Friday, August 31, 2018

Perception of Number

Filed under: General,Geometry — Tags: , — m759 @ 8:31 PM

Review of yesterday's post Perception of Space

From Harry Potter and the Philosopher's Stone  (1997),
republished as "… and the Sorcerer's Stone ," Kindle edition:


In a print edition from Bloomsbury (2004), and perhaps in the
earliest editions, the above word "movements" is the first word
on page 168:


Click the above ellipse for some Log24 posts on the eightfold cube,
the source of the 168 automorphisms ("movements") of the Fano plane.

"Refined interpretation requires that you know that
someone once said the offspring of reality and illusion
is only a staggering confusion."

— Poem, "The Game of Roles," by Mary Jo Bang

Related material on reality and illusion
an ad on the back cover of the current New Yorker


"Hey, the stars might lie, but the numbers never do." — Song lyric

Thursday, August 30, 2018

Twenty Years

Filed under: General — Tags: — m759 @ 10:16 PM

This post was suggested by the final inside page, 23,
of next Sunday's New York Times Book Review ,
"Memorabilia/ Happy 20th Anniversary, Harry Potter."


From VOA Learning English, June 26, 2017

J.K. Rowling's Harry Potter Books
Turn 20 Years Old

. . . .

" J.K. Rowling’s first book about Harry and his friends at Hogwarts School of Witchcraft and Wizardry was released on June 26, 1997.

The publisher, Bloomsbury, only released 500 copies to stores in Britain and sent 500 to British libraries.

Now, thanks to 450 million more copies of the first book and six others, Harry Potter and his friends are known around the world.

Adults and children loved the books. But 12 publishers rejected the first one, known in many countries as 'Harry Potter and the Philosopher’s Stone.' "

. . . .

See as well this  journal on June 26, 2017 in
posts now tagged Ron Shaw In Memoriam.

Perception* of Space

Filed under: General,Geometry — Tags: — m759 @ 2:12 PM




* A footnote in memory of a dancer who reportedly died
  yesterday, August 29 —  See posts tagged Paradigm Shift.

"Birthday, death-day — what day is not both?" — John Updike

Tuesday, August 28, 2018

For St. Augustine’s Day

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


Whether the word "condescension" functions as purple Kool-Aid
here or in the previous post, the reader may decide.

See Becomes Saw

Filed under: General — Tags: — m759 @ 2:46 PM




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


Monday, August 27, 2018

Geometry and Simplicity

Filed under: General,Geometry — Tags: — m759 @ 9:27 PM


Thinking in Four Dimensions
By Dusa McDuff

"I’ve got the rather foolhardy idea of trying to explain
to you the kind of mathematics I do, and the kind of
ideas that seem simple to me. For me, the search
for simplicity is almost synonymous with the search
for structure.

I’m a geometer and topologist, which means that
I study the structure of space
. . . .

In each dimension there is a simplest space
called Euclidean space … "

— In Roman Kossak, ed.,
Simplicity:  Ideals of Practice in Mathematics and the Arts
(Kindle Locations 705-710, 735). Kindle Edition.

For some much simpler spaces of various
dimensions, see Galois Space in this journal.

Some small Galois spaces (the Cullinane models)


Children of the Six Sides

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



From the former date above —

Saturday, September 17, 2016

A Box of Nothing

Filed under: Uncategorized — m759 @ 12:13 AM


"And six sides to bounce it all off of.

From the latter date above —

Tuesday, October 18, 2016


Filed under: Uncategorized — m759 @ 6:00 AM

The term "parametrization," as discussed in Wikipedia, seems useful for describing labelings that are not, at least at first glance, of a vector-space  nature.

Examples: The labelings of a 4×4 array by a blank space plus the 15 two-subsets of a six-set (Hudson, 1905) or by a blank plus the 5 elements and the 10 two-subsets of a five-set (derived in 2014 from a 1906 page by Whitehead), or by a blank plus the 15 line diagrams of the diamond theorem.

Thus "parametrization" is apparently more general than the word "coodinatization" used by Hermann Weyl —

“This is the relativity problem:  to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them.”

— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16

Note, however, that Weyl's definition of "coordinatization" is not limited to vector-space  coordinates. He describes it as simply a mapping to a set of reproducible symbols

(But Weyl does imply that these symbols should, like vector-space coordinates, admit a group of transformations among themselves that can be used to describe transformations of the point-space being coordinatized.)

From March 2018 —


Sunday, August 26, 2018

For the Green Man

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




Mathematics and Narrative: Queensland

Filed under: General — Tags: — m759 @ 3:56 AM

Mathematics —


Narrative —


See also other recent posts tagged Queensland.

Saturday, August 25, 2018


Filed under: General — m759 @ 8:55 PM


Schoolgirl Problem

Filed under: General — Tags: , — m759 @ 5:40 PM

For Pagan Moore


See also "as frivolous as a willow on a tombstone."

“Waugh, Orwell. Orwell, Waugh.”

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

Suggested by a review of Curl on Modernism —


Related material —

Waugh + Orwell in this journal and

Cube Bricks 1984

An Approach to Symmetric Generation of the Simple Group of Order 168

Point at Infinity

Filed under: General,Geometry — Tags: , — m759 @ 5:20 AM

In literature —


In film —


In mathematics —


Friday, August 24, 2018

The Wandelweiser Manifesto

Filed under: General — Tags: — m759 @ 5:35 PM

Or:  Signpost of Change

From a cartoon graveyard



Alex Ross on Wandelweiser, September 2016

Academic and Transformations

Filed under: General — m759 @ 4:59 PM

For Doctor Sleep .



See as well "STEAM" in this journal.

“1, 2, 3” . . .

Filed under: General — m759 @ 6:00 AM

See previous post.

Update of 6:29 AM — Click to enlarge

Oppenheimer homecoming, with ad for 'Pussy-Footer' alarm clock

Thursday, August 23, 2018


Filed under: General — m759 @ 7:23 PM


See related posts.

Bar or Club?

Filed under: General — m759 @ 1:37 AM

The title is from an Instagram caption yesterday.

Related material —


See as well "Alcoholic Club" in this  journal.

Wednesday, August 22, 2018

Castle Rock

Filed under: General — Tags: — m759 @ 2:03 PM

See the title in a TV review* from io9 this morning and in
this  journal.


* Spoiler alert


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


Tuesday, August 21, 2018

Purported Endgame

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


A search for "IMA" yields, at ima.org.au . . .

"Since 1975, the Institute of Modern Art (IMA) has been Queensland’s 
leading independent forum for art and its discourses." And



"Clog, therefore, purple Jack and crimson Jill."

— Wallace Stevens

Available Light

Filed under: General — Tags: — m759 @ 12:16 PM


Click the image above for an interview dated Nov. 9, 2015.
Also on that date —


Monday, August 20, 2018

Available Legend

Filed under: General — m759 @ 1:27 PM



See also the recent post Apollo and the Furies.

A Wheel for Ellmann

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

The title was suggested by Ellmann's roulette-wheel analogy
in the previous post, "The Perception of Coincidence."

I Ching hexagrams as a Singer 63-cycle, plus zero

The Perception of Coincidence

Filed under: General — Tags: — m759 @ 2:15 AM

Ellmann on Joyce and 'the perception of coincidence' —

"Samuel Beckett has remarked that to Joyce reality was a paradigm,
an illustration of a possibly unstatable rule. Yet perhaps the rule
can be surmised. It is not a perception of order or of love; more humble
than either of these, it is the perception of coincidence. According to
this rule, reality, no matter how much we try to manipulate it, can only
assume certain forms; the roulette wheel brings up the same numbers
again and again; everyone and everything shift about in continual
movement, yet movement limited in its possibilities."

— Richard Ellmann, James Joyce , rev. ed.. Oxford, 1982, p. 551

Sunday, August 19, 2018

Possible Permutations

Filed under: General,Geometry — Tags: — m759 @ 9:18 PM

John Calder, an independent British publisher who built a prestigious list
of authors like Samuel Beckett and Heinrich Böll and spiritedly defended
writers like Henry Miller against censorship, died on Aug. 13 in Edinburgh.
He was 91.

— Richard Sandomir in the online New York Times  this evening

On Beckett —


Also on August 13th


The Search for Veritas

Filed under: General — m759 @ 8:16 PM


See as well the search for Veritas  in this  journal.

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."

Saturday, August 18, 2018

Pagan Song Trilogy

Filed under: General — m759 @ 2:45 PM

Trilogy about the fictional schoolgirl Pagan Moore

"I can feel the Devil walking next to me"

Song lyric from the musical "Chess"

Friday, August 17, 2018

Hogwarts Peak

Filed under: General — m759 @ 2:00 PM

Or:  Misery, Jessica …  Jessica, Misery .



Related material from The Harvard Crimson

"The beach and the castle on the hill and the waves
would always be here, always moving, always changing,
but always constant." 

— Robert Miranda, "The Simplicity of Waves," August 8, 2018

Related material on waves (i.e. , "Fourier's laboratory") —

See also this  journal on August 8.

Thursday, August 16, 2018

Mathematics and Narrative

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



Alperin, Groups and Representations, p. 61


The Tale of the Flux Capacitor

Hardware and Software

Filed under: General — m759 @ 10:01 PM

See the title in this journal.

The Offspring of Reality and Illusion*

Filed under: General — m759 @ 3:35 PM


* See some related images from this  journal.

Wednesday, August 15, 2018

An Illusion of Brilliance

Filed under: General,Geometry — Tags: , , — m759 @ 5:25 PM

” . . . the 3 by 3, the six-sided, three-layer configuration of
the original Rubik’s Cube, which bestows an illusion of brilliance
on those who can solve it.”

— John Branch in the online New York Times  today,
“Children of the Cube”:


Cube-solving, like other sports, allows for displays of
impressive and admirable skill, if not “brilliance.”

The mathematics — group theory — that is sometimes associated
with Rubik’s Cube is, however, not  a sport.  See Rubik + Group
in this journal.


An Exceptional Isomorphism

Filed under: General,Geometry — Tags: , , — m759 @ 5:40 AM

Why PSL(2,7) is isomorphic to GL(3.2)

From previous posts on this topic —



Tuesday, August 14, 2018

Fake News?

Filed under: General — m759 @ 11:19 PM



Filed under: General — Tags: — m759 @ 4:38 PM


Also on Feb. 2, 2014 —



Filed under: General,Geometry — Tags: , , , — m759 @ 12:06 AM




Monday, August 13, 2018

Noetic Acts and Horizonal Contexts

Filed under: General — m759 @ 3:00 PM

From recent posts on the Sandywell lexicon

This suggests . . .


Trojan Horsitude

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

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."

— Simon Blackburn, Think,
    Oxford University Press, 1999, page 268

". . . a perfect triptych of horsitude"

James Parker on the 2007 film "Michael Clayton"

Related material —

Horsitude in the 4×2 grid, and



Sunday, August 12, 2018


Filed under: General — m759 @ 12:00 PM

Two articles by James Parker


"The Cardinal seemed a little preoccupied today."

Saturday, August 11, 2018

People’s Temple of Doom

Filed under: General — m759 @ 9:10 PM


The above phrase in a different edition (click to enlarge) —



Filed under: General — m759 @ 1:28 PM

In three generations of MacDonalds




Fantasy (Etymology)

Filed under: General — m759 @ 2:45 AM


Friday, August 10, 2018

For Noah Cross in Chinatown

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


Geometry of the I Ching (Box Style)

Thursday, August 9, 2018

Drama Queen in Yellow Dress

Filed under: General — Tags: — m759 @ 9:09 PM


Related literature —


Related video —

(Recall, in light of the previous post, that
Apollo is the lord of the dance.)

The Girl in the Yellow Dress
(from the Broadway musical "Contact")

True Grids

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

From a search in this journal for "True Grid,"
a fanciful description of  the 3×3 grid —

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

A fanciful instance of the 4×2 grid in
a scene from the film "The Master" —

IMAGE- Joaquin Phoenix, corridor scene in 'The Master'

A fanciful novel referring to the number 8,
and a not -so-fanciful reference:


Illustrated above are Katherine Neville's novel The Eight  and the
"knight" coordinatization of the 4×2 grid from a page on the exceptional
isomorphism between PSL(3,2) (alias GL(3,2)) and PSL(2,7) — groups
of, respectively, degree 7 and degree 8.

Literature related to the above remarks on grids:

Ross Douthat's New York Times  column yesterday purported, following
a 1946 poem by Auden, to contrast students of the humanities with
technocrats by saying that the former follow Hermes, the latter Apollo.

I doubt that Apollo would agree.

“Just” a Metaphor?

Filed under: General — m759 @ 11:34 AM

    Marvel's Jessica Jones, S1 E13


These are questions to which we might hope
the New York Times 's film critics know the answers.

Annals of Phenomenology

Filed under: General — Tags: — m759 @ 12:29 AM

(Continued from yesterday)


Wednesday, August 8, 2018

ART WARS: Poetry for Drama Queens

Filed under: General — Tags: — m759 @ 6:08 PM


Annals of Phenomenology

Filed under: General — Tags: — m759 @ 4:44 PM

The Return of Purple Man
Or:  This Just In

Detail from a post of yesterday morning taken from
the laptop of private investigator Jessica Jones —


The above image, together with yesterday's date, suggested, rather
fancifully, yesterday morning's later post on just intonation, "Seventh."

The nemesis of Jessica Jones, the Purple Man


A New York Times  piece today* is related to both just intonation and
the color purple —


* Published at 1:50 PM ET —
itemprop="datePublished" content="2018-08-08T17:50:30.000Z"


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

Dates from math forums mentioned in the previous post

Dec. 7, 2016  and  Aug. 2, 2010.

Connoisseurs of synchonology may like to click on those dates.


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

From mathoverflow.net on Dec. 7, 2016 —

The exceptional isomorphism between
PGL(3,2) and PSL(2,7): geometric origin?

Essentially the same question was asked earlier at

math.stackexchange.com on Aug. 2, 2010.

See also this  journal in November 2017 —

"Read something that means something."
                — New Yorker  ad

'Knight' octad labeling by the 8 points of the projective line over GF(7) .

Background — Relativity Problem in Log24.

Tuesday, August 7, 2018

The Search for Harmonic Analysis

Filed under: General — m759 @ 11:45 AM

See Harmonic Analysis in this journal.

See also Loop.

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

"Here we go loop de lie."


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

 A Requiem Chord

Tom Stoppard, Jumpers —

“Heaven, how can I believe in Heaven?” 
she sings at the finale.

“Just a lying rhyme for seven!”



Annals of E-Romance:

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

Smartphone Meets Laptop —


Some related narrative from the previous post

“All right, Jessshica. It’s time to open the boxsssschhh.”

Monday, August 6, 2018

The Girl with Kaleidoscope Eyes

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


“All right, Jessshica. It’s time to open the boxsssschhh.”

“Gahh,” she said. She began to walk toward the box, but her heart failed her and she retreated back to the chair. “Fuck. Fuck.” Something mechanical purred. The seam she had found cracked open and the top of the box began to rise. She squeezed shut her eyes and groped her way into a corner, curling up against the concrete and plugging her ears with her fingers. That song she’d heard the busker playing on the train platform with Eliot, “Lucy in the Sky with Diamonds”; she used to sing that. Back in San Francisco, before she learned card tricks. It was how she’d met Benny: He played guitar. Lucy was the best earner, Benny said, so that was mainly what she sang. She must have sung it five times an hour, day after day. At first she liked it but then it was like an infection, and there was nothing she could do and nowhere she could go without it running across her brain or humming on her lips, and God knew she tried; she was smashing herself with sex and drugs but the song began to find its way even there. One day, Benny played the opening chord and she just couldn’t do it. She could not sing that fucking song. Not again. She broke down, because she was only fifteen, and Benny took her behind the mall and told her it would be okay. But she had to sing. It was the biggest earner. She kind of lost it and then so did Benny and that was the first time he hit her. She ran away for a while. But she came back to him, because she had nothing else, and it seemed okay. It seemed like they had a truce: She would not complain about her bruised face and he would not ask her to sing “Lucy.” She had been all right with this. She had thought that was a pretty good deal.

Now there was something coming out of a box, and she reached for the most virulent meme she knew. “Lucy in the sky!” she sang. “With diamonds!”

•   •   •

Barry, Max. Lexicon: A Novel  (pp. 247-248).
Penguin Publishing Group. Kindle Edition.

Related material from Log24 on All Hallows' Eve 2013

"Just another shake of the kaleidoscope" —

Related material:

Kaleidoscope Puzzle,  
Design Cube 2x2x2, and 
Through the Looking Glass: A Sort of Eternity.

Summer in Philadelphia

Filed under: General — Tags: — m759 @ 2:59 PM


See also this  journal on June 21st, 2013.

A Connecting Link

Filed under: General — m759 @ 2:00 PM


From New York City on All Hallows' Eve 2013 —


From this  journal on All Hallows' Eve 2013 —

Sunday, August 5, 2018

For Gothamists

Filed under: General — m759 @ 9:33 PM


Not so good —


Board Structure

Filed under: General,Geometry — m759 @ 11:48 AM



Go Set a Structure

Filed under: General — m759 @ 11:00 AM

See the title in this journal.

Saturday, August 4, 2018

The Corrections

Filed under: General — m759 @ 10:42 PM




"Forget it, Jake. It's Chinatown."

Triple Cross

Filed under: General — m759 @ 9:57 PM


See also

This post was suggested by Log24 remarks on May 4, 2014,
the date of Garrett Lisi's Twitter post announcing the opening
of his Pacific Science Institute (see previous post).

The Public Life of Harry Albers

Filed under: General — m759 @ 9:20 PM

Suggested by the previous post, "The Secret Life of Harry Albers" —


The fictional "Pacific Science Institute" in novels by Albers
seems to have appeared first in his Murder at Lake Tomahawk
(Dec. 14, 2000). Its name may or may not have influenced the
founder of the later non -fictional Pacific Science Institute


The Secret Life of Harry Albers

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

A novel by Harry Albers featuring his fictional Pacific Science Institute:


See the real  Pacific Science Institute (PSI) in the previous post.

Synchronology check —


Related literary remarks —

— Cloud Atlas , by David Mitchell (2004).


Filed under: General — m759 @ 2:19 PM

Pacific Science Institute

Related material:

Two-Year College (May 14, 2014) and
Easter Eggs for Rosalind (July 7, 2018).

Manifestations of Exquisite Geometry

Filed under: General,Geometry — m759 @ 1:23 PM

An alleged manifestation in physics, from Scientific American  —


Manifestations in pure mathematics, from Plato and R. T. Curtis  —

Counting symmetries with the orbit-stabilizer theorem

For some entertaining literary  manifestations, see Wrinkle.

Friday, August 3, 2018

An Emoji for Hanks

Filed under: General — m759 @ 2:47 PM





Filed under: General — m759 @ 1:03 AM



Beep Beep, Alan.

Thursday, August 2, 2018

The Lost Code

Filed under: General — m759 @ 11:00 PM



"God Gave Noah the Rainbow Sign"

National Comedy

Filed under: General — m759 @ 12:44 PM

   "No one expected a fire tornado."
California governor Jerry Brown

Infinity War

Filed under: General — m759 @ 12:00 PM

See also Lexicon in this journal.

Quantum-Realm Logos

Filed under: General — m759 @ 11:34 AM

For Ant-Man —

For Spider-Man —

Annals of Computation

Filed under: General — m759 @ 10:56 AM

Wednesday, August 1, 2018


Filed under: General — m759 @ 9:45 PM

* Mathematical term, not related to "Perfect Number/Universe."

Publish or …

Filed under: General — m759 @ 9:00 PM

From The New York Times  online on July 29 —

" Ms. Appelbaum’s favorite authors, she said in an interview with The Internet Writing Journal in 1998, were too many to count, but they included George Eliot, Anthony Trollope, Anne Tyler and Julian Barnes.

'I love to see writers expand our range of understanding, experience, knowledge, even happiness,' she said in that interview. 'Publishing has always struck me as a way to change the world.' "

A version of this article appears in print on , on Page B6 of the New York edition with the headline: Judith Appelbaum, Guru On Publishing, Dies at 78.

See a review of the new Anne Tyler novel Clock Dance
in today's  online New York Times .

For a more abstract dance, see Ballet Blanc .

"A blank underlies the trials of device." — Wallace Stevens


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

“… I realized that to me, Gödel and Escher and Bach
were only shadows cast in different directions
by some central solid essence.
I tried to reconstruct the central object . . . ."

— Douglas Hofstadter (1979)

See also posts of July 23, 2007, and April 7, 2018.

* Term from a visual-culture lexicon —


Filed under: General — m759 @ 1:00 PM

"Visual culture is the aspect of culture expressed in visual images.
Many academic fields study this subject, including 
cultural studiesart historycritical theoryphilosophymedia studies,
and anthropology." — Wikipedia


“Ready Player One” Mnemonic:

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



See also other posts tagged "Is and As."

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