “The Waste Land

Coxeter exhuming Geometry

Ball and Coxeter, 'Mathematical Recreations,' Twelfth Edition

Click the book for a video.

Wednesday, March 15, 2017

Middle March:

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

The Key to All Mythologies  in a Cartoon Graveyard

This is a sequel to yesterday's post Review, which
suggested a look at Lévi-Strauss's The Raw and The Cooked  
in Derrida's “Structure, Sign, and Play," and then a look at the

Financial Times  of February 26, 2010

"The metaphor for metamorphosis no keys unlock."

Steven H. Cullinane, November 7, 1986

Tuesday, March 14, 2017


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

In Adam’s Fall / We Sinnèd All

Filed under: Uncategorized — Tags: — m759 @ 11:18 AM

Backstory for Westworld —

"Don't want to end up a cartoon in a cartoon graveyard."


Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

"Backstories do more than amuse guests.
They anchor the hosts.
It's their cornerstone.
The rest of their identity is built around it, layer by layer."

— Elsie Hughes in "Westworld," Season 1, Episode 3,
     "The Stray," at 30:09

See also cornerstone in the Bible.

Dr. Robert Ford (Anthony Hopkins) earlier in that same episode —

Westworld S1E3 23:15- Dr. Ford on fiction

Monday, March 13, 2017

Pragmatism at the Church of the Transformers*

Filed under: Uncategorized — Tags: — m759 @ 9:17 PM

"I would drop the keystone into my arch . . . ."

Click the Auto Body image for some backstory.

* For the church, see Transformers in this journal.

Gray Space

Filed under: Uncategorized — Tags: — m759 @ 8:35 PM

Image in Log24 from the date of the architecture writer's death —

See also the post Gray Space of Palm Sunday, 2014.

Saturday, March 11, 2017

Atque Vale

Filed under: Uncategorized — Tags: — m759 @ 1:28 PM

Jeremy Irons and the Apple of Eden —

Jeremy Gray, Valediction —

See also this journal on Thursday, 11 September, 2014.

Thursday, March 9, 2017

Yale Architectural Figure

Filed under: Uncategorized — Tags: — m759 @ 5:48 PM

Edwin Schlossberg, 'Still Changes Through Structure' text piece

See also Log24 posts related to "Go Set a Structure"
as well as "New Haven" + Grid.

Thursday, March 2, 2017


Filed under: Uncategorized — Tags: — m759 @ 1:40 PM

Or:  "A Hologram for the King" Meets "Big"

* A reference to an alleged motto of Plato's Academy


Filed under: Uncategorized — Tags: — m759 @ 12:48 PM

"We tell ourselves stories in order to live." — Joan Didion

The New York Times Magazine  online today

"As a former believer and now a nonbeliever, Carrère,
seeking answers, sets out, in The Kingdom , to tell
the story of the storytellers. He is trying to understand
what it takes to be able to tell a story, any story.
And what he finds, once again, is that you have to find
your role in it."

Wyatt Mason in The New York Times Magazine ,
     online March 2, 2017 

Like Tom Hanks?

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

Click image for related posts.

Monday, February 20, 2017

Mathematics and Narrative

Filed under: Uncategorized — 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."

Monday, February 13, 2017

Soundtracked Meets Sidetracked

Filed under: Uncategorized — 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.


Friday, February 3, 2017

Hard Kernel

Filed under: Uncategorized — 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.

Thursday, February 2, 2017

Y* is for Yale

Filed under: Uncategorized — 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: Uncategorized — 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.

Wednesday, February 1, 2017

Hollywood Arrival

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

In the new film ArrivalAmy 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.

Monday, January 30, 2017

Puck Award

Filed under: Uncategorized — Tags: — m759 @ 1:44 PM

The number 8775 in the previous post suggested, via a lottery search,
a look at the date August 16, 2016. The number was from a Hollywood
street address in a 1941 Robert A. Heinlein story.  Heinlein himself lived
on the same street, at number 8777.

A lottery search for 8777 like that for 8775 in the previous post
yields the date July 10, 2000. Remark from that date in the
Los Angeles Times

"As in any company of size, some of the performances
stand out sharply. Walker almost steals the show as Puck
and the officious Quince of the group of dummies who
put on the play-within-a-play at the end." 

Walker is "the group's conceptual leader" Matt Walker.

Another conceptual leader — Denzel Washington

Setting for the La La Playhouse adaptation of "Fences" —

"But if memories were all I sang, I'd rather drive a truck."

Sunday, January 29, 2017

Lottery Hermeneutics

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

For some backstory, see Lottery in this journal,
esp. a post of June 28, 2007:

Real Numbers: An Object Lesson.

One such number, 8775, is suggested by 
a Heinlein short story in a Jan. 25 post.

A search today for that number —

That Jan. 25 post, "For Your Consideration," also mentions logic.

Logic appears as well within a post from the above "8775" date,
August 16, 2016 —

Update of 10 am on August 16, 2016 —

See also Atiyah on the theology of 
(Boolean) algebra vs. (Galois) geometry:

Related:  Remarks by Charles Altieri on Wittgenstein in
today's previous post.

For remarks by  Wittgenstein related to geometry and logic, see 
(for instance) "Logical space" in "A Wittgenstein Dictionary," by
Hans-Johann Glock (Wiley-Blackwell, 1996).

Wednesday, January 25, 2017

For Your Consideration

Filed under: Uncategorized — Tags: — m759 @ 10:22 PM

Monday, January 16, 2017

Interality Illustrated

Filed under: Uncategorized — Tags: — m759 @ 11:18 AM

For the "interality" of the title, click on the tag.

Click the above image for posts tagged "The Positive."

Sunday, January 15, 2017


Filed under: Uncategorized — Tags: — m759 @ 11:48 PM

See also previous posts now tagged with this term.

April First Interality

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Data for an essay titled "Interality in Heidegger" —

See also Log24 posts
on that same date —
April 1, 2015.

Saturday, January 14, 2017

The Thing and I

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM


Thursday, January 12, 2017


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

Despite a remark at ichingpsychics.com, the I Ching's underlying group actually has 1,290,157,424,640 permutations.

Sunday, January 1, 2017

9 PM New Year’s Day

Filed under: Uncategorized — Tags: , , — m759 @ 9:00 PM

See "Four Gods" in this journal.

Phaedrus  265b "And we made four divisions
of the divine madness, ascribing them to four gods . . . ."

The Unhurried Curve

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

From today's previous post

"The unhurried curve got me. 
It was like the horizon of a world
that made a non-world of
all of the space outside it."

— Peter Schjeldahl, "Postscript: Ellsworth Kelly,"
The New Yorker , December 30, 2015

Related figures —

Art critic Robert Hughes in "The Space of Horizons,"
a Log24 post of August 7, 2012:

Religion writer Huston Smith, who reportedly died
on December 30, 2016:

Like the Horizon

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

(Continued from a remark by art critic Peter Schjeldahl quoted here
last  year on New Year's Day in the post "Art as Religion.")

"The unhurried curve got me. 
It was like the horizon of a world
that made a non-world of
all of the space outside it."

— Peter Schjeldahl, "Postscript: Ellsworth Kelly,"
The New Yorker , December 30, 2015

This suggests some further material from the paper 
that was quoted here yesterday on New Year's Eve —

"In teaching a course on combinatorics I have found
students doubting the existence of a finite projective
plane geometry with thirteen points on the grounds
that they could not draw it (with 'straight' lines)
on paper although they had tried to do so. Such a
lack of appreciation of the spirit of the subject is but
a consequence of the elements of formal geometry
no longer being taught in undergraduate courses.
Yet these students were demanding the best proof of
existence, namely, production of the object described."

— Derrick Breach (See his obituary from 1996.)

A related illustration of the 13-point projective plane 
from the University of Western Australia:

Projective plane of order 3

(The four points on the curve
at the right of the image are
the points on the line at infinity .)

The above image is from a post of August 7, 2012,
"The Space of Horizons."  A related image — 

Click on the above image for further remarks.

Sunday, December 25, 2016

Credit Where Due

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

See also Robert M. Pirsig in this journal on Dec. 26, 2012.

Saturday, December 24, 2016

Early X Piece

Filed under: Uncategorized — Tags: — m759 @ 11:00 AM

In memory of an American artist whose work resembles that of
the Soviet constructivist Karl Ioganson (c. 1890-1929).

The American artist reportedly died on Thursday, Dec. 22, 2016.

"In fact, the (re-)discovery of this novel structural principle was made in 1948-49 by a young American artist whom Koleichuk also mentions, Kenneth Snelson. In the summer of 1948, Snelson had gone to study with Joseph Albers who was then teaching at Black Mountain College. . . . One of the first works he made upon his return home was Early X Piece  which he dates to December 1948 . . . . "

— "In the Laboratory of Constructivism:
      Karl Ioganson's Cold Structures,"
      by Maria GoughOCTOBER  Magazine, MIT,
      Issue 84, Spring 1998, pp. 91-117

The word "constructivism" also refers to a philosophy of mathematics.
See a Log24 post, "Constructivist Witness,"  of 1 AM ET on the above
date of death.

Friday, December 23, 2016

Memory, History, Geometry

Filed under: Uncategorized — Tags: — m759 @ 6:48 PM


Code Blue

Update of 7:04 PM ET —

The source of the 404 message in the browsing history above
was the footnote below:

Thursday, December 22, 2016

The Laugh-Hospital

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Constructivism in mathematics and the laughing academy

See also, from the above publication date, Hudson's Inscape.
The inscape is illustrated in posts now tagged Laughing Academy.

Constructivist Witness

Filed under: Uncategorized — Tags: — m759 @ 1:00 AM

The title refers to a philosophy of mathematics.

For those who prefer metaphor Folk Etymology.

See also Stages of Math at Princeton's  
Institute for Advanced Study in March 2013 —

— and in this journal starting in August 2014.

Monday, December 19, 2016


Filed under: Uncategorized — Tags: — m759 @ 10:25 PM

See also all posts now tagged Memory, History, Geometry.

Tetrahedral Cayley-Salmon Model

Filed under: Uncategorized — Tags: — m759 @ 9:38 AM

The figure below is one approach to the exercise
posted here on December 10, 2016.

Tetrahedral model (minus six lines) of the large Desargues configuration

Some background from earlier posts —

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

Click the image below to enlarge it.

Polster's tetrahedral model of the small Desargues configuration

Sunday, December 18, 2016

Two Models of the Small Desargues Configuration

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Click image to enlarge.

Polster's tetrahedral model of the small Desargues configuration

See also the large  Desargues configuration in this journal.

Saturday, December 17, 2016

Tetrahedral Death Star

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM

Continuing the "Memory, History, Geometry" theme
from yesterday

See Tetrahedral,  Oblivion,  and Tetrahedral Oblivion.

IMAGE- From 'Oblivion' (2013), the Mother Ship

"Welcome home, Jack."

Friday, December 16, 2016

Read Something That Means Something

Filed under: Uncategorized — Tags: — m759 @ 5:29 PM

Memory, History, Geometry

Filed under: Uncategorized — Tags: — m759 @ 9:48 AM

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 —

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

Rothko’s Swamps

Filed under: Uncategorized — Tags: — m759 @ 2:45 AM

"… 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

Tuesday, December 13, 2016

The Thirteenth Novel

Filed under: Uncategorized — Tags: — m759 @ 4:00 PM

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

Monday, December 12, 2016

Raiders of the Lost Chord

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM

Readings for Sinatra's birthday

She Sings at the Finale

Filed under: Uncategorized — Tags: — m759 @ 10:14 AM

The title is from a post of last Thursday afternoon — Dec. 8, 2016.

An image from that post appeared here last year

In related news ….

See also philosophy notes from Infinite Jest .

Some backstory

Saturday, December 10, 2016

Folk Etymology

Filed under: Uncategorized — Tags: , — m759 @ 9:00 AM

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
, 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.

Thursday, December 8, 2016

Finite Groups and Their Geometric Representations

Filed under: Uncategorized — Tags: — m759 @ 8:06 AM

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 .

Friday, November 25, 2016


Filed under: Uncategorized — Tags: , — m759 @ 12:00 AM

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.

Monday, November 21, 2016

Inner, Outer

Filed under: Uncategorized — Tags: , — m759 @ 1:04 PM

Detail of a note from 7/11, 1986

Backstory: Notes on Groups and Geometry, 1978-1986.

Laughing-Academy Cartography

Filed under: Uncategorized — Tags: — m759 @ 2:45 AM

See also "Both Hands and an Ass Map"
in posts tagged "Academy Map."

Older Posts »

Powered by WordPress