Friday, April 27, 2018

Mountain View

Filed under: Uncategorized — m759 @ 1:25 AM

Thursday, April 26, 2018

Defining Form

Filed under: Uncategorized — m759 @ 7:00 PM

Images related to the previous post

Wednesday, April 25, 2018

A Deathly Triangle

Filed under: Uncategorized — Tags: — m759 @ 11:27 PM

Triangle Publications

Filed under: Uncategorized — Tags: — m759 @ 8:12 PM

Notes related to Shakespeare's Birthday, 2018

An Idea

Filed under: Uncategorized — m759 @ 11:45 AM

"There was an idea . . ." — Nick Fury in 2012

". . . a calm and objective work that has no special
dance excitement and whips up no vehement
audience reaction. Its beauty, however, is extraordinary.
It’s possible to trace in it terms of arithmetic, geometry,
dualism, epistemology and ontology, and it acts as
a demonstration of art and as a reflection of
life, philosophy and death."

New York Times  dance critic Alastair Macaulay,
    quoted here in a post of August 20, 2011.

Illustration from that post —

A 2x4 array of squares

See also Macaulay in
last night's 10 PM post.

Tuesday, April 24, 2018

Dance, Music, Space

Filed under: Uncategorized — m759 @ 10:00 PM

". . . dance, fueled by music, opens up space."

—  Alastair Macaulay in the online New York Times  today

Putting aside the unfortunate fuel metaphor, this suggests a review —

A video published on the above date —

The video has six-plus-two dancers, a more concise arrangement
than the eight-plus-two discussed by Macaulay.

Another approach to six plus two:  the diamond-theorem correlation.

Alma Maman

Filed under: Uncategorized — m759 @ 1:16 PM

"Almost 9 meters tall, Maman  is one of the most ambitious
of a series of sculptures by Bourgeois that take as their subject
the spider, a motif that first appeared in several of the artist's
drawings in the 1940s and came to assume a central place in
her work during the 1990s. Intended as a tribute to her mother,
who was a weaver, Bourgeois's spiders are highly contradictory
as emblems of maternity: they suggest both protector and predator—
the silk of a spider is used both to construct cocoons and to bind prey—
and embody both strength and fragility."

A Guggenheim Bilbao page

Illustrators of the Word

Filed under: Uncategorized — m759 @ 1:30 AM

Tom Wolfe in The Painted Word  (1975) 

“I am willing (now that so much has been revealed!)
to predict that in the year 2000, when the Metropolitan
or the Museum of Modern Art puts on the great
retrospective exhibition of American Art 1945-75,
the three artists who will be featured, the three seminal
figures of the era, will be not Pollock, de Kooning, and
Johns-but Greenberg, Rosenberg, and Steinberg.
Up on the walls will be huge copy blocks, eight and a half
by eleven feet each, presenting the protean passages of
the period … a little ‘fuliginous flatness’ here … a little
‘action painting’ there … and some of that ‘all great art
is about art’ just beyond. Beside them will be small
reproductions of the work of leading illustrators of
the Word from that period….”

The above group of 322,560 permutations appears also in a 2011 book —

From 'Beautiful Mathematics,' by Martin Erickson, an excerpt on the Cullinane diamond theorem (with source not mentioned)

— and in 2013-2015 papers by Anne Taormina and Katrin Wendland:

Monday, April 23, 2018

Blockbuster Exhibition

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

Mike Hale in The New York Times  online today —

Review ‘Genius’ Paints Picasso by the Numbers

"… the production’s tinselly soul.

For instance, it’s on the record that Picasso’s lovers
Dora Maar and Marie-Thérèse Walter had
a wrestling match in his studio while he was
painting 'Guernica.'  'Genius' includes that
scene, naturally, but adds its own detail:
The altercation helps Picasso overcome a creative block
and gleefully set to work on the gigantic painting.
It may be news to scholars that one of art’s
greatest testaments to the horror of war was
inspired, in part, by the excitement of being
fought over by a pair of jealous women."

Related Art


A Creative Block

Super Symmetry Surfing

Filed under: Uncategorized — Tags: — m759 @ 11:17 AM

Midrash —


Backstory — Search this journal for Taormina.


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

Counting symmetries with the orbit-stabilizer theorem

See also the Feb. 17, 2017, post on Bertram Kostant
as well as "Mathieu Moonshine and Symmetry Surfing."

Sunday, April 22, 2018

No Joke

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

Dialogue from "All the Money in the World" —

A related video — New Dakotas, "Hold That Pose."

No Point

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

"Check out the … unexpected major chord
in the chorus of 'Time of the Season;' 
each moment defies expectations,
but at no point do the surprises themselves
take center stage or detract from the [song’s]
other elements."

— Alasdair P. MacKenzie, April 20 in
     The Harvard Crimson

Illustration —

The Omega Matrix

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


Angels and Demons cross within a diamond (page 306), and Finite Geometry logo

Saturday, April 21, 2018

Kalispell Images

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

A Getty logo —

J. Paul Getty and Minotaur, according to Hollywood —

Michelle Williams on art —

A page on Kalispell, Williams's home town

A book by Vachel Lindsay on the area near Kalispell —

Bottom Line

Filed under: Uncategorized — Tags: — m759 @ 11:16 AM

See also May 19 Gestalt.

Friday, April 20, 2018

Art Death

Filed under: Uncategorized — Tags: — m759 @ 10:13 PM

The New York Times  this evening at 8:07 PM ET

"Richard Oldenburg, who as the longtime director
of the Museum of Modern Art in New York City
oversaw blockbuster exhibitions of Picasso,
Matisse and Cézanne and a transformative
expansion that doubled its exhibition space in the
1980s, died on Tuesday at his home in Manhattan.
He was 84."  — Richard Sandomir  [Link added.]

See also "the crux of the matter" in a Tuesday post
and the crux from 4 PM ET today.

Time and Money

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

Emblematizing the Modern

The Cross of Descartes: coordinate axes

The Cross of Descartes 

Note that in applications, the vertical axis of the Cross of Descartes often symbolizes the timeless (money, temperature, etc.) while the horizontal axis often symbolizes time.

T.S. Eliot

“Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint….”

Once Upon a Matrix

Filed under: Uncategorized — m759 @ 2:01 PM


Thursday, April 19, 2018


Filed under: Uncategorized — m759 @ 10:18 PM

Peter Woit in his weblog today

"Keating’s book is very much in the tradition of Watson’s The Double Helix, giving a portrayal of himself and others that doesn’t leave out the very human aspects of ambition, competitiveness and jealousy.

Unlike the Watson book, which is about a great scientific achievement, the unusual aspect of Keating’s story is that what he was involved in was not a success, but the biggest fiasco in the history of his field. On March 17th, 2014, the New York Times reported on its front page that Space Ripples Reveal Inflation’s Smoking Gun, and this same story was reported by most media outlets."

This  weblog on that date, St. Patrick's Day 2014 — 

The New York Times  front page story linked to above —

'Ripples in Space-Time Support Big Bang'

Something to Behold

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

From a review of a Joyce Carol Oates novel
at firstthings.com on August 23, 2013 —

"Though the Curse is eventually exorcised,
it is through an act of wit and guile,
not an act of repentance or reconciliation.
And so we may wonder if Oates has put this story
to rest, or if it simply lays dormant. A twenty-first
century eruption of the 'Crosswicks Curse
would be something to behold." [Link added.]

Related material —

A film version of A Wrinkle in Time

The Hamilton watch from "Interstellar" (2014) —

See also a post, Vacant Space, from 8/23/13 (the date
of the above review), and posts tagged Space Writer.

Wednesday, April 18, 2018

A Missing Link

Filed under: Uncategorized — m759 @ 10:31 PM

Ben Brantley's review  tonight of an Irish Repertory Theater
production of "The Seafarer" suggests a look at an
earlier New York Times  article on the same play.

From that article  (Sunday, Nov. 11, 2007) —

The target of a link in this  journal on the above 2007 date —

Reflection groups in Wikipedia

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

All in the Timing

Filed under: Uncategorized — m759 @ 2:46 PM

Broom Bridge*

Filed under: Uncategorized — m759 @ 1:29 PM

The Hamilton watch from "Interstellar" (2014) —

On the above date — Nov. 17, 2016 —

* See posts tagged Broomsday 2014.

Tuesday, April 17, 2018

A Necessary Possibility*

Filed under: Uncategorized — m759 @ 10:00 AM

"Without the possibility that an origin can be lost, forgotten, or
alienated into what springs forth from it, an origin could not be
an origin. The possibility of inscription is thus a necessary possibility,
one that must always be possible."

— Rodolphe Gasché, The Tain of the Mirror ,
     Harvard University Press, 1986

IMAGE- Harvard University Press, 1986 - A page on Derrida's 'inscription'

An inscription from 2010 —

An inscription from 1984 —

American Mathematical Monthly, June-July 1984, p. 382


Triangles are square

"Every triangle consists of  n congruent copies of itself"
is true if and only if  n is a square. (The proof is trivial.) 
— Steven H. Cullinane

* See also other Log24 posts mentioning this phrase.

Always a Joker

Filed under: Uncategorized — m759 @ 2:00 AM

"Ay que bonito es volar . . ."

Monday, April 16, 2018

“Say Hello to My Little Friend”

Filed under: Uncategorized — m759 @ 11:00 PM

Continued from Nov. 29, 2015.  See Interview + Emma Watson.

The Brooklyn Game

Filed under: Uncategorized — Tags: — m759 @ 2:12 PM

"Can you bring me some players?"

— Molly Bloom in "Molly's Game"

Happy birthday to Pope Emeritus Benedict XVI.

Sunday, April 15, 2018

Focus Up.

Filed under: Uncategorized — Tags: — m759 @ 10:42 PM

From subtitles to the recent film "Molly's Game" —

01:19:40,423 –> 01:19:42,633
I'm the only
Irish guy they let play.

01:19:42,718 –> 01:19:43,851
-I'm not Irish.

01:19:46,549 –> 01:19:48,729
-You're not?

01:19:50,367 –> 01:19:51,594
-Molly Bloom?

01:19:51,695 –> 01:19:53,570
-You're thinking of the
James Joyce character.

01:19:55,434 –> 01:19:57,286
-I always thought you were Irish.

01:19:57,809 –> 01:19:58,473
-I'm not.

01:19:58,543 –> 01:19:59,856
Can you bring me some players?

01:19:59,881 –> 01:20:02,200
-Isn't there a famous book?
-Okay, Douglas.

01:20:02,239 –> 01:20:04,231
Focus up. Yes, there's
a book by James Joyce

01:20:04,279 –> 01:20:06,482
called <i>Ulysses</i> and there's
a character named Molly Bloom

01:20:06,529 –> 01:20:07,974
and that is why
you think I'm Irish

Blue Fire

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

"By means of an idea we can see
the idea cloaked in the passing parade."

James Hillman in  A Blue Fire 

Related material:  Cloak and Dagger

See as well Barbara Rose.

Colorado Olympiad

Filed under: Uncategorized — Tags: — m759 @ 1:01 PM

Or:  Personalities Before Principles

Personalities —

Principles —

This  journal on April 28, 2004 at 7:00 AM.

Backstory —

Square Triangles in this journal.

A Job in West Hollywood

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

For the title, see "Inking," a post of Aug. 5, 2015.

See also West Hollywood in a film written and directed by Aaron Sorkin.

Search for Viper Room in this journal.

Saturday, April 14, 2018


Filed under: Uncategorized — Tags: — m759 @ 9:34 PM

See as well an interview in this evening's online New York Times
by Maureen Dowd with "Exorcist" director William Friedkin —

“I don’t drink,” he says. “I’ve never done drugs.
I’ve never tried grass. But I think Miles Davis
is a reason to live.” 

Snow for Hunter*

Filed under: Uncategorized — m759 @ 7:25 PM

"Like a rose under the April snow . . ." — Streisand

* For the "Hunter" of the title, see the previous post.

Spider Jerusalem

Filed under: Uncategorized — m759 @ 6:06 PM

The square and diamond in recent posts tagged ImTran
(short for "immanent form, transcendent content")
appear also in some posts tagged "Spider Jerusalem."

The image “http://www.log24.com/log/pix05/050224-Symbols.gif” cannot be displayed, because it contains errors.


Thanking the Academy

Filed under: Uncategorized — m759 @ 10:56 AM

"Again, Oscars for best director and best picture . . . ."

See also the previous post and a search for
"Plato thanks the Academy."

Immanentizing the Transcendence

Filed under: Uncategorized — m759 @ 10:15 AM

The title refers to the previous two posts.

Related literature —

Plato's Ghost: The Modernist Transformation of Mathematics
(Princeton University Press, 2008)  and . . .

Plato's diamond-in-a-matrix:

Plato's diamond in Jowett's version of the Meno dialogue

Philosophical Logos

Filed under: Uncategorized — Tags: — m759 @ 4:14 AM

Cover illustration: © Béatrice Machet

On the above book cover, presumably the diamond
represents transcendence; the square, immanence.

See also the logos in a Log24 post of April 10.

Friday, April 13, 2018


Filed under: Uncategorized — Tags: , — m759 @ 11:23 PM

Or:  A Magic Circle for Penny 

The subtitle was suggested by the character Penny
in today's post on Mathmagic Land.

* Ray-circle. See an image search.

Madison Time

Filed under: Uncategorized — m759 @ 8:59 PM

From the BBC America series "Intruders" —

See posts now tagged Madison Time.

Mathmagic Land

Filed under: Uncategorized — Tags: — m759 @ 5:45 PM

Continued from yesterday.

From Log24 on July 24, 2014

Later . . .

"Button, Button, Who's Got the Button?"

Manil Suri?

See also The Abacus Conundrum.

Identity Check

Filed under: Uncategorized — m759 @ 3:30 PM

Own this business?


See, however,

Philosophy 101

Filed under: Uncategorized — Tags: — m759 @ 2:48 PM

See also Log24 posts now tagged "Is and As."

Thursday, April 12, 2018


Filed under: Uncategorized — Tags: — m759 @ 1:51 PM

Continued from Monday morning, for Lev Grossman —

Wednesday, April 11, 2018

Behance Post

Filed under: Uncategorized — m759 @ 9:17 PM

I just came across the 2010 web page
associated with the Adobe site "Behance.net." That page suggested
I too should have a Behance web presence.

And so the diamond theorem now appears at . . .


Tuesday, April 10, 2018


Filed under: Uncategorized — Tags: — m759 @ 2:15 PM

Arts & Letters Daily  today links to a piece on critic James Wood —

"More than anything else, for Wood, Updike failed in
the novelistic duty of helping readers to appreciate
the arc of their own lives and, just a little bit, their own

See also, in this  journal, Dimensión de Arco .


Filed under: Uncategorized — m759 @ 1:28 PM

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

"Nietzsche, Wittgenstein.
Wittgenstein, Nietzsche.

— After David Letterman
at the Academy Awards

Monday, April 9, 2018

The Long Hello

Filed under: Uncategorized — m759 @ 9:17 PM

Transportes Ometochtli   >>

Es la línea de transporte más antigua que va de Cuernavaca a Tepoztlán . . . .

Image from the 1973 Elliott Gould film "The Long Goodbye" —

Some backstory . . . .

  1. https://hidden-films.com/2014/11/09/the-little-movie-that-couldnt-

  2. https://en.wikipedia.org/wiki/A_Glimpse_of_Tiger
  3. http://m759.net/wordpress/?p=71956 —

Monday, January 8, 2018


Filed under: Uncategorized — m759 @ 12:00 AM 


Filed under: Uncategorized — Tags: — m759 @ 7:21 PM

NY Times wire, Ivor Guest obituary, screenshot at 7:09:09 PM ET

This journal on the above date of death, March 30, had a quote from
the author of the graphic novel Aleister & Adolf

"Program or be programmed."

I prefer Barbra to Aleister —

"Spirits rise and their dance is unrehearsed."

See as well spirits in the previous post.

Nicht Spielerei…

Filed under: Uncategorized — Tags: — m759 @ 8:25 AM

Continued  (for Lev Grossman  fans)

From the above Wikipedia article

  • In the Robert Frost poem, "The Witch of Coos," the game
    is referenced in lines 7-8:
    "Summoning spirits isn't 'Button, button,
    who's got the button,' I would have them know."

Fact check:  From the Frost poem at Bartleby.com

  • "Summoning spirits isn’t 'Button, button,
    Who’s got the button,' you’re to understand."

Sunday, April 8, 2018


Filed under: Uncategorized — m759 @ 11:00 PM

From a Log24 post of Feb. 5, 2009 —

Design Cube 2x2x2 for demonstrating Galois geometry

An online logo today —

See also Harry Potter and the Lightning Bolt.


OK Movie

Filed under: Uncategorized — m759 @ 11:00 AM

See also Chess War posts.

Raiders of the Lost Circle

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

Today is Orthodox Easter.

From a search in this journal for "Magic Circle" —

Saturday, April 7, 2018


Filed under: Uncategorized — Tags: — m759 @ 10:41 PM

The late Philip J. Davis in his 2004 essay 

"A Brief Look at Mathematics and Theology,"
Humanistic Mathematics Network Journal ,
Issue 27, Article 14. Available at:

wrote —

"In my childhood, the circle persisted as a potent magic figure
in the playtime doggerel 'Make a magic circle and sign it with a dot.'
The interested reader will find thousands of allusions to the phrase
'magic circle' on the Web."

There are fewer allusions to "magic circle" + "sign it with a dot."

One such allusion (click to enlarge) is . . .

Davis died on Pi Day .

Word and Image: Backstory for James Spader

Filed under: Uncategorized — m759 @ 2:14 PM

Actor James Spader in a 2014 interview

". . . my father taught English. My mother taught art . . . ."

Detail of part of a text by Magritte (1929) that appeared  
without attribution in the online New York Times  today —

See also, from a search for the phrase "Word and Image"
in this  journal —

The Philosophers' Stone as originally
illustrated in The New York Times 

http://www.log24.com/log/pix10A/100518-TheStoneNYT.jpg .

Related images —

Juliette Binoche in 'Blue'  The
 24 2x2 Cullinane Kaleidoscope animated images

See as well a Log24 search for "Philosophers' Stone"
and remarks related to the Magritte pictures above 
in the post Story of March 13, 2014.


Filed under: Uncategorized — Tags: — m759 @ 11:47 AM

The FBI holding cube in "The Blacklist" —

" 'The Front' is not the whole story . . . ."

— Vincent Canby, New York Times  film review, 1976,
     as quoted in Wikipedia.

See also Solomon's Cube in this  journal.

IMAGE- 'Solomon's Cube'

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

Friday, April 6, 2018

Watching the Zero

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

From "The Blacklist" Season 5, Episode 11 —

– Remind me again what it is that we think we're doing here.
– The phone acts as a passive packet sniffer.
It's a trick Tom taught me.
– Packet sniffer? Ugh.
– The FBI uses them.
I'm sure your tech people know all about them.
It can intercept and log traffic that passes over a digital network.
– It is an absolute mystery to me how these gadgets work —
the Dick Tracy phones, these blueteeth connections.
Quite frankly, I miss the rotary phone.
Except for that zero.
Watching that zero crawl back.
Oh, my God.
It was painful.
– We have the code.
– Great.

Read more:  https://www.springfieldspringfield.co.uk/

And more:

Philip J. Davis reportedly turned 86 on January 2, 2009.
An image from this journal on that date

Rotary telephone dial

“You have the incorrect number.
I will tell you what you are doing:
you are turning the letter O
instead of the zero.”

— "Symbols and Signs,"
Vladimir Nabokov, 1948

Plan 9

Filed under: Uncategorized — Tags: — m759 @ 2:18 PM

Salinger's 'Nine Stories,' paperback with 3x3 array of titles on cover, adapted in a Jan. 2, 2009, Log24 post on Nabokov's 1948 'Signs and Symbols'

The Thread Phantom: A Death on Pi Day*

Filed under: Uncategorized — Tags: , — m759 @ 12:42 PM

The American Mathematical Society on April 4 posted a story
about a death that they said occurred on March 14  (Pi Day):

* Notes on the Title —

The Thread Part 

The Phantom Part 

"What a yarn!" — Raymond Reddington in "The Blacklist"

Fact check on the death date reported by the AMS —

But Davis's funeral-home obituary agrees with the Pi Day date.

A Service

Filed under: Uncategorized — m759 @ 11:36 AM

From a Boston Globe obituary for Andrew Lewis, an Oscar-nominated
screenwriter who reportedly died at 92 on Feb. 28, 2018 —

"A service has been held for Mr. Lewis . . . ."

—  Bryan Marquard, Globe staff, April 5, 2018

From this  journal on the reported date of his death —

The Globe reports that Lewis's father was Clarence Irving Lewis,
a professor of philosophy at Harvard University.

Fact check:  See page 246 of C. I. Lewis: The Last Great Pragmatist ,
by Murray G. Murphey (SUNY Press, 2005).

Figure (a) above is not unrelated to philosophy. See Plato 's Meno  dialogue.
See also a different diamond — a symbol devised by C. I. Lewis for use in
modal logic — in the post Wittgenstein's Diamond (July 10, 2011).

Thursday, April 5, 2018


Filed under: Uncategorized — m759 @ 11:00 PM


Geometry of the I Ching (Box Style)

Box-style I Ching , January 6, 1989


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

The above title may be regarded as a poetic variant
of the title of Katherine Neville's 1988 novel The Eight .

Related material —

See also The Black Queen, a note from 2001.

Easter Fantasy

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

From this journal at midnight (12 AM ET) on April 4

Related material —

From the weblog of Ready Player One  author Ernest Cline —

"Recently, a lot of people have asked me if a real person
inspired the character of James Halliday, the eccentric
billionaire video game designer in my book. Steve Jobs
and Steve Wozniak are both mentioned in the text,
because their world changing partnership inspired the
relationship between James Halliday and Ogden Morrow,
with Morrow being a charismatic tech industry leader like
Jobs, and Halliday being the computer geek genius of the
duo like Woz. But the character of James Halliday was
inspired by two other very different people.

As I told Wired magazine earlier this year, from the
beginning, I envisioned James Halliday’s personality as
a cross between Howard Hughes and Richard Garriott.
If I had to break it down mathematically, I’d estimate that
about 15% of Halliday’s character was inspired by
Howard Hughes (the crazy reclusive millionaire part), with
most of the other 85% being inspired by Richard Garriott."

Mrs.  Garriott

See as well Log24 posts tagged "Space Writer"
and the classic tune "Midnight at the Oasis."

Wednesday, April 4, 2018

D8ing the Joystick

Filed under: Uncategorized — Tags: — m759 @ 11:45 PM

Or: "Show me all  the blueprints!"
— A saying attributed to Howard Hughes.

Krysten Ritter narrates a podcast that asks 'R We D8ting?'

From the Blacklist episode in the previous post, "Date," blueprints
allegedly describing the boiler room in the Denver Mint —

Note the Thrust/Translation Controller Assembly (TTCA) at upper left
and the Attitude Controller Assembly (ACA) at lower right.

A NASA publication dated April 1, 1971, illustrates the Attitude Controller —

Krysten Ritter was born more than ten years later, in 1981.

For more on Attitude Control, see Boiler Room in this journal.


Filed under: Uncategorized — Tags: , — m759 @ 2:08 PM

An image discussed in the previous post

From a search for "1943" in this journal — 

"Paradine found himself growing slightly confused . . . ."

Gold Bug Variations (Continued)

Filed under: Uncategorized — Tags: , — m759 @ 1:32 PM

See as well a search for "Gold Bug"  in this  journal.

From that search —

Richard Powers, The Gold Bug Variations , first published in 1991—

Botkin, whatever her gifts as a conversationist, is almost as old
as the rediscovery of Mendel. The other extreme in age, 
Joe Lovering, beat a time-honored path out of pure math 
into muddy population statistics. Ressler has seen the guy 
potting about in the lab, although exactly what the excitable kid 
does is anybody's guess. He looks decidedly gumfooted holding
any equipment more corporeal than a chi-square. Stuart takes
him to the Y for lunch, part of a court-your-resources campaign.
He has the sub, Levering the congealed mac and cheese. 
Hardly are they seated when Joe whips out a napkin and begins
sketching proofs. He argues that the genetic code, as an 
algorithmic formal system, is subject to Gödel's Incompleteness
Theorem. "That would mean the symbolic language of the code 
can't be both consistent and complete. Wouldn't that be a kick 
in the head?"

Kid talk, competitive showing off, intellectual fantasy. 
But Ressler knows what Joe is driving at. He's toyed with similar 
ideas, cast in less abstruse terms. We are the by-product of the 
mechanism in there. So it must be more ingenious than us. 
Anything complex enough to create consciousness may be too 
complex for consciousness to understand. Yet the ultimate paradox
is Lovering, crouched over his table napkin, using proofs to 
demonstrate proof's limits. Lovering laughs off recursion and takes
up another tack: the key is to find some formal symmetry folded
in this four-base chaos
. Stuart distrusts this approach even more.
He picks up the tab for their two untouched lunches, thanking 
Lovering politely for the insight.

"The key is to find some formal symmetry…."

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

The Key

Filed under: Uncategorized — Tags: — m759 @ 12:32 PM

"The complete projective group of collineations and dualities of the
[projective] 3-space is shown to be of order [in modern notation] 8! ….
To every transformation of the 3-space there corresponds
a transformation of the [projective] 5-space. In the 5-space, there are
determined 8 sets of 7 points each, 'heptads' …."

— George M. Conwell, "The 3-space PG (3, 2) and Its Group," 
The Annals of Mathematics , Second Series, Vol. 11, No. 2 (Jan., 1910),
pp. 60-76.

"It must be remarked that these 8 heptads are the key to an elegant proof…."

— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in 
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference 
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.

For those who, like the author of The Eight  (a novel in which today's
date figures prominently), prefer fiction —

See as well . . .

Literary theorists may, if they wish, connect
cabalistically the Insidious  address "414" 
with the date  4/14 of the above post, and
the word Appletree with the biblical Garden.

Easter Entertainment Fix

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

Tuesday, April 3, 2018

Easter at Cambridge

Filed under: Uncategorized — m759 @ 11:33 PM

Three geometric readings, in chronological order —

Easter at Harvard

Filed under: Uncategorized — m759 @ 4:04 PM

See also The Crimson Passion.

Montana Wildhack

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

"On Tralfamadore, Billy is put in a transparent geodesic dome 
exhibit in a zoo; the dome represents a house on Earth.
The Tralfamadorians later abduct a movie star named
Montana Wildhack, who had disappeared and was believed to
have drowned herself in the Pacific Ocean. They intend to
have her mate with Billy." — Wikipedia on Kurt Vonnegut's 
Slaughterhouse-Five .

See also the previous post and (from Log24 on Jan. 22) "Hollywood Moment"

Matt B. Roscoe and Joe Zephyrs, both of Missoula, Montana, authors of article on quilt block symmetries

The Cage Country

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

See also "Black Mountain Meets Blue Ridge" (Log24, Feb. 22, 2018).

Entertainment Overload

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

From a May 13, 2010, New York Times  theater review

From a link in a post from yesterday evening —

"Why don't you come with me, little girl,
on a magic carpet ride?" — Steppenwolf lyrics

These lyrics are heard in  Star Trek: First Contact  (1996).

Related entertainment —

The production of "Passion Play" reviewed above opened May 12, 2010.

See also this journal on that date.

Monday, April 2, 2018

A Puzzle for the Clueless

Filed under: Uncategorized — Tags: — m759 @ 10:29 PM

From this evening's online New York Times

Or ask Log24.

The Steppenwolf Carpet

Filed under: Uncategorized — Tags: — m759 @ 9:20 PM

See posts tagged Steppenwolf Carpet in this journal.

Related fiction:  Weaveworld .

Three Mother Cubes

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

From a Toronto Star video pictured here on April 1 three years ago:

The three connected cubes are labeled "Harmonic Analysis," 'Number Theory,"
and "Geometry."

Related cultural commentary from a review of the recent film "Justice League" —

"Now all they need is to resurrect Superman (Henry Cavill),
stop Steppenwolf from reuniting his three Mother Cubes
(sure, whatever) and wrap things up in under two cinematic
hours (God bless)."

The nineteenth-century German mathematician Felix Christian Klein
as Steppenwolf —

Volume I of a treatise by Klein is subtitled
"Arithmetic, Algebra, Analysis." This covers
two of the above three Toronto Star cubes.

Klein's Volume II is subtitled "Geometry."

An excerpt from that volume —

Further cultural commentary:  "Glitch" in this journal.


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

See the posts of April 1 three years ago.

Some context from a personal Kindle library —

"Elementary Mathematics from an Ad" suggests . . .

Sunday, April 1, 2018

The Truth Cube

Filed under: Uncategorized — m759 @ 12:16 PM

Or:  Hector and the Horse

"How many roads . . . . ?" — Bob Dylan


Filed under: Uncategorized — Tags: — m759 @ 11:07 AM

The Eightfold Cube

Quantum logo

Business logo

Happy April 1.

Saturday, March 31, 2018

Burying the Lede

Filed under: Uncategorized — Tags: — m759 @ 10:30 PM

"Those seeking an understanding of the historical elements
of Jesus’ saga might find it profitable to engage the vast work
of David Friedrich Strauss, the German intellectual, whose
monumental 'The Life of Jesus, Critically Examined' was
translated into English in the 19th century by George Eliot.
(At times, the translation reads like a scholarly 'Middlemarch,'
much to its credit.)"

— Jon Meacham in the Easter Sunday print edition of
     The New York Times.  The above passage is
     paragraph 10 of Meacham's article.

See also "Over the Mountains" (Log24, Feb. 21, 2018).

Cube Theory

Filed under: Uncategorized — m759 @ 9:00 PM

For Greta Gerwig and Saoirse Ronan —

See also a Log24 post from the above Cube Theory date —
April 12, 2016 — Lyrics for a Cartoon Graveyard — as well as . . .

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


Filed under: Uncategorized — m759 @ 2:56 PM

“The greatest obstacle to discovery
is not ignorance —
it is the illusion of knowledge.”

— Daniel J. Boorstin,
Librarian of Congress,
quoted here in 2006.

Related material —

Remarks on Rubik's Cube from June 13, 2014 and . . .

See as well a different Gresham, author of Nightmare Alley 
and Log24 posts on that book and the film of the same name .

Notes for the Harrowing of Hell

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

From a post of April 15, 2006

From elsewhere

Friday, March 30, 2018

Unorthodox Drama

Filed under: Uncategorized — Tags: , — m759 @ 9:29 PM

The online New York Times  this evening has an obituary
for "an unorthodox … drama scholar" who reportedly died 
on Thursday, March 22, 2018.

Some drama in this journal from around that date — in posts
tagged "The Cubes" — includes the following excerpt from
a graphic novel:

"Program or be programmed."
— A saying by the author of the above graphic novel.

Thursday, March 29, 2018

To Imagine (or, Better, to Construct)

Filed under: Uncategorized — m759 @ 8:10 PM

The title reverses a phrase of Fano —
costruire (o, dirò meglio immaginare).

Illustrations of imagining (the Fano plane) and of constructing (the eightfold cube) —


The Fano plane and the eightfold cube

“Before Creation Itself . . .”

Filed under: Uncategorized — m759 @ 10:13 AM

 From the Diamond Theorem Facebook page —

A question three hours ago at that page

"Is this Time Cube?"

Notes toward an answer —

And from Six-Set Geometry in this journal . . .

Asymmetry: An Historical YA Fantasy

Filed under: Uncategorized — Tags: — m759 @ 8:48 AM

Or:  The Discreet Charm of Stéphane

For Lisa Halliday

Supplementary images —

Wednesday, March 28, 2018

On Unfairly Excluding Asymmetry

Filed under: Uncategorized — Tags: — m759 @ 12:28 AM

A comment on the the Diamond Theorem Facebook page

Those who enjoy asymmetry may consult the "Expert's Cube" —

For further details see the previous post.

Tuesday, March 27, 2018

Compare and Contrast

Filed under: Uncategorized — Tags: — m759 @ 4:28 PM

Weyl on symmetry, the eightfold cube, the Fano plane, and trigrams of the I Ching

Related material on automorphism groups —

The "Eightfold Cube" structure shown above with Weyl
competes rather directly with the "Eightfold Way" sculpture 
shown above with Bryant. The structure and the sculpture
each illustrate Klein's order-168 simple group.

Perhaps in part because of this competition, fans of the Mathematical
Sciences Research Institute (MSRI, pronounced "Misery') are less likely
to enjoy, and discuss, the eight-cube mathematical structure  above
than they are an eight-cube mechanical puzzle  like the one below.

Note also the earlier (2006) "Design Cube 2x2x2" webpage
illustrating graphic designs on the eightfold cube. This is visually,
if not mathematically, related to the (2010) "Expert's Cube."

Monday, March 26, 2018


Filed under: Uncategorized — m759 @ 12:00 PM

See also this journal on the above publication date.

Sunday, March 25, 2018

Musical Midrash

Filed under: Uncategorized — m759 @ 12:23 PM

A detail from the previous post

A Meyer Levin subtitle: 'A Tale of Love in Je...'

A song lyric

Song lyric: 'Je suis, j'ai dit'

Saturday, March 24, 2018

Soul Notes

Filed under: Uncategorized — m759 @ 8:25 PM

From a personal Kindle library —

From the world of mass entertainment —

Poster Boys

Filed under: Uncategorized — m759 @ 7:42 PM

See also a search in this journal for Compulsion.


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

Sure, Whatever.

Filed under: Uncategorized — Tags: — m759 @ 11:13 AM

The search for Langlands in the previous post
yields the following Toronto Star  illustration —

From a review of the recent film "Justice League" —

"Now all they need is to resurrect Superman (Henry Cavill),
stop Steppenwolf from reuniting his three Mother Cubes
(sure, whatever) and wrap things up in under two cinematic
hours (God bless)."

For other cubic adventures, see yesterday's post on A Piece of Justice 
and the block patterns in posts tagged Design Cube.

Friday, March 23, 2018


Filed under: Uncategorized — Tags: — m759 @ 7:00 PM

Copy editing — From Wikipedia

"Copy editing (also copy-editing or copyediting, sometimes abbreviated ce)
is the process of reviewing and correcting written material to improve accuracy,
readability, and fitness for its purpose, and to ensure that it is free of error,
omission, inconsistency, and repetition. . . ."

An example of the need for copy editing:

Related material:  Langlands and Reciprocity in this  journal.

Piece Prize

Filed under: Uncategorized — Tags: — m759 @ 6:15 PM

The Waymark Prize from 'A Piece of Justice' (1995) by Jill Paton Walsh

The Waymark Prize Mystery - 'A Piece of Justice' (1995) p. 138

From the Personal to the Platonic

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

On the Oslo artist Josefine Lyche —

"Josefine has taken me through beautiful stories,
ranging from the personal to the platonic
explaining the extensive use of geometry in her art.
I now know that she bursts into laughter when reading
Dostoyevsky, and that she has a weird connection
with a retired mathematician."

Ann Cathrin Andersen

Personal —

The Rushkoff Logo

— From a 2016 graphic novel by Douglas Rushkoff.

See also Rushkoff and Talisman in this journal.

Platonic —

The Diamond Cube.

Compare and contrast the shifting hexagon logo in the Rushkoff novel above 
with the hexagon-inside-a-cube in my "Diamonds and Whirls" note (1984).

Thursday, March 22, 2018

In Memoriam

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

Also on March 18, 2015 . . .

The Diamond Cube

Filed under: Uncategorized — Tags: — m759 @ 11:32 AM

The Java applets at the webpage "Diamonds and Whirls"
that illustrate Cullinane cubes may be difficult to display.

Here instead is an animated GIF that shows the basic unit
for the "design cube" pages at finitegeometry.org.

Wednesday, March 21, 2018

The Social Network: At RISC for MIPS

Filed under: Uncategorized — m759 @ 9:09 PM

MIPS Illustrated  (The above computing  meaning from Wiktionary,
                                   "millions of instructions per second") —


Filed under: Uncategorized — Tags: — m759 @ 2:15 PM

WISC = Wechsler Intelligence Scale for Children

RISCReduced Instruction Set Computer   or
             Rust Inventory of Schizotypal Cognitions

See related material in earlier WISC RISC posts.

See also . . .

"Many parents ask us about the Block Design section
on the WISC and hope to purchase blocks and exercises
like those used on the WISC test. We explain that doing that
has the potential to invalidate their child's test results.
These Froebel Color Cubes will give you a tool to work with
your child on the skills tested for in the Block Design section
of the WISC in an ethical and appropriate way. These same
skills are applicable to any test of non-verbal reasoning like  
the NNAT, Raven's or non-verbal sections of the CogAT or OLSAT. "

An online marketing webpage

For a webpage that is perhaps un ethical and in appropriate,
see Block Designs in Art and Mathematics.

RISC Sects

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

The title is from the URL of a paper discussed here yesterday
in the post "Mad Men vs. Math Men" —


Abstract   (See also a webpage on this and related publications.)  —

Related material from today's news

Update:  For further background, see a WIRED article from today.

Tuesday, March 20, 2018

Mad Men vs. Math Men

Filed under: Uncategorized — Tags: — m759 @ 2:36 PM

Video starring the CEO of Cambridge Analytica —

Alexander Nix, 'From Mad Men to Math Men,' Hamburg Messe, 'Online Marketing Rockstars' speech, 2017

Related material from John Rust, now the director of the
Psychometrics Centre at the University of Cambridge —

My own sympathies are with the Mad Men.

See also Rust in the previous post, Cambridge Psychometrics.
He is known for the UK version of the Wechsler Intelligence Scale
for Children.

Cambridge Psychometrics*

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

* Not to be confused with Cambridge Analytica.

  See also Wechsler in this journal.

Springtime for Bavaria

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

Monday, March 19, 2018

Such an Air of Spring About It

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

"Ready for More?" — The Times

Tough Crowd.

Filed under: Uncategorized — Tags: — m759 @ 7:04 PM

Sunday, March 18, 2018

Draper at the Mother Church

Filed under: Uncategorized — Tags: — m759 @ 1:01 PM

From The Atlantic , September 2017 issue, online —
"How America Lost Its Mind," by former Harvard Lampoon  
writer Kurt Andersen —

Related material —

"There is a transformation, a metamorphosis that's going on here."
— Alexander Nix, CEO of Cambridge Analytica

The Lucasian Version —

Saturday, March 17, 2018

A Question for Cambridge Analytica

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

Detail —

Related material —

See as well a search in this journal for (mixed) Emojis.


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

From "Star Wars: The Last Jedi" —

From elsewhere —

Friday, March 16, 2018


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

Wednesday, March 14, 2018


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

Recent Log24 posts on a mobile phone —

Stephen Hawking, 1942-2018

Filed under: Uncategorized — m759 @ 12:15 AM

Tuesday, March 13, 2018


Filed under: Uncategorized — m759 @ 1:33 PM

For Andrew Cusack.

A flashback from this  journal on the above remaking-myths date

See too The Crosswicks Curse.

Siempre con Dignidad

Filed under: Uncategorized — m759 @ 12:00 PM

(Motto of Los Amigos High School, Fountain Valley, CA)

Monday, March 12, 2018


Filed under: Uncategorized — m759 @ 9:55 PM

Stein reportedly died at 100 last Friday (March 9).

Related material —

Textiles by Stein arranged on the six faces of a cube —

Ethel Stein, "Circus & Slapstick," 1996

See also a less amusing approach to
patterns on the faces of a cube.

“Quantum Tesseract Theorem?”

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

Remarks related to a recent film and a not-so-recent film.

For some historical background, see Dirac and Geometry in this journal.

Also (as Thas mentions) after Saniga and Planat —

The Saniga-Planat paper was submitted on December 21, 2006.

Excerpts from this  journal on that date —

     "Open the pod bay doors, HAL."

Sunday, March 11, 2018


Filed under: Uncategorized — m759 @ 12:41 PM

"You know my methods."

— Robert Downey Jr. to Jude Law in
     A Game of Shadows  (2011)

Blackboard Jungle Continues . . .

Filed under: Uncategorized — m759 @ 10:28 AM

. . . With intolerable disrespect for the word …
In particular, the word "theorem."

See also "Quantum Tesseract Theorem" in this  journal.

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