Friday, December 13, 2019

Apollo’s 13 Revisited

Filed under: General — Tags: — m759 @ 12:59 AM

IMAGE- The 13 symmetry axes of the cube

(Adapted from Encyclopaedia Britannica,
 Eleventh Edition (1911), Crystallography .)

Friday, May 13, 2011

Apollo’s 13

Filed under: General,Geometry — Tags: — m759 @ 6:36 AM

Continued … See related previous posts.

IMAGE- The 13 symmetry axes of the cube

Those who prefer narrative to mathematics
may consult Wikipedia on The Cosmic Cube.

Sunday, August 19, 2018

Apollo and the Furies

Filed under: General — m759 @ 1:40 AM

Narration by the fictional schoolgirl Pagan Moore in a novel
apparently first published on March 4, 2004

"Now, can anyone else tell me or shall I ask Miss Moore again to help us out?” 

Apollo is a symbol for the male, the rational, the young, and the civilized. The Furies represent the female, the violent, the old, and the primal. Aeschylus captures a mythical moment in history, one in which the world was torn between a savage and archaic past and the bold new order of Greek civilization, the young Olympian gods, and rationality. The difficulty of the struggle between these two worlds is dramatized by the cycle of violence in the House of Atreus and the clash between Apollo and the Furies.” 

No one giggled after Dank finished.

Existence  (first novel of a trilogy), pp. 80-81.
By Abbi Glines. Kindle Edition.

Update at 1:37 PM ET the same day —

A check for the source of the above speech yields

"Apollo is a symbol for the male, the rational, the young, and the civilized.
The Furies represent the female, the violent, the old, and the primal."

This passage is from
From the citation data there —
"By Borey, Eddie. 'The Eumenides Themes.'
GradeSaver, 24 October 2000 Web."

Tuesday, July 26, 2016

Installation: Area 51 Meets Apollo

Filed under: General — m759 @ 6:45 PM

Ben Lerner on Judd's art at Marfa

"as if the installation were waiting to be visited
 by an alien or god" — 10:04: A Novel

Oslo artist Josefine Lyche's public Instagram today

See also Space (May 13, 2015).

Wednesday, October 9, 2013

To Apollo*

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

From Log24

From Josefine Lyche's website —

* For the title, see Apollo + Outram in this journal.


Saturday, July 9, 2011

Blessings from the Apollo

Filed under: General — m759 @ 4:13 AM

Part I, Midday —

Yesterday's midday NY Lottery "689" suggests (from April 3, 2005)—

689 IMAGE- Chinese character 'Fu' [fú] blessing, good fortune

IMAGE- Strokes of the Chinese Character 'Fu'

   Diagram taken from R. Sing,
  “Chinese New Year’s Dragon Teacher’s Guide”

— and the 4-digit midday number suggests a NASA Picture of the Day
     that was published (not taken) on 7795 (7/7/95)—


Part II, Evening —

Suggested by yesterday's evening NY Lottery "068"
and by Weltschmerz  and the Ursprache


— Walter Benjamin, “On Language as Such and On the Language of Man”  (1916),
Edmund Jephcott, tr., Walter Benjamin, Selected Writings, Volume I:  1913-1926  ,
Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA,
Harvard University Press, 1996, pp. 62-74. The above is page 68.

A more entertaining meditation is suggested by yesterday's 4-digit evening NY number—
a video tribute to a song said to have been released as a single on 7383 (7/3/83)—


Related material— "Dark Side of the Moon" in this journal.

Sunday, June 27, 2010

Sunday at the Apollo

Filed under: General,Geometry — m759 @ 9:00 PM



The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
  subcubes in the 27-part (Galois) 3×3×3 cube–

The 13 symmetry axes of the cube

Sunday, May 13, 2007

Sunday May 13, 2007

Filed under: General — m759 @ 12:31 PM

Prime Blue

“To the two gods of art, Apollo and Dionysus, we owe our recognition that… there is a tremendous opposition, as regards both origins and aims, between the Apolline art of the sculptor and the non-visual, Dionysiac art of music.”
The Birth of Tragedy,
    by Friedrich Nietzsche,
    Penguin, 1993, page 14.
    Quoted in “A Mass for Lucero.”

Half the Answer:
Commentary by spookytruth
from Log24, 2/22/2005:

“I mean, come on, Hunter, a stupid bullet through the head??? how creative, you brain-addled simpleton… if you take the assignment, if you are going to hook up your afterlife keyboard and transmit back and tell us about what it is REALLY like out there, if you decided to let your electric-shock fingers hot wire us the truth of the afterlife… if you really planned to tell us the answer to our ultimate, emotional question…… ‘does God prefer beer, wine, or a shot of whiskey.’ well, if that is what you decided to do well then, for God’s sake, don’t forget (oh, wait, yeah, you already DID FORGET, you half-baked, half brained, half witted, half-a-loaf, half pint pin head, you forgot, THE JOURNEY IS HALF THE ANSWER!!!!!!!!!!!!!!!!”

On Dionysus:

“For wine, he loves to view
    his altars stain,
 But prime blue ruin*–
    goes against the grain.”
— page 69, Jack Randall’s Diary

  *name “given by
   the modern Greeks to gin
— page 4, Jack Randall’s Diary

Sunday May 13, 2007

Filed under: General — m759 @ 5:01 AM

After Winter

Apollo's Temple

Monday, June 13, 2005

Monday June 13, 2005

Filed under: General — m759 @ 9:00 PM


The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

Picture from Feb. 8
(Martin Buber’s birthday)

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Sunday, April 13, 2003

Sunday April 13, 2003

Filed under: General — m759 @ 11:59 PM

Palm Sunday, Part II:

Cold Mountain

From the notes to the CD of Songs From the Mountain (John Herrmann, Dirk Powell, Tim O’Brien):

“John [Herrmann, banjo player] would like to dedicate his work on this recording to Philip Kapleau Roshi, Kalu Rimpoche, and Harada Tangen Roshi, who all know the way to Cold Mountain….”

 See Buddha’s Birthday (April 8) and The Diamond Project.

“What are you thinking of? What thinking? What? 
  I never know what you are thinking. Think.”

— Tom Eliot, The Waste Land 

“I am thinking…
… of the midnight picnic
Once upon a time….”

Suzanne Vega, “Tom’s Diner

Once upon a time…

Later the Same Day
Enormous Changes
At the Last Minute

Grace Paley

“De donde crece la palma” — Song lyric 

From On Beauty, by Elaine Scarry, Princeton University Press, 1999, a quotation from Homer —

in Delos, beside Apollo’s altar
the young slip of a palm-tree
springing into the light.”

See also A Mass for Lucero and The Shining of Lucero.  

How much story do you want?”

— George Balanchine

Sunday, October 2, 2016


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

"I don't care about what anything was designed  to do,
 I care about what it can  do."

Ed Harris in "Apollo 13"

Tuesday, August 10, 2010

A Problem

Filed under: General,Geometry — m759 @ 7:35 PM

From Telegraph.co.uk (published: 5:56 PM BST 10 Aug 2010), a note on British-born Canadian journalist Bruce Garvey, who died at 70 on August 1—

In 1970, while reporting on the Apollo 13 mission at Nasa Mission Control for the Toronto Star, he was one of only two journalists— alongside Richard Killian of the Daily Express— to hear the famous message: "Houston we've had a problem."

See also Log24 posts of 10 AM and noon today.

The latter post poses the problem "You're dead. Now what?"

Again, as in this morning's post, applying Jungian synchronicity—

A check of this journal on the date of Garvey's death yields a link to 4/28's "Eightfold Geometry."

That post deals with a piece of rather esoteric mathematical folklore. Those who prefer easier problems may follow the ongoing struggles of Julie Taymor with "Spider-Man: Turn Off the Dark."

The problems of death, geometry, and Taymor meet in "Spider Woman" (April 29) and "Memorial for Galois" (May 31).

Friday, September 1, 2006

Friday September 1, 2006

Filed under: General — Tags: — m759 @ 7:59 AM
Dirty Business

Some friends of mine
are in this band
— David Auburn, Proof 

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

And if the band you’re in
starts playing different tunes
I’ll see you on
the dark side of the moon.”

Quoted in Log24 on the
July 20, 2005, anniversary
of the 1969 Apollo 11
“one small step” moon landing

Last night’s entry on Glenn Ford, freemasonry, and the business of narrative leads to the following meditation.

This morning’s New York Times obituary of the Apollo 11 launch director brings back memories of Dean Martin’s classic refrain “when the moon hits your eye like a big pizza pie….”  This in turn is a reminder of one of the great subtitles– Dino: Living High in the Dirty Business of Dreams (by Nick Tosches, published by Secker & Warburg on November 9, 1992).  I respect the launch director, Rocco A. Petrone, who later headed the successful recovery of Apollo 13 (and also headed the entire Apollo program), but I also greatly respect Nick Tosches as a guide to the dark side of humanity.  Secular humanism and the religion of scientism are all very well as cheerleaders for physics, but Tosches and the Roman Catholic Church have a much better understanding of human nature and original sin.

Monday, February 17, 2020

RIP Charles Portis

Filed under: General — Tags: , — m759 @ 4:04 PM

     See also "True Grid " in this  journal.

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo, the field of Reason…."
– John Outram, architect    

See as well . . .

Monday, December 23, 2019


Filed under: General — Tags: , , — m759 @ 8:16 AM

See as well the previous post and Pacific Science Institute.

Monday, March 25, 2019


Filed under: General — Tags: , , , , , — m759 @ 1:46 PM

(Continued from the previous post.)

In-Between "Spacing" and the "Chôra "
in Derrida: A Pre-Originary Medium?

By Louise Burchill

(Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.),  Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010)

"The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance  (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing  (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)."

1  Jacques Derrida, “La Différance,” in Marges – de la philosophie  (Paris: Minuit, 1972), p. 14. Henceforth cited as  D  .

2  Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and  Difference  (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW .

3  Jacques Derrida, Le Toucher, Jean-Luc Nancy  (Paris: Galilée, 2000), p. 207.

. . . .

"… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance  consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance  and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus  and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance  that Derrida must, in a 'properly' apotropaic  gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…."

16  Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger  2 (1990): 207-227.

. . . .

… "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.'

For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements )  between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).


For the Church of Synchronology

See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.

Tuesday, February 13, 2018

A Titan of the Field

Filed under: General,Geometry — 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, October 9, 2017

Plan 9 Continues

Filed under: General — m759 @ 7:20 PM

From the posts of October 9 four years ago —

Tuesday, March 21, 2017

Special Topics

Filed under: General,Geometry — Tags: , — m759 @ 12:41 PM

A roundup of posts now tagged "Apollo Psi" led to the name
Evan Harris Walker in the post Dirac and Geometry of
Dec. 14, 2015. That post mentions

" Evan Harris Walker’s ingenious theory of
the psi force, a theory that assigned psi
both positive and negative values in such a way
that the mere presence of a skeptic in the near
vicinity of a sensitive psychic investigation could
force null results. Neat, Dr. Walker, thought
Peter Slater— neat, and totally without content."

— From the 1983 novel Broken Symmetries  
     by Paul Preuss 

It turns out that Walker died "on the evening of August 17, 2006." 

From this journal on that date

Friday, March 3, 2017


Filed under: General — Tags: — m759 @ 2:56 PM

(Notes for Josefine, continued from December 22, 2013) 

From a prequel to The Shining , by Stephen King—

You had to keep an eye on the boiler
because if you didn’t, she would creep on you. 

What did that mean, anyway? Or was it just
one of those nonsensical things that sometimes
came to you in dreams, so much gibberish?
Of course there was undoubtedly a boiler
in the basement or somewhere to heat the place,
even summer resorts had to have heat sometimes,
didn’t they (if only to supply hot water)? But creep ?
Would a boiler creep ?
You had to keep an eye on the boiler.
It was like one of those crazy riddles,
why is a mouse when it runs,
when is a raven like a writing desk,
what is a creeping boiler? 

The boiler room from Kubrick's 'The Shining'

A related figure —


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

The New York Times  on Wednesday, Sept. 19, 2012 —

This  journal on the previous afternoon —

For greater artistic depth, see Tetrads in this journal.

Friday, January 13, 2017

Elsewhere …

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


Filed under: General — Tags: , — m759 @ 9:45 AM

For the title, see Wiktionary.

Charles Taylor, 'Sources of the Self'

Thursday, January 12, 2017

The Cherished Gift

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

From "Solomon's Cube" —

Related material —

"Is this a dagger I see before me?

"No." (A line suggested by Polanski's 2010 "The Ghost Writer")


Filed under: General,Geometry — 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.

Saturday, November 12, 2016

Good Questions

Filed under: General — Tags: — m759 @ 7:13 AM

1 Corinthians 15:55

Wednesday, July 27, 2016

Deathly Hallows

Filed under: General — Tags: — m759 @ 7:00 AM

The previous post, on the July 13 death of computer scientist Robert Fano,
suggests a review of "Deathly Hallows" posts in this journal. From that review —



The Fano plane block design



The Deathly Hallows symbol—
Two blocks short of  a design.

For further information, click the image below —


Tuesday, July 26, 2016

In Nomine Patris

Filed under: General — Tags: , , — m759 @ 9:48 PM

"Robert Fano, an electrical engineer who was instrumental
in creating a world of instantly responsive computers, died
on July 13 in Naples, Fla. He was 98."

John Markoff in this evening's online New York Times

Wikipedia on Robert Fano

"Fano's father was the mathematician Gino Fano . . . .

A mnemonic I associate with the Fano plane — "Seven is Heaven . . . .

Log24 on the date of Robert Fano's death —

Wednesday, July 13, 2016


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

"At CERN the LHC has reached design luminosity,
and is breaking records with a fast pace of new
collisions. This may have something to do with the
report that the LHC is also about to tear open
a portal to another dimension

— Peter Woit, Thursday, June 30, 2016,
    at 1:01 PM ET 

Another sort of design luminosity —

IMAGE- Massimo Vignelli, his wife Lella, and cube


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

For one meaning of the title, see The Faustian Merry-Go-Round.

Look Busters

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

See a search in this journal for "Look, Buster."

Fritz Leiber's 'Spider' symbol

Block That Metaphor

Filed under: General — Tags: , — m759 @ 8:38 PM

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points (The 6 cube faces are mapped to the 6 hexagram lines.)

Happy dies natalis  to the late Frida Kahlo.

Art Wars

Filed under: General — Tags: — m759 @ 10:45 AM

Wil S. Hylton today in the online New York Times

"It seems to me now, with greater reflection,
that the value of experiencing another person’s art
is not merely the work itself, but the opportunity
it presents to connect with the interior impulse of another.
The arts occupy a vanishing space in modern life:
They offer one of the last lingering places to seek out
empathy for its own sake, and to the extent that
an artist’s work is frustrating or difficult or awful,
you could say this allows greater opportunity to try to
meet it. I am not saying there is no room for discriminating 
taste and judgment, just that there is also, I think,
this other portal through which to experience creative work
and to access a different kind of beauty, which might be
called communion."

Or damnation.

Always Nice to See You

Filed under: General — Tags: — m759 @ 9:00 AM

“It is always
Nice to see you”
Says the man
Behind the counter

— Suzanne Vega. "Tom's Diner"

Wednesday, December 23, 2015

Class of 64

Filed under: General — m759 @ 9:00 PM

The previous post dealt with one of the 64 symbols
(in a redesigned format) of the ancient Chinese classic 
The I Ching .

For those who prefer to be guided by programmed
responses to alphabetical  symbols

A lyric by Ira Gershwin —

A cinematic "T"

See also "T for Texas" in this journal and
George Clooney's recent attempt to commercialize
both the space program and the letter Omega: 

From a post of May 13, 2015 —

Monday, December 14, 2015

Dirac and Geometry

Filed under: General,Geometry — Tags: , — m759 @ 10:30 AM


See a post by Peter Woit from Sept. 24, 2005 — Dirac's Hidden Geometry.

The connection, if any, with recent Log24 posts on Dirac and Geometry
is not immediately apparent.  Some related remarks from a novel —

From Broken Symmetries by Paul Preuss
(first published by Simon and Schuster in 1983) —

"He pondered the source of her fascination with the occult, which sooner or later seemed to entangle a lot of thoughtful people who were not already mired in establishmentarian science or religion. It was  the religious impulse, at base. Even reason itself could function as a religion, he supposed— but only for those of severely limited imagination. 

He’d toyed with 'psi' himself, written a couple of papers now much quoted by crackpots, to his chagrin. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand— for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox. Quantum theory was inextricable from the uncertainty relations. 

The classical fox knows many things, but the quantum-mechanical hedgehog knows only one big thing— at a time. 'Complementarity,' Bohr had called it, a rubbery notion the great professor had stretched to include numerous pairs of opposites. Peter Slater was willing to call it absurdity, and unlike some of his older colleagues who, following in Einstein’s footsteps, demanded causal explanations for everything (at least in principle), Peter had never thirsted after 'hidden variables' to explain what could not be pictured. Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once. It was a thin nectar, but he was convinced it was the nectar of the gods. 

The psychic investigators, on the other hand, demanded to know how  the mind and the psychical world were related. Through ectoplasm, perhaps? Some fifth force of nature? Extra dimensions of spacetime? All these naive explanations were on a par with the assumption that psi is propagated by a species of nonlocal hidden variables, the favored explanation of sophisticates; ignotum per ignotius

'In this connection one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all…' The words were Heisenberg’s, lecturing in 1929 on the irreducible ambiguity of the uncertainty relations. They reminded Peter of Evan Harris Walker’s ingenious theory of the psi force, a theory that assigned psi both positive and negative values in such a way that the mere presence of a skeptic in the near vicinity of a sensitive psychic investigation could force null results. Neat, Dr. Walker, thought Peter Slater— neat, and totally without content. 

One had to be willing to tolerate ambiguity; one had to be willing to be crazy. Heisenberg himself was only human— he’d persuasively woven ambiguity into the fabric of the universe itself, but in that same set of 1929 lectures he’d rejected Dirac’s then-new wave equations with the remark, 'Here spontaneous transitions may occur to the states of negative energy; as these have never been observed, the theory is certainly wrong.' It was a reasonable conclusion, and that was its fault, for Dirac’s equations suggested the existence of antimatter: the first antiparticles, whose existence might never have been suspected without Dirac’s crazy results, were found less than three years later. 

Those so-called crazy psychics were too sane, that was their problem— they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry."

Particularly relevant

"Mathematical relationships were enough to satisfy him,
mere formal relationships which existed at all times,
everywhere, at once."

Some related pure  mathematics

Anticommuting Dirac matrices as spreads of projective lines

Wednesday, June 24, 2015

It’s 10 PM

Filed under: General — m759 @ 10:00 PM

Do you know where your watch is?

From a post of May 13, 2015 —

From the recent film "Interstellar" —

Wednesday, May 13, 2015


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

See the previous post, "Space," as well as

SymOmega in this journal and a suggested motto
for The University of Western Australia.


Filed under: General,Geometry — Tags: — m759 @ 2:00 PM

Notes on space for day 13 of May, 2015 —

The 13 symmetry axes of the cube may be viewed as
the 13 points of the Galois projective space PG(2,3).
This space (a plane) may also be viewed as the nine points
of the Galois affine space AG(2,3) plus the four points on
an added "line at infinity."

Related poetic material:

The ninefold square and Apollo, as well as 


Wednesday, June 18, 2014

A Dark and Stormy Night

Filed under: General — m759 @ 9:00 AM

This journal on the morning of January 27, 2010,
the day of J. D. Salinger’s death, had a post on
Nietzsche and Heraclitus titled “To Apollo.”

Related material:

“… the wind was noisy the way it is in spooky movies
on the night the old slob with the will gets murdered.”

— From the opening sentence of the first Holden Caulfield
story, published in the Collier’s  of December 22, 1945

See also Peter Matthiessen on Zen,   Salinger and Vedanta,
and Heraclitus in this journal.  Some background—

A quotation from Nietzsche…
(Sämtliche Werke, Kritische Studienausgabe in 15 Bänden  (KSA).
Herausgegeben von Giorgio Colli und Mazzino Montinari.
Berlin: De Gruyter, 1980):

“Nietzsche wrote:

‘Seeing the world as a divine game and beyond good and evil:
in this both the Vedanta and Heraclitus are my predecessors.'”

— KSA vol. 11, page 26, as quoted by André van der Braak
     in a chapter from his 2011 book Nietzsche and Zen

(Darin, dass die Welt ein göttliches Spiel sei
jenseits von Gut und Böse —
habe ich die Vedanta-
und Heraklit zum Vorgänger

Thursday, February 13, 2014

Plan 9

Filed under: General — Tags: , — m759 @ 6:29 PM


The final link in today's previous post leads to
a post whose own final link leads to

Thursday, December 13, 2012


Filed under: Uncategorized — m759 @ 12:00 PM                

 The sequel to Vibrations

Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) — 

“… the object sets up a kind of 
 frame or space or field 
 within which there can be epiphany.”

Or place.

See  A Prince of Darkness 
and "A Clean, Well-Lighted Place."

Fashion Week — The Conclusion

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

Frank Langella as Dracula 
(opened on Broadway in October, 1977)

Related material: Bat Signal.

Winter’s Game*

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

Part I:  Continued from January 20 — "Arising Heaven" —

Part II:  The Stars My Destination  in this journal

'The Stars My Destination,' current edition (with cover slightly changed)

Part III:  Ender's Game  —

* The title refers to a character, Rogue Winter, in Alfred Bester's
  1981 novel The Deceivers .

Wednesday, December 25, 2013

A Midnight Clear

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

Click image for a meditation.

Tuesday, December 24, 2013

Through a Mirror, Darkly

Filed under: General — Tags: — m759 @ 12:26 PM

Review of a book first published in 1989—

Reality's Mirror: Exploring the Mathematics of Symmetry —

"Here is a book that explains in laymen language
what symmetry is all about, from the lowliest snowflake
and flounder to the lofty group structures whose
astonishing applications to the Old One are winning
Nobel prizes. Bunch's book is a marvel of clear, witty
science writing, as delightful to read as it is informative
and up-to-date. The author is to be congratulated on
a job well done." — Martin Gardner

A completely different person whose name
mirrors that of the Mathematics of Symmetry  author —

IMAGE- Daily Princetonian, Dec. 23, 2013

See also this  journal on the date mentioned in the Princetonian .

"Always with a little humor." — Yen Lo

Wednesday, December 18, 2013

Bing Bang Theory

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

Microsoft in 2009 on its new search engine name—

"We like Bing because it sounds off in our heads
when we think about that moment of discovery
and decision making— when you resolve those
important tasks."

A search on Bing today —

IMAGE- Top search result on Bing for 'diamond space' on Dec. 18, 2013

A colorful tale —

IMAGE- The Diamond 16 Puzzle, with commentary

"Bing bang, I saw the whole gang
Bobby Darin, 1958

Saturday, December 14, 2013

Beautiful Mathematics

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

The title, which I dislike, is taken from a 2011 publication
of the MAA, also sold by Cambridge University Press.

Some material relevant to the title adjective:

"For those who have learned something of higher mathematics, nothing could be more natural than to use the word 'beautiful' in connection with it. Mathematical beauty, like the beauty of, say, a late Beethoven quartet, arises from a combination of strangeness and inevitability. Simply defined abstractions disclose hidden quirks and complexities. Seemingly unrelated structures turn out to have mysterious correspondences. Uncanny patterns emerge, and they remain uncanny even after being underwritten by the rigor of logic."— Jim Holt, opening of a book review in the Dec. 5, 2013, issue of The New York Review of Books

Some relevant links—

The above list was updated on Jan. 31, 2014, to include the
"Strangeness" and "Hidden quirks" links.  See also a post of
​Jan. 31, 2014.

Update of March 9, 2014 —

The link "Simply defined abstractions" is to the construction of the Steiner
system S(5, 8, 24) described by R. T. Curtis in his 1976 paper defining the
Miracle Octad Generator. It should be noted that this construction is due
to Richard J. Turyn, in a 1967 Sylvania research report. (See Emily Jennings's
talk of 1 Nov. 2012.) Compare  the Curtis construction, written in 1974,
with the Turyn construction of 1967 as described in Sphere Packings, Lattices
and Groups , by J. H. Conway and N. J. A. Sloane (first published in 1988).

Bend Sinister

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

I Ching hexagram 14, box style

Click image for background.
See also related posts.

American Beauty

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

Or: Blackboard Jungle, Continued

  Click image for
  a related story.

Sacred and Profane

Filed under: General,Geometry — Tags: , — m759 @ 10:00 AM

(Continued from yesterday afternoon)

This journal on December 12th, 2009

Rothstein's 'Emblems of Mind,' 1995, cover illustrations by Pinturicchio from Vatican

Cover illustration— Arithmetic and Music,
Borgia Apartments, The Vatican

Compare and contrast with Frenkel at the Fields Institute

Thursday, December 12, 2013

Outsider Art

Filed under: General,Geometry — Tags: — m759 @ 4:10 PM

"… Galois was a mathematical outsider…."

— Tony Mann, "head of the department of mathematical sciences,
University of Greenwich, and president, British Society for the
History of Mathematics," in a May 6, 2010, review of Duel at Dawn
in Times Higher Education.

Related art: 

(Click for a larger image.)

IMAGE- Google search for 'Diamond Space' + Galois

For a less outside  version of the central image
above, see Kunstkritikk  on Oct. 15, 2013.

Thursday, December 5, 2013

Blackboard Jungle

Filed under: General,Geometry — Tags: , — m759 @ 11:07 AM

Continued from Field of Dreams, Jan. 20, 2013.

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

That post mentioned the March 2011 AMS Notices ,
an issue on mathematics education.

In that issue was an interview with Abel Prize winner
John Tate done in Oslo on May 25, 2010, the day
he was awarded the prize. From the interview—

Research Contributions

Raussen and Skau: This brings us to the next
topic: Your Ph.D. thesis from 1950, when you were
twenty-five years old. It has been extensively cited
in the literature under the sobriquet “Tate’s thesis”.
Several mathematicians have described your thesis
as unsurpassable in conciseness and lucidity and as
representing a watershed in the study of number
fields. Could you tell us what was so novel and fruitful
in your thesis?

Tate: Well, first of all, it was not a new result, except
perhaps for some local aspects. The big global
theorem had been proved around 1920 by the
great German mathematician Erich Hecke, namely
​the fact that all L -functions of number fields,
abelian -functions, generalizations of Dirichlet’s
L -functions, have an analytic continuation
throughout the plane with a functional equation
of the expected type. In the course of proving
it Hecke saw that his proof even applied to a new
kind of L -function, the so-called L -functions with
Grössencharacter. Artin suggested to me that one
might prove Hecke’s theorem using abstract
harmonic analysis on what is now called the adele
ring, treating all places of the field equally, instead
of using classical Fourier analysis at the archimedian 
places and finite Fourier analysis with congruences 
at the p -adic places as Hecke had done. I think I did
a good job —it might even have been lucid and
concise!—but in a way it was just a wonderful 
exercise to carry out this idea. And it was also in the
air. So often there is a time in mathematics for 
something to be done. My thesis is an example. 
Iwasawa would have done it had I not.

[For a different perspective on the highlighted areas of
mathematics, see recent remarks by Edward Frenkel.]

"So often there is a time in mathematics for something to be done."

— John Tate in Oslo on May 25, 2010.

See also this journal on May 25, 2010, as well as
Galois Groups and Harmonic Analysis on Nov. 24, 2013.


Filed under: General,Geometry — Tags: , , — m759 @ 1:20 AM

Edward Frenkel recently claimed for Robert Langlands
the discovery of a link between two "totally different"
fields of mathematics— number theory and harmonic analysis.
He implied that before Langlands, no relationship between
these fields was known.

See his recent book, and his lecture at the Fields Institute
in Toronto on October 24, 2013.

Meanwhile, in this journal on that date, two math-related
quotations for Stephen King, author of Doctor Sleep

"Danvers is a town in Essex County, Massachusetts, 
United States, located on the Danvers River near the
northeastern coast of Massachusetts. Originally known
as Salem Village, the town is most widely known for its
association with the 1692 Salem witch trials. It is also
known for the Danvers State Hospital, one of the state's
19th-century psychiatric hospitals, which was located here." 

"The summer's gone and all the roses fallin' "

For those who prefer their mathematics presented as fact, not fiction—

(Click for a larger image.)

The arrows in the figure at the right are an attempt to say visually that 
the diamond theorem is related to various fields of mathematics.
There is no claim that prior to the theorem, these fields were not  related.

See also Scott Carnahan on arrow diagrams, and Mathematical Imagery.

Tuesday, December 3, 2013

Diamond Space

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

A new website illustrates its URL.
See DiamondSpace.net.

IMAGE- Site with keywords 'Galois space, Galois geometry, finite geometry' at DiamondSpace.net

Thursday, November 21, 2013


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

The Mitgang Menu

Related material: This morning's 6 AM post and Wiener News.

Update of 3:29 PM:

From Herbert Mitgang's New York Times  
obituary of Cleanth Brooks

"The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background."

Twelfth Step

Filed under: General — Tags: , , — m759 @ 7:59 AM

Continued from 24 hours ago.

From this morning's 6 AM (ET) post

"… you never made a Twelfth Step
call on an active alcoholic by yourself,
unless the alkie in question was safely
incarcerated in a hospital, detox, or the
local bughouse."

— Stephen King, Doctor Sleep

Related material from a math addict, a likely victim
of a professor's misleading rhetoric —

"Frenkel is the real deal, a professor at Berkeley…."

— "Math Porn Update" by David Justice,
       Nov. 20, 2013

The rhetoric link above leads to remarks by Frenkel.
For a similar professor's earlier misleading remarks,
see Barry Mazur in this journal.

But It Rings…

Filed under: General — Tags: — m759 @ 6:29 AM

"The shaving razor's cold and it stings."

The above image is from Ulysses “Seen,”   adapted
by Robert Berry from the novel by James Joyce.

Quad Rants

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

Continued from 24 hours ago.

"AA had no rules but many traditions (that were, in fact, rules).
One of the most ironclad was that you never made a Twelfth Step
call on an active alcoholic by yourself, unless the alkie in question
was safely incarcerated in a hospital, detox, or the local bughouse.
If you did, you were apt to end up matching him drink for drink and
line for line."

— King, Stephen (2013-09-24). Doctor Sleep: A Novel
     (p. 272). Scribner. Kindle Edition.


" Aus 'It' wurde 'Es', und King sprach es so aus,
dass man sich alleine vom Klang des Titels
gruselte: 'Essssss!' " 

— Last night's online
Hamburger Abendblatt 

"You want Frye's with that?"

Tuesday, November 12, 2013

The X-Men Tree

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

Related material:

The comments on a Log24 post of Nov. 6, 2013,
remarks by Michael Worton on the tree in 
"Waiting for Godot," images from the film
"The Tree of Life," and, in memory of Robert
de Marrais, an image search from this evening:
"Spelling the Tree" + "de Marrais," 2 MB.

Funeral Canticle

Filed under: General — Tags: — m759 @ 8:02 PM

For and by composer Sir John Tavener, 69,
who reportedly died today.

Update of 8:28 PM ET Nov. 12—
The obituary link above is to The Telegraph.
Here is a link to the version in The New York Times


Filed under: General,Geometry — Tags: , , — m759 @ 6:45 AM

IMAGE- 'Devil Music' from 'Kaleidoscopes- Selected Writings of H.S.M. Coxeter'


20 pages of incidental music written at school
for G. K. Chesterton’s play MAGIC

by D. Coxeter.”

See also

Related material —  Chesterton + Magic in this journal.

Tuesday, October 15, 2013

The Field of Reason*

Filed under: General — m759 @ 12:00 PM

IMAGE- Adolf Holl on the Roman emperor Julian and Apollo

Or perhaps the Richman.

Roger Richman, agent who represented image rights for the
estates of celebrities, reportedly died on October 9, 2013.

This journal on that date —

* For the title, see Apollo + Outram in this journal.

Wednesday, October 9, 2013

Sign in

Filed under: General — Tags: — m759 @ 7:20 PM

From the upper right of the Google search screen —

For related religious remarks, see "The Ninth."

According to Hoyle

Filed under: General — Tags: — m759 @ 1:13 PM

IMAGE- Quote from Hoyle's 'October the First is Too Late'

See also the previous post.

"Some like it in the pot, nine days old."

Friday, October 4, 2013

Christian’s Question

Filed under: General — Tags: — m759 @ 9:16 PM

"Now, who's the master?"

— Christian Bale in "American Hustle," a film
     scheduled for limited release on St. Lucy's Day
     and wide release on Christmas Day, 2013

See also this journal on November 26, 2012.

Walter’s Wake

Filed under: General — Tags: , — m759 @ 8:12 PM

(Continued from October First)

"It gets to the end
We get to run it again"

— James Taylor,
    "One More Go Round" from
    New Moon Shine  album

For the Feast of St. Francis

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

"According to Vladimir Nabokov, Salvador Dalí
 was 'really Norman Rockwell’s  twin brother
 kidnapped by gypsies in babyhood.'
 But actually there were triplets: the third one is
 Stephen King."

 — Margaret Atwood, "Shine On,"  
      online Sept. 19, 2013

"The metaphor for metamorphosis
  no keys unlock."

 — Steven H. Cullinane, Nov. 7, 1986

Color News

Filed under: General — Tags: , — m759 @ 12:48 PM

(Continued from yesterday's STEM and Truman Show.)

Old Soldier

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

Roll Credits

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

See also Howl in this journal.

Related material from a June 22, 2013, post

Kitty in Uncanny X-Men #168 (April 1983)


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

From Inception  (2010) :

From Diamonds Studio Generative Identity (2013) :

Sunday, September 22, 2013

Incarnation, Part 2

Filed under: General,Geometry — Tags: , , — m759 @ 10:18 AM

From yesterday —

"…  a list of group theoretic invariants
and their geometric incarnation…"

David Lehavi on the Kummer 166 configuration in 2007

Related material —

IMAGE- 'This is not mathematics; this is theology.' - Paul Gordan

"The hint half guessed, the gift half understood, is Incarnation."

T. S. Eliot in Four Quartets

"This is not theology; this is mathematics."

— Steven H. Cullinane on  four quartets

To wit:

Click to enlarge.

Saturday, September 21, 2013

Geometric Incarnation

The  Kummer 166  configuration  is the configuration of sixteen
6-sets within a 4×4 square array of points in which each 6-set
is determined by one of the 16 points of the array and
consists of the 3 other points in that point's row and the
3 other points in that point's column.

See Configurations and Squares.

The Wikipedia article Kummer surface  uses a rather poetic
phrase* to describe the relationship of the 166 to a number
of other mathematical concepts — "geometric incarnation."

Geometric Incarnation in the Galois Tesseract

Related material from finitegeometry.org —

IMAGE- 4x4 Geometry: Rosenhain and Göpel Tetrads and the Kummer Configuration

* Apparently from David Lehavi on March 18, 2007, at Citizendium .

Mathematics and Narrative (continued)

Filed under: General,Geometry — Tags: , — m759 @ 1:00 AM


A review of posts from earlier this month —

Wednesday, September 4, 2013


Filed under: Uncategorized — m759 @ 4:00 PM

Unexpected connections between areas of mathematics
previously thought to be unrelated are sometimes referred
to as "moonshine."  An example—  the apparent connections
between parts of complex analysis and groups related to the
large Mathieu group M24. Some recent work on such apparent
connections, by Anne Taormina and Katrin Wendland, among
others (for instance, Miranda C.N. Cheng and John F.R. Duncan),
involves structures related to Kummer surfaces .
In a classic book, Kummer's Quartic Surface  (1905),
R.W.H.T. Hudson pictured a set of 140 structures, the 80
Rosenhain tetrads and the 60 Göpel tetrads, as 4-element
subsets of a 16-element 4×4 array.  It turns out that these
140 structures are the planes of the finite affine geometry
AG(4,2) of four dimensions over the two-element Galois field.
(See Diamond Theory in 1937.)

Thursday, September 5, 2013

Moonshine II

Filed under: Uncategorized — Tags:  — m759 @ 10:31 AM

(Continued from yesterday)

The foreword by Wolf Barth in the 1990 Cambridge U. Press
reissue of Hudson's 1905 classic Kummer's Quartic Surface
covers some of the material in yesterday's post Moonshine.

The distinction that Barth described in 1990 was also described, and illustrated,
in my 1986 note "Picturing the smallest projective 3-space."  The affine 4-space
over the the finite Galois field GF(2) that Barth describes was earlier described—
within a 4×4 array like that pictured by Hudson in 1905— in a 1979 American
Mathematical Society abstract, "Symmetry invariance in a diamond ring."

"The distinction between Rosenhain and Goepel tetrads
is nothing but the distinction between isotropic and
non-isotropic planes in this affine space over the finite field."

The 1990 paragraph of Barth quoted above may be viewed as a summary
of these facts, and also of my March 17, 2013, note "Rosenhain and Göpel
Tetrads in PG(3,2)



Happy birthday to Stephen King.

Monday, September 9, 2013

ART WARS Midrash

Filed under: General — Tags: , — m759 @ 5:48 PM

Poster shown here last night

IMAGE- Poster for film 'MAX'- 'Art + Politics = Power'

Politics this afternoon —

IMAGE- News: Norway's center-right heads for big win.

Viking Book

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

For the late Billy Wilder, director of Ace in the Hole  (1951)

IMAGE- Book by Halvor Bodin on the art of Josefine Lyche and others. See halvorbodin.com.

Click image for a larger version.

See, too, this morning's quarter-to-three post, and The Vikings  (1958)—

The art by Josefine Lyche in the Bodin book shown 
above is, as the artist notes, based on my own work.

Ace in the Hole

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

Some random thoughts suggested by the Norwegian ice hole
in the opening scene of the 2012 film Kon-Tiki .

From a Log24 post of August 2, 2013

IMAGE-Kristen Wiig in 'The Secret Life of Walter Mitty'

See, too, the secret life of Marsden Hartley :

IMAGE- Two pictures by Marsden Hartley- 'The Ice Hole' and 'Portrait of a German Officer'


Filed under: General — Tags: — m759 @ 1:09 AM

For the star of Platoon 

* Continued from July 28, 2011.

Sunday, September 8, 2013

The Importance of Being Ernst

Filed under: General — Tags: , — m759 @ 11:14 PM

For John Cusack and Menno Meyjes —

"I still haven't found what I'm looking for." — Bono

"In fact Surrealism found what it had been looking for
from the first in the 1920 collages [by Max Ernst],
which introduced an entirely original scheme of visual structure…."

Rosalind Krauss quoting André Breton
    in "The Master's Bedroom"

See also tonight's 10 PM post.

"Artistic Genesis and Perspective of Surrealism" (1941),
   in Surrealism and Painting  (New York, Harper & Row, 1972, p. 

Monday, August 26, 2013

Dark Side Tales

Filed under: General — m759 @ 3:00 PM

"Got to keep the loonies on the path."

Lyrics to Dark Side of the Moon

For those who, like Tom Stoppard, prefer the dark side—

He runs, panting, until he ends up
in front of a tall, brilliantly lit office building.
As he approaches, the lights in the building
are going off floor by floor.

He rushes into
the lobby, running for the elevator.

Burning the midnight oil, Mr. Smith?
You forgot to sign in.

Bateman wheels around and shoots him.
He runs toward the revolving doors.
As he swings around in the doors, he notices
a JANITOR who has witnessed the shooting.
He revolves back into the lobby and shoots the janitor.

He runs out of the building
and across the street to an identical office building,
the one that houses Pierce & Pierce.

Bateman nods at the Pierce & Pierce NIGHT WATCHMAN
and signs in. He breathes a sigh of relief as
​the elevator doors close behind him.

by Mary Harron and Guinevere Turner
(Based on the novel by Bret Easton Ellis, 
Fourth Draft, November 1998)

Not quite so dark—

"And then one day you find ten years have got behind you."

— Lyrics to Dark Side of the Moon

This journal ten years ago, on August 25, 2003

         … We seek

The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object

At the exactest point at which it is itself,
Transfixing by being purely what it is,
A view of New Haven, say, through the certain eye,

The eye made clear of uncertainty, with the sight
Of simple seeing, without reflection. We seek
Nothing beyond reality. Within it,

Everything, the spirit's alchemicana
Included, the spirit that goes roundabout
And through included, not merely the visible,

The solid, but the movable, the moment,
The coming on of feasts and the habits of saints,
The pattern of the heavens and high, night air.

— Wallace Stevens, "An Ordinary Evening
     in New Haven," Canto IX
    (Collected Poems , pp. 471-472)

"A view of New Haven, say…." —

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect 

A similar version of this Apollonian image —


Related material for the loonies:

"the spirit's alchemicana."

Saturday, August 24, 2013

Being’s Road

Filed under: General — Tags: — m759 @ 9:16 PM

For the late Julie Harris —

By slow and carefully modulated steps Bradford's narrative
has brought his community of separatists to the place he
calls Cape Harbor… where, face-to-face with the bleak
and wintry reduction that is his image for American space,
he finds himself stopped, able to do nothing but come to
an astonished pause. The final step, that of imaginative
crossing into the land that lies before them, remains
beyond the power of narrative to take. Narrative falters, and
finding his journey advanced to an "odd Fork in Being's Road"
and himself nothing so much as an "empty spirit / In vacant
space" (to adopt apt phrases from Dickinson and Stevens…),
Bradford requires the sublime if he is to continue moving
forward: separation becomes exaltation as it becomes
manifest that only an influx 
of "the Spirit of God and His
grace" can have permitted the community to survive its
passage to the limit depicted.

— David Laurence, "William Bradford's American Sublime,"
PMLA , Vol. 102, No. 1, 1987, pp. 55-65

Cast (continued)

Filed under: General — Tags: , — m759 @ 3:31 AM

The death yesterday of British cinematographer
Gilbert Taylor suggests an image from last evening's
Log24 search Point Omega —


The die in the above image (shown here Dec. 28, 2012
displays the numbers 3-6-5 in counterclockwise order.
A similar die in an earlier post served as a metaphor for
a time-jump to 365 days in the past.

For some religious remarks by Umberto Eco that may
serve as a small memorial to Taylor, see this journal 
a year before  the day he died— August 23, 2012.

"Everybody comes to Rick's."

Friday, August 23, 2013

Vacant Space

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

A passage from Wallace Stevens

The spirit and space,
The empty spirit 
In vacant space.

A frame from the film American Psycho  (2000), starring Christian Bale—

IMAGE- 'espace' sign from the film 'American Psycho'

The rest of the film is not recommended.

Related material—

"24 Hour Psycho" at the Museum of Modern Art in the novel Point Omega .

Illustration from a New York Times  review

IMAGE- NY Times headline 'A Wrinkle in Time' with 24 Hour Psycho and Point Omega scene

Ten Years of Nothing

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

For insatiable actor Patrick Bateman (protagonist of
American Psycho) and anti-theologian Kirk Varnedoe
Pictures of Nothing, this journal ten years ago today )

Philip Rieff, The Crisis of the Officer Class,
University of Virginia Press, 2007

From page 73:

The third culture's life-style, its way, is no way: it is abandonment, 
an ethos of empty seriousness best expressed, I think, by the 
greatest of American poets in the tradition that began with 
Emerson. Wallace Stevens was the greatest American maker of 
that "fictive music" of the "unreal" by which poets "give back to us 
what you [God] gave," Creation itself, now understood, in the third
culture, as the "imagination that we spurned and crave." Stevens
understood the fictive music of faith, that intensity which

The near, the clear …
. . . . . . . . . . . . . . . . .
… an image that is sure,
. . . . . . . . . . . . . . . . . . .
Yet not too like, yet not so like to be
Too near, too clear, saving a little to endow
Our feigning with the strange unlike…. [12]

This is masterly anti-theology. This is what no "mickey mockers" of 
the spirit can ever become: the "American sublime," the mar-

[12] Wallace Stevens, "To the One of Fictive Music," in Collected 
 (New York: Alfred A. Knopf, 1954), 87-88; all citations of 
Stevens are to this edition.

From page 74:

velous panic and emptiness of belief by which the "sublime comes 
down/To the spirit itself" and terrifies the American self:

The spirit and space,
The empty spirit 
In vacant space.
What wine does one drink?
What bread does one eat? [13]

This poet is no great character, nor temple priest. He is a virtuoso 
chef, preparing the food for the American feast of unbeliefs. This 
supreme fictionist invents bread and wine, anything that will act as 
that "act of the mind." [14] Stevens had a shrewd Emersonian idea 
of myth, or Freudian, the "sexual myth" or any other "images of 
metaphors." [15] He knew that it was in "this invented world" that "the 
death of one god is the death of all." This is the most supreme of all 
fictions, by which "He imposes orders as he thinks of them." [16]

[13] Stevens, "The American Sublime," 130-31
[14] Stevens, "Of Modern Poetry," 239-40; modern poetry, which is 
"the finding of a satisfaction," or a script for a theater– whatever 
"will suffice" for the "insatiable actor" of the third culture, even the 
script of "cuisine bourgeoise," where we may "feast on human 
heads" (240, 227).
[15] Stevens, "Men Made out of Words," 355; and "Thinking of a 
Relation between the Images of Metaphors," 356-57.
[16] Stevens, "Notes toward a Supreme Fiction," 380-81, 403.

Wednesday, July 24, 2013

Dark Humor

Filed under: General — Tags: — m759 @ 5:09 AM

Arts and Letters Daily  today links to a July 17
Washington Post  review of two books on the
occult and the enlightenment. The review, by
Michael Dirda, ends on a cheerful note:

"Happy synchronicity."

In related news, a Walpurgisnacht obituary also
ends cheerfully:

"He was still trying to get out a joke
with his final breath."

That obituary describes a life that reportedly ended
on April 21, 2013. Synchronicity involving that date—

The posts of April 21, 2013 (and related material in
this morning's previous post).

The Broken Tablet

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

This post was suggested by a search for the
Derridean phrase "necessary possibility"* that
led to web pages on a conference at Harvard
on Friday and Saturday, March 26**-27, 2010,
on Derrida and Religion .

The conference featured a talk titled
"The Poetics of the Broken Tablet."

I prefer the poetics of projective geometry.

An illustration— The restoration of the full
15-point "large" Desargues configuration in
place of the diminished 10-point Desargues
configuration that is usually discussed.

IMAGE- The proof of the converse of Desargues' theorem involves a third triangle.

Click on the image for further details.

* See a discussion of this phrase in
  the context of Brazilian religion.

** See also my own philosophical reflections
   on Friday, March 26, 2010:
   "You Can't Make This Stuff Up." 

Saturday, July 13, 2013


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

The Inner Ring

Filed under: General — Tags: — m759 @ 9:29 PM

The title refers to Brad Leithauser's remarks
in the previous post.

This way to the egress.


Filed under: General,Geometry — Tags: , — m759 @ 2:22 AM

A sort of poem
by Gauss and Weyl —

Click the circle for the context in Weyl's Symmetry .

For related remarks, see the previous post.

A literary excursus—

Brad Leithauser in a New Yorker  post of July 11, 2013:

Reading Poems Backward

If a poet determines that a poem should begin at point A and conclude at point D, say, the mystery of how to get there—how to pass felicitously through points B and C—strikes me as an artistic task both genuine and enlivening. There are fertile mysteries of transition, no less than of termination.

And I’d like to suppose that Frost himself would recognize that any ingress into a poem is better than being locked out entirely. His little two-liner, “The Secret,” suggests as much: “We dance round in a ring and suppose / But the Secret sits in the middle and knows.” Most truly good poems might be said to contain a secret: the little sacramental miracle by which you connect, intimately, with the words of a total stranger. And whether you come at the poem frontward, or backward, or inside out—whether you approach it deliberately, word by word and line by line, or you parachute into it borne on a sudden breeze from the island of Serendip—surely isn’t the important thing. What matters is whether you achieve entrance into its inner ring, and there repose companionably beside the Secret.

One should try, of course, to avoid repose in an inner circle of Hell .

Monday, July 1, 2013


Filed under: General — Tags: , — m759 @ 2:07 PM

Continued from Sunday's post Book Award and last
midnight's post Holding the Frame

The nineteenth-century German writer Rudolf Haym on
German romantic Hellenism—

"In the enjoyment of this fair picture-world, our nation must 
needs delude itself a moment with the dream of Greek felicity 
and Greek repose to awaken directly poorer and more restless 
than before. To Poetry such a delusion was indeed natural, and 
who would dispute it with her after she had offered to our 
enjoyment what was sweetest and most perfect! But we see 
now all at once Metaphysic seized with the same illusion. 
Turning aside from the strait path of sober inquiry and from the 
labour of deliverance through the most conscientious criticism, 
Hegel begins to expand over our spiritual world his ideal that 
was found in Hellas, that was strengthened by exhaustive 
penetration into the ultimate grounds of all religion. A dreamed-of 
and yearned-for future is treated as present. A system tricked 
out with the entire dignity of the science of truth raises itself 
beside our poetry, and with diamond net spins us into an idea 
with which the want, the incompleteness, and the unbeauty of 
our political and historical actuality is at every point in contradiction."

Rudolf Haym, Hegel und seine Zeit  (1857), 91-92, translated 
and quoted in  The Secret of Hegel , by James Hutchison Stirling
(1898 edition, p. 626)

Holding the Frame

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

High praise for a 1941 film

Major Barbara  (Gabriel Pascal, 1941) — "There are some performances
that bypass your critical faculties altogether, connecting not with your brain
but with your soul. They are desperately few, those characterisations of
such heightened sensitivity, such emotional resonance that the effect is
both exalting and suffocating. You might chance upon one every three or 
four years, if you're lucky. I don't know why, or how, but every time Wendy
Hiller utters a line or holds the frame in Major Barbara , I am on the verge
of tears." — Rick Burin

Friday, June 21, 2013


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

From the final pages of the new novel
Lexicon , by Max Barry:

“… a fundamental language
of the human mind—
the tongue in which the human animal
speaks to itself at the basest level.
The machine language, in essence….”

“… the questions raised by
this underlying lexicon.
What are its words?
How many are there? ….
Can we learn to speak them?
What does it sound like
when who we are is expressed
in its most fundamental form?
Something to think about.”

       R. Lowell

Related material:

IMAGE- Hypokeimenon in Liddell and Scott's Greek-English Lexicon

“… the clocks were striking thirteen.” — 1984

Thirty Years Ago

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM

Wednesday, June 19, 2013


Filed under: General — Tags: — m759 @ 11:09 PM

See Juneteenth in this journal.

For related meditations, see last October 27th.


Filed under: General — Tags: — m759 @ 10:27 PM

Ein Eck

Filed under: General,Geometry — Tags: , — m759 @ 9:29 PM

"Da hats ein Eck" —

"you've/she's (etc.) got problems there"

St. Galluskirche:

St. Gallus's Day, 2012:

Click image for a St. Gallus's Day post.

A related problem: 

Discuss the structure of the 4x4x4 "magic" cube
sent by Pierre de Fermat to Father Marin Mersenne
on April 1, 1640, in light of the above post.


Filed under: General — Tags: — m759 @ 9:10 AM


Midnight in the Garden

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


See Robert Hughes in this journal.

Tuesday, June 18, 2013


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

IMAGE- 'Lexicon,' a novel by Max Barry published June 18, 2013

This journal on May 14, 2013:

IMAGE- Valéry on ornament in 'Method of Leonardo,' with Valéry's serpent-and-key emblem

"And let us finally, then, observe the
parallel progress of the formations of thought
across the species of psychical onomatopoeia
of the primitives, and elementary symmetries
and contrasts, to the ideas of substances,
to metaphors, the faltering beginnings of logic,
formalisms, entities, metaphysical existences."

— Paul Valéry, Introduction to the Method of
    Leonardo da Vinci

But first, a word from our sponsor


Filed under: General,Geometry — Tags: — m759 @ 4:48 PM


For those who prefer Trudeau's
"Story Theory" of truth to his "Diamond Theory"

IMAGE- Janet Maslin's review of Max Barry's novel 'Lexicon'

Related material: Click images below for the original posts.

See as well the novel  "Lexicon" at Amazon.com 
and the word  "lexicon" in this journal.

Friday, June 14, 2013

Amy’s Shadow

Filed under: General — Tags: , — m759 @ 2:18 PM

Why knows what evil lurks…? — The Shadow

Backstory: "Amy Adams" + Shadow in this journal.

Related material —

Amy Adams as Lois Lane:

In the new Amy Adams version, Superman's Smallville mom
is played by Diane  Lane.

Lane also played George Reeves's sugar mommy
in the 2006 film Hollywoodland .

Ben Affleck and Diane Lane at the 2006 Venice Film Festival
premiere of  Hollywoodland :

See, too, today's previous post, and Amy Adams as Lacey Yeager
in the yet-to-be-made film version of An Object of Beauty .

Object of Beauty

Filed under: General,Geometry — Tags: , — m759 @ 2:01 AM

This journal on July 5, 2007 —

The Eightfold Cube and its Inner Structure

“It is not clear why MySpace China will be successful."

— The Chinese magazine Caijing  in 2007, quoted in
Asia Sentinel  on July 12, 2011

This  journal on that same date,  July 12, 2011 —


See also the eightfold cube and kindergarten blocks
at finitegeometry.org/sc.

Friedrich Froebel, Froebel's Chief Writings on Education ,
Part II, "The Kindergarten," Ch. III, "The Third Play":

"The little ones, who always long for novelty and change,
love this simple plaything in its unvarying form and in its
constant number, even as they love their fairy tales with
the ever-recurring dwarfs…."

This journal, Group Actions, Nov. 14, 2012:

"Those who insist on vulgarizing their mathematics
may regard linear and affine group actions on the eight
cubes as the dance of  Snow White (representing (0,0,0))
and the Seven Dwarfs—


Edwin M. Knowles Fine China Company, 1991

Sunday, May 12, 2013


Filed under: General,Geometry — Tags: — m759 @ 7:12 PM

Western Washington University in Bellingham maintains a
website to benefit secondary-school math: MathNEXUS.

The MathNEXUS "website of the week" on April 14, 2013,
was the Diamond 16 Puzzle and its related webpages.

Click on the above image for the April 14 webpage.

Language Game

Filed under: General — Tags: — m759 @ 8:00 AM

The above images are from a prequel (March 29, 2013)
to 'Nauts  (March 26, 2006.)

See also Spider Mother,  Gamer Post,  and Spider Tale.

Friday, April 26, 2013

Master Class

Filed under: General — Tags: , — m759 @ 8:00 PM

Philip Seymour Hoffman in "Doubt"—

and in "A Late Quartet"—

High White

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


For Times Square Church
Click image for a video.

Tuesday, April 23, 2013

Say When

Filed under: General — Tags: — m759 @ 2:01 PM

IMAGE- The author of a book on 'Solomon's Seal' in mathematics once introduced Mark Twain to George Bernard Shaw.

Beneath the word "When" above, there appears
the date of a journal post— "July 27, 2012."

A check of synchronicity for this  journal on that date
yields two posts related to this morning's remarks.

The Six-Set

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

The configurations recently discussed in
Classical Geometry in Light of Galois Geometry
are not unrelated to the 27 "Solomon's Seal Lines
extensively studied in the 19th century.

See, in particular—

IMAGE- Archibald Henderson on six-set geometry (1911)

The following figures supply the connection of Henderson's six-set
to the Galois geometry previously discussed in "Classical Geometry…"—

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

Sunday, April 21, 2013

The Grandmother Ship

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

Tina Jordan at EW.com yesterday:

"E.L. Konigsburg— the author of one of my favorite
childhood books, the brilliantly quirky mystery
From The Mixed-Up Files of Mrs. Basil E. Frankweiler
died April 19 at the age of 83."

From other mixed-up files:



Filed under: General,Geometry — Tags: — m759 @ 2:00 PM

(Continued from December 31st, 2012)

"Principles before personalities." — AA saying

Art Principles

Part I:

Part II:

Baker's 1922 Principles of Geometry

IMAGE- The Large Desargues Configuration

Art Personalities

Stoppard Update

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


   Daily Princetonian  @princetonian

Related material:

A sermon by the man named today the new President of Princeton.
The sermon is from October 7, 2012. See also Log24 on that date.


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

"There is  such a thing as a figure in four dimensions."

Adapted from a novel

Wednesday, April 10, 2013

Caution: Slow Art

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

"Of course, DeLillo being DeLillo,
it’s the deeper implications of the piece —
what it reveals about the nature of
film, perception and time — that detain him."

— Geoff Dyer, review of Point Omega

Related material:

A phrase of critic Robert Hughes,
"slow art," in this journal.

A search for that phrase yields the following
figure from a post on DeLillo of Oct. 12, 2011:

The 3x3 square

The above 3×3 grid is embedded in a 
somewhat more sophisticated example
of conceptual art from April 1, 2013:

IMAGE- A Galois-geometry key to Desargues' theorem

Update of April 12, 2013

The above key uses labels from the frontispiece
to Baker's 1922 Principles of Geometry, Vol. I ,
that shows a three-triangle version of Desargues's theorem.

A different figure, from a site at National Tsing Hua University,
shows the three triangles of Baker's figure more clearly:

IMAGE- Desargues' theorem with three triangles (the large Desargues configuration) and Galois-geometry version

Art Wars (continued)

Filed under: General — Tags: — m759 @ 5:01 PM

This Way to the Egress:

Click images for some background.

A Text (continued)

Filed under: General — Tags: — m759 @ 9:00 AM

This journal on July 2, 2007:

(Click for more of the post)

IMAGE- Wallace Stevens, 'A text that is an answer, although obscure'

A text:

IMAGE- Epigraph to 'Things Fall Apart,' by Chinua Achebe

Related material from July 3, 2007:

(Click for a clearer image of the quiz below.)

For answers to the quiz, see Jonathan Langdale.

For a deeper look at Achebe, see the following quote
in the context of last night's post on Hitchcock 

— as well as Time + Eternity + Cloth in this journal.

Tuesday, April 2, 2013


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

A sequel to the quotation here March 8 (Pinter Play)
of Joan Aiken's novel The Shadow Guests

Supposing that one's shadow guests are
Rosenhain and Göpel (see March 18)

Hans Freudenthal at Encyclopedia.com on Charles Hermite:

"In 1855 Hermite took advantage of Göpel’s and Rosenhain’s work
when he created his transformation theory (see below)."

"One of his invariant theory subjects was the fifth-degree equation,
to which he later applied elliptic functions.

Armed with the theory of invariants, Hermite returned to
Abelian functions. Meanwhile, the badly needed theta functions
of two arguments
had been found, and Hermite could apply what
he had learned about quadratic forms to understanding the
transformation of the system of the four periods. Later, Hermite’s
1855 results became basic for the transformation theory of Abelian
functions as well as for Camille Jordan’s theory of 'Abelian' groups.
They also led to Herrnite’s own theory of the fifth-degree equation
and of the modular equations of elliptic functions. It was Hermite’s
merit to use ω rather than Jacobi’s q = eπω as an argument and to
prepare the present form of the theory of modular functions.
He again dealt with the number theory applications of his theory,
particularly with class number relations or quadratic forms.
His solution of the fifth-degree equation by elliptic functions
(analogous to that of third-degree equations by trigonometric functions)
was the basic problem of this period."

See also Hermite in The Catholic Encyclopedia.

Intercultural Whatever

Filed under: General — Tags: — m759 @ 6:29 PM

University Diaries on March 22:

"An Intercultural Whatever professor at Florida Atlantic University…" (FAU).

An obituary in this afternoon's New York Times :

Related Log24 posts:

Pinter Play (March 8, about FAU) and a post
from the reported day of Gumperz's death.

Rota in a Nutshell

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

"The proof of Desargues' theorem of projective geometry
comes as close as a proof can to the Zen ideal.
It can be summarized in two words: 'I see!' "

— Gian-Carlo Rota in Indiscrete Thoughts (1997)

Also in that book, originally from a review in Advances in Mathematics,
Vol. 84, Number 1, Nov. 1990, p. 136:

IMAGE- Rota's review of 'Sphere Packings, Lattices and Groups'-- in a word, 'best'

Related material:

Pascal and the Galois nocciolo ,
Conway and the Galois tesseract,
Gardner and Galois.

See also Rota and Psychoshop.

Baker on Configurations

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

The geometry posts of Sunday and Monday have been
placed in finitegeometry.org as

Classical Geometry in Light of Galois Geometry.

Some background:

See Baker, Principles of Geometry , Vol. II, Note I
(pp. 212-218)—

On Certain Elementary Configurations, and
on the Complete Figure for Pappus's Theorem

and Vol. II, Note II (pp. 219-236)—

On the Hexagrammum Mysticum  of Pascal.

Monday's elucidation of Baker's Desargues-theorem figure
treats the figure as a 15420configuration (15 points, 
4 lines on each, and 20 lines, 3 points on each).

Such a treatment is by no means new. See Baker's notes
referred to above, and 

"The Complete Pascal Figure Graphically Presented,"
a webpage by J. Chris Fisher and Norma Fuller.

What is new in the Monday Desargues post is the graphic
presentation of Baker's frontispiece figure using Galois geometry :
specifically, the diamond theorem square model of PG(3,2).

See also Cremona's kernel, or nocciolo :

Baker on Cremona's approach to Pascal—

"forming, in Cremona's phrase, the nocciolo  of the whole."

IMAGE- Definition of 'nocciolo' as 'kernel'

A related nocciolo :

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Click on the nocciolo  for some
geometric background.

Older Posts »

Powered by WordPress