Friday, March 23, 2018


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

Also on March 18, 2015 . . .

The Diamond Cube

Filed under: Uncategorized — 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.

Saturday, March 10, 2018


Filed under: Uncategorized — m759 @ 12:25 PM

See also the undefined phrase "projective model" in a 2012 MIT thesis,
and the following book —

Check and Mate

Filed under: Uncategorized — m759 @ 4:04 AM

Update of 4:30 AM —

Friday, March 9, 2018

The Cemetery Plot

Filed under: Uncategorized — m759 @ 7:20 PM

The New York Times  today on a philosopher of
history who reportedly died on Monday, March 5 —

“Perhaps White’s most controversial idea,
and one for which he was so often shunned
by his fellow historians, is that ‘all stories
are fictions,’ ” Robert Doran, a professor at
the University of Rochester … said by email.
"White held that while historical facts are
scientifically verifiable, stories are not.
Stories are made, not found in the historical data;
historical meaning is imposed on historical facts
by means of the choice of plot-type, and this choice
is inevitably ethical and political at bottom.

"This is what White called 'emplotment,' a term
he coined," Dr. Doran continued. "Even the most basic
beginning-middle-end structure of a story represents
an imposition: The historian chooses where to begin,
where to end, and what points are important in the middle.
There is no scientific test for 'historical significance.' "

From this  journal on Monday, White's reported date of death —

Plan 9  continues.

Thursday, March 8, 2018

L’Engle Time Fold

Filed under: Uncategorized — m759 @ 10:04 PM

Search this journal for the three words of the title.

Thanking the Academy…

Filed under: Uncategorized — m759 @ 9:11 PM


The Trial

Filed under: Uncategorized — m759 @ 8:08 PM

"At the heart of the trial was the question of
whether the complainant could have agreed
to have sex with the defendant . . .
on Halloween night in 2015 . . . ."

Vivian Wang in The New York Times  this evening

This  journal on Halloween night in 2015 —


Filed under: Uncategorized — m759 @ 7:00 PM

"We tell ourselves stories . . . ." — Joan Didion

New York Times Wire, 6:40 PM ET Thursday, March 8, 2018 

3h ago
How Lies Spread Online

They diffuse farther, faster and more broadly than the truth does.

4h ago
It’s True: False News Spreads Faster and Wider.
And Humans Are to Blame.

False claims posted on Twitter were 70 percent more likely
to be shared than the truth, researchers at M.I.T. found.
And people appear to prefer false news.

Women’s Day: The Hateful Eight

Filed under: Uncategorized — m759 @ 10:45 AM

The image “http://www.log24.com/log/pix05B/051202-Axe.jpg” cannot be displayed, because it contains errors.

— From Katherine Neville's novel The Eight  (1988)

Related logic —

Nothing Fails Like Success, by Barbara Johnson

Enlarge the above.  Detail:

Barbara Johnson, Nothing Fails Like Success, detail

Wednesday, March 7, 2018


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

"How do you  get young people excited about space?"

— Megan Garber in The Atlantic , Aug. 16, 2012

The above quote is from this  journal  on 9/11, 2014.

Related material —

Synchronology for the above date — 9/11, 2014 —

A BuzzFeed article with that date, and in reply

"A Personal Statement from Michael Shermer" with that date.

Unite the Seven.

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

Related material —

The seven points of the Fano plane within 

The Eightfold Cube.

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

"Before time began . . . ."

  — Optimus Prime

Tuesday, March 6, 2018

Define Misconduct.

Filed under: Uncategorized — Tags: — m759 @ 11:36 AM

Not to mention fish-men.

Fields Medal

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

For "The Shape of Fluids"

Related material — Posts tagged Aqua.

Monday, March 5, 2018

Sacramento Legend

Filed under: Uncategorized — m759 @ 7:00 PM

"Russell M. Solomon’s story was a Sacramento legend . . . ."

What of the Night?

Filed under: Uncategorized — m759 @ 10:18 AM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of "Sonatina to Hans Christian,"
by Wallace Stevens (in Harmonium  (second edition, 1931))

Sunday, March 4, 2018

The Square Inch Space: A Brief History

Filed under: Uncategorized — m759 @ 11:21 AM

1955  ("Blackboard Jungle") —

1976 —

2009 —

2016 —

 Some small Galois spaces (the Cullinane models)

Saturday, March 3, 2018

Thanking the Academy

Filed under: Uncategorized — m759 @ 11:05 PM

Blackboard Jungle , 1955 —

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

“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….”

— Hermann Hesse, The Glass Bead Game

“How strange the change from major to minor….”

— Cole Porter, “Every Time We Say Goodbye“


Filed under: Uncategorized — m759 @ 1:00 PM

For the Marvel Comics surgeon  Dr. Stephen Strange

For a real-life surgeon who reportedly died on Feb. 24,
a quotation from this journal on that date —

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of "Sonatina to Hans Christian,"
by Wallace Stevens (in Harmonium  (second edition, 1931))

Related material —

Friday, March 2, 2018

A Snowflake on the Iceberg

Filed under: Uncategorized — m759 @ 11:00 AM

A scholium on the previous post, "Mother Ship Meets Mother Church" —

"Consider Saint Hedwig of Silesia (1174–1243), for example,
who is elegantly depicted in this catalogue, striking a pose
with her prayer book, rosary, and Virgin and child statue
(a reminder of the legitimacy of her sex), along with boots
slung over her elbow so she could walk barefoot like
the apostles. Between miracles, she was also known to 
supervise con­struction of new convents. Hedwig is but
a snowflake on the iceberg  of the extra­ordinary role of
actual women in the Middle Ages, to which more evidence
is added continually thanks the Feminae database."

— From "Wonder Women," by Matthew J. Milliner

Thursday, March 1, 2018

Mother Ship Meets Mother Church

Filed under: Uncategorized — m759 @ 7:03 PM

See posts tagged Tsimtsum and, more specifically, Mother Church.

Women and Children First

Identity Icon

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

See also the previous two posts.

Bridge Program

Filed under: Uncategorized — Tags: — m759 @ 11:40 AM

Too late .

Time Magazine  December 25, 2017 – January 1, 2018 —
The cover features "A Wrinkle in Time," opening March 9, 2018:

The Movement of Analogy: Hume vs. Paz

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

Hume, from posts tagged "four-set" in this journal —

"The mind is a kind of theatre, where several perceptions
successively make their appearance; pass, repass, glide away,
and mingle in an infinite variety of postures and situations.
There is properly no simplicity in it at one time, nor identity
in different, whatever natural propension we may have
to imagine that simplicity and identity."

Paz, from a search for Paz + Identity in this journal —

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

Wednesday, February 28, 2018

A Girl’s Guide to Chaos

Filed under: Uncategorized — m759 @ 9:55 AM

The title is that of a play mentioned last night in
a New York Times  obituary .

Related recent film lines —

  • Thor:  How do I escape?
  • Heimdall:  You're on a planet surrounded by doorways.
    Go through one.
  • Thor:  Which one?
  • Heimdall:  The big one!

Related material from this  journal on Jan. 20, 2018 —

The Chaos Symbol of Dan Brown.

Mathematics and Narrative

Filed under: Uncategorized — m759 @ 9:00 AM


Excerpts from a post of May 25, 2005 —

Above is an example I like of mathematics….

Here is an example I like of narrative:

Kate felt quite dizzy. She didn't know exactly what it was
that had just happened, but she felt pretty damn  certain  that
it  was  the  sort of experience that her mother would not have
approved of on a first date.
     "Is this all part of what we have to do to go to  Asgard?"
she said. "Or are you just fooling around?"
     "We will go to Asgard...now," he said.
     At that moment he raised his hand as if to pluck an apple,
but instead of plucking he made a tiny, sharp turning movement.
The effect  was as if he had twisted the entire world through a
billionth part of a billionth  part  of  a  degree.  Everything
shifted,  was  for  a  moment  minutely  out of focus, and then
snapped back again as a suddenly different world.

— Douglas Adams, The Long Dark Tea-Time of the Soul

Image from a different  different world —

Hat-tip to a related Feb. 26 weblog post
at the American Mathematical Society.

Tuesday, February 27, 2018

Risin’ Meets Oozin’

Filed under: Uncategorized — m759 @ 9:15 PM

For the former, see the previous post.

For the latter, see yesterday's The Unfolding.

Related material —

(Screenshot at 9:08 PM ET)

Heimel on Dating —

She adapted “Sex Tips” and “But Enough About You,” a 1986 collection, into a play, “A Girl’s Guide to Chaos,” which opened later that year off Broadway at the American Place Theater. The play is largely a conversation among four friends, one of whom, Cynthia (played by Debra Jo Rupp in the original production) realizes to her horror that she will have to start dating again.

“Please, God, no, don’t make me do it!” she says. “I’ll be good from now on, I promise! I’ll stop feeding the dog hashish! I’ll be kind, thoughtful, sober, industrious, anything. But please, God, not the ultimate torture of dating!”

— Richard Sandomir tonight in The New York Times 
on an author who reportedly died on Sunday, Feb. 25, 2018

<meta property="article:published"
content="2018-02-27T19:37:54-05:00" />

Die Welt, Die Zeit, and the Frankfurter

Filed under: Uncategorized — m759 @ 7:42 PM

"Risin' up to the challenge of our rival" — Eye of the Tiger

Raiders of the Lost Images

Filed under: Uncategorized — m759 @ 11:28 AM

On the recent film "Justice League" —

From DC Extended Universe Wiki, "Mother Box" —

"However, during World War I, the British rediscovered
mankind's lost Mother Box. They conducted numerous studies
but were unable to date it due to its age. The Box was then
shelved in an archive, up until the night Superman died,
where it was then sent to Doctor Silas Stone, who
recognized it as a perpetual energy matrix. . . ." [Link added.]

The cubic shape of the lost Mother Box, also known as the
Change Engine, is shared by the stone in a novel by Charles Williams,
Many Dimensions . See the Solomon's Cube webpage.

See too the matrix of Claude Lévi-Strauss in posts tagged
Verwandlungslehre .

Some literary background:

Who speaks in primordial images speaks to us
as with a thousand trumpets, he grips and overpowers,
and at the same time he elevates that which he treats
out of the individual and transitory into the sphere of
the eternal. 
— C. G. JUNG

"In the conscious use of primordial images—
the archetypes of thought—
one modern novelist stands out as adept and
grand master: Charles Williams.
In The Place of the Lion  he incarnates Plato’s
celestial archetypes with hair-raising plausibility.
In Many Dimensions  he brings a flock of ordinary
mortals face to face with the stone bearing
the Tetragrammaton, the Divine Name, the sign of Four.
Whether we understand every line of a Williams novel
or not, we feel something deep inside us quicken
as Williams tells the tale.

Here, in The Greater Trumps , he has turned to
one of the prime mysteries of earth . . . ."

— William Lindsay Gresham, Preface (1950) to
Charles Williams's The Greater Trumps  (1932)

For fans of what the recent series Westworld  called "bulk apperception" —

Monday, February 26, 2018

The Unfolding

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

From the website of Richard P. Gabriel

" As part of my studies, I came up with a 'theory of poetry' 
based loosely on Christopher Alexander’s 'Nature of Order.' "
[The Alexander link is mine, not Gabriel’s.]

A phrase from this  journal a year ago today — "poetic order" —
links to the theory of Gabriel —

From Gabriel's "The Nature of Poetic Order" —

Positive Space

• Positive space is the characteristic of a center
that moves outward from itself, seemingly oozing life
rather than collapsing on itself
• An image that resonates is showing positive space
• A word that has many connotations that fit with the
other centers in the poem is showing positive space
• It is an expansion outward rather than a contraction
inward, and it shows that the poem is unfolding
in front of us and not dying

Related material —

From a post of April 26, 2017

Sunday, February 25, 2018

The Dark, Seductive Art of Groton

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

A sequel to Friday's "The Dark, Seductive Art of Phillips Exeter."

From Twitter today —

Groton School‏ @GrotonSchool  Feb 1

Groton School Theater Department Presents: CABARET
Friday, February 23rd at 7:30 pm
Saturday, February 24th at 7:30 pm
Sunday, February 25th at 3 pm
All performances are free to the public. Please make ticket
reservations in advance online: http://bit.ly/CABARET2018.

Saturday, February 24, 2018

The Ugly Duck

Filed under: Uncategorized — m759 @ 7:11 PM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium  (second edition, 1931))

From "Mathmagic Land" (May 22, 2015)

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

From "The Trials of Device" (April 24, 2017)

Wittgenstein's pentagram and 4x4 'counting-pattern'

Pentagon with pentagram    

Friday, February 23, 2018

The Dark, Seductive Art of Phillips Exeter

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

From two pedagogues in Montana —


Related material from author Dan Brown's father,
a pedagogue who taught at Phillips Exeter Academy :

Click the above image for some background.

Related material from Log24 —


Compare and contrast with the above
Transformational Geometry  cover:

Related material from Vienna — The previous post and
Wittgenstein on Bewitchment.

See as well . . .

Click to enlarge.

Snow Games

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

'Origin' (NOT by Dan Brown)

Related material — (Click to enlarge) —

"Risin' up to the challenge of our rival"

Eye of the Tiger

Detail —

Thursday, February 22, 2018

The Melody

Filed under: Uncategorized — m759 @ 8:26 PM

Click for the source.

Ojo de Dios

Filed under: Uncategorized — m759 @ 7:55 PM

Black Mountain Meets Blue Ridge

Filed under: Uncategorized — m759 @ 10:48 AM

Click to enlarge

Related material —

Wednesday, February 21, 2018

Crusader’s End

Filed under: Uncategorized — m759 @ 12:12 PM

"He made the Gallup Organization’s list of Ten Most Admired Men
in the World 54 times, a record, and his fame and influence as a
spiritual leader rivaled the pope’s." — Mark Feeney, Globe staff

Over the Mountains

Filed under: Uncategorized — m759 @ 5:14 AM

Judith Wilt on the fictional Casaubon of Middlemarch

Related material from Wikipedia:

The non -fictional Casaubon and Ultramontanism.

From the former:

"Neither side could understand that Casaubon's reading of
the church fathers led him to adopt an intermediate position
between Genevan Calvinism and Ultramontanism."

See as well Wilt on "Storytelling and Catholicism"
(Boston College syllabus, Spring 2016), and Enda's Game
(Log24, April 5, 2016).

Tuesday, February 20, 2018


Filed under: Uncategorized — m759 @ 7:07 AM

Instagram, August 4, 2017 —

See posts on Suppes and Child Buyers.

Bottom line — See also a post from August 4, 2017.

The System

Filed under: Uncategorized — m759 @ 6:00 AM

"It's the system  that matters. 
How the data arrange themselves inside it."

— Gravity's Rainbow  

"Examples are the stained-glass windows of knowledge."

— Vladimir Nabokov   

Map Systems (decomposition of functions over a finite field)

A Sharper Image

Filed under: Uncategorized — m759 @ 5:15 AM

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design

Click for some related posts.

Sunday, February 18, 2018


Filed under: Uncategorized — m759 @ 2:56 PM

"Butt rock is sincere as hell, the place where irony came to die."

— Deborah Kennedy of Portland, Oregon, in an essay,
"How Butt Rock Helped Me Find Love," dated July 25, 2014.

See also July 25, 2014, in Log24 posts tagged April Awareness 2014.

Side ad with an SFGate story this morning — 


Filed under: Uncategorized — m759 @ 8:48 AM

Heuristic Evaluation: A Major Tool

Filed under: Uncategorized — m759 @ 7:07 AM

"Heuristic evaluation is a well established method for quickly evaluating
the efficacy of new media solutions to interface issues."

Neil Gordon et al. , University of Hull

Click or touch to enlarge.

Related material:

Saturday, February 17, 2018

The Binary Revolution

Filed under: Uncategorized — m759 @ 5:00 PM

Michael Atiyah on the late Ron Shaw

Phrases by Atiyah related to the importance in mathematics
of the two-element Galois field GF(2) —

  • "The digital revolution based on the 2 symbols (0,1)"
  • "The algebra of George Boole"
  • "Binary codes"
  • "Dirac's spinors, with their up/down dichotomy"

These phrases are from the year-end review of Trinity College,
Cambridge, Trinity Annual Record 2017 .

I prefer other, purely geometric, reasons for the importance of GF(2) —

  • The 2×2 square
  • The 2x2x2 cube
  • The 4×4 square
  • The 4x4x4 cube

See Finite Geometry of the Square and Cube.

See also today's earlier post God's Dice and Atiyah on the theology of 
(Boolean) algebra vs. (Galois) geometry:

Frosties: A Sequel to “Frozen”

Filed under: Uncategorized — m759 @ 11:48 AM

See as well a search in this  journal for Frost at Wanganui.

God’s Dice

Filed under: Uncategorized — m759 @ 10:45 AM

On a Trinity classmate of Ian Macdonald (see previous post)—

Atiyah's eulogy of Shaw in Trinity Annual Record 2017 
is on pages 137 through 146.  The conclusion —


Friday, February 16, 2018

Two Kinds of Symmetry

Filed under: Uncategorized — m759 @ 11:29 PM

The Institute for Advanced Study (IAS) at Princeton in its Fall 2015 Letter 
revived "Beautiful Mathematics" as a title:

This ugly phrase was earlier used by Truman State University
professor Martin Erickson as a book title. See below. 

In the same IAS Fall 2015 Letter appear the following remarks
by Freeman Dyson —

". . . a special case of a much deeper connection that Ian Macdonald 
discovered between two kinds of symmetry which we call modular and affine.
The two kinds of symmetry were originally found in separate parts of science,
modular in pure mathematics and affine in physics. Modular symmetry is
displayed for everyone to see in the drawings of flying angels and devils
by the artist Maurits Escher. Escher understood the mathematics and got the
details right. Affine symmetry is displayed in the peculiar groupings of particles
created by physicists with high-energy accelerators. The mathematician
Robert Langlands was the first to conjecture a connection between these and
other kinds of symmetry. . . ." (Wikipedia link added.)

The adjective "modular"  might aptly be applied to . . .

The adjective "affine"  might aptly be applied to . . .

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

The geometry of the 4×4 square combines modular symmetry
(i.e., related to theta functions) with the affine symmetry above.

Hudson's 1905 discussion of modular symmetry (that of Rosenhain
tetrads and Göpel tetrads) in the 4×4 square used a parametrization
of that square by the digit 0 and the fifteen 2-subsets of a 6-set, but 
did not discuss the 4×4 square as an affine space.

For the connection of the 15 Kummer modular 2-subsets with the 16-
element affine space over the two-element Galois field GF(2), see my note
of May 26, 1986, "The 2-subsets of a 6-set are the points of a PG(3,2)" —

— and the affine structure in the 1979 AMS abstract
"Symmetry invariance in a diamond ring" —

For some historical background on the symmetry investigations by
Dyson and Macdonald, see Dyson's 1972 article "MIssed Opportunities."

For Macdonald's own  use of the words "modular" and "affine," see
Macdonald, I. G., "Affine Lie algebras and modular forms," 
Séminaire N. Bourbaki , Vol. 23 (1980-1981), Talk no. 577, pp. 258-276.

Nicht Spielerei

Filed under: Uncategorized — m759 @ 2:19 PM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium  (second edition, 1931))

". . . in the end the space itself is the star. . . ."

Related material — The death Tuesday night
of Prince Consort Henrik of Denmark, and the
New Year's Eve speech on Dec. 31, 2015, of
Queen Margrethe II of Denmark.

Distantly  related material — Yesterday morning's
post The Search for Child's Play.

Thursday, February 15, 2018

The Search for Child’s Play

Filed under: Uncategorized — m759 @ 8:00 AM

Yesterday morning's post "Child's  Play" suggests . . .

"Jinx! Jinx again!"

— "Love is an Open Door," from Disney's "Frozen"

Wednesday, February 14, 2018

Child’s Play

Filed under: Uncategorized — m759 @ 11:19 AM

From a search for Child's Play in this journal —

See also the previous post.

"In pascuis herbarum adclinavit me."

Tuesday, February 13, 2018

Babble On

Filed under: Uncategorized — m759 @ 9:00 PM

Symbology for Tom Hanks and for a Latin teacher
who reportedly died on Saturday, Feb. 10, 2018 —

Click the image below to search Log24 for "green fields."

See also Space Cross.

Attention Must Be Paid

Filed under: Uncategorized — m759 @ 7:06 PM

For the late Anne M. Treisman, who reportedly died Friday, Feb. 9:

From "A Feature-Integration Theory of Attention" —

"The controversy between analytic and synthetic theories
of perception goes back many years: the Associationists
asserted that the experience of complex wholes is built
by combining more elementary sensations, while the
Gestalt psychologists claimed that the whole precedes
its parts, that we initially register unitary objects and
relationships, and only later, if necessary, analyze these
objects into their component parts or properties. This view 
is still active now . . . ."

— Anne M. Treisman, University of British Columbia,
and Garry Gelade, Oxford University, in
Cognitive Psychology  12, 97-136 (1980)

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

A Titan of the Field

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

On the late Cambridge astronomer Donald Lynden-Bell —

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

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

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

Related material —

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

See as well the field GF(9)


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


Monday, February 12, 2018

The Void

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

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

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

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

Related material —

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

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

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

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

See as well this  journal on that date.

Art Wars

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

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

See also Krauss Cross.

Sunday, February 11, 2018

Visions of Hell

Filed under: Uncategorized — m759 @ 9:45 PM

In memory of  a Manhattan art figure
who reportedly died on
Wednesday, February Seventh, 2018 —


Ascension Variations is a magical adventure
woven from grand and pedestrian touches, and
in the end the space itself is the star
or Ms. Monk's transformation of it.
For an hour, we've lived in a spiral,
where up is down and down is up.
It's a sacred place.”

— Gia Kourlas, The New York Times , March 6, 2009

See also the previous post — yesterday's Into the Upside Down
and two posts of February Seventh:

Conceptual Art  and  Conceptual Minimalism.

For some related artistic remarks, see this  journal on March 6-7, 2009.

Saturday, February 10, 2018

Into the Upside Down

Filed under: Uncategorized — m759 @ 10:45 AM

(Title suggested by the TV series Stranger Things )

" 'Untitled' (2016) is the most recent painting in the show
and includes one of Mr. Johns’s recurring images of a ruler."

— Image caption in an article by Deborah Solomon
     in The New York Times  online, Feb. 7, 2018

From a Log24 search for "Ruler"

Related art —

See also, in this journal, Magic Mountain and Davos.

Einstein and Thomas Mann, Princeton, 1938

Wednesday, February 7, 2018

Village Voices

Filed under: Uncategorized — m759 @ 12:01 PM

It Takes a Village 

Cutting-Edge Research

See as well The Prisoner of the Village

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

Conceptual Minimalism

Filed under: Uncategorized — m759 @ 10:08 AM


"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

See also AS IS.

Conceptual Art

Filed under: Uncategorized — m759 @ 9:17 AM

Related conceptual  art —

Tom Wolfe in The Painted Word :

Click the automat image above to enlarge.

See as well a new retrospective at Facebook.

Tuesday, February 6, 2018

For Times Square Church*

Filed under: Uncategorized — m759 @ 1:01 AM


Image--Chess game from 'The 
Seventh Seal'

The metaphor for metamorphosis no keys unlock.
— Steven H. Cullinane, "Endgame"

* See Times Square Church in this journal and
   the posts of July 2010.  Related material:

   A Monday night death —

Monday, February 5, 2018

Stranger Things than Pulp Fiction

Filed under: Uncategorized — m759 @ 12:30 PM

Diamond Theory cover, said to resemble Proginoskes in 'A Wind in the Door'

Click on the image for a
relevant Wallace Stevens poem.

A new Facebook page will describe
some background for the above image.

Sunday, February 4, 2018

Picture at Eleven

Filed under: Uncategorized — m759 @ 11:00 AM

Logos for Sunday, February 4

Filed under: Uncategorized — m759 @ 10:00 AM

"The walls in the back of the room show geometric shapes
that remind us of the logos on a space shuttle. "

Web page on an Oslo art installation by Josefine Lyche.

See also Subway Art posts.

The translation above was obtained via Google.

The Norwegian original —

"På veggene bakerst i rommer vises geometriske former
som kan minne om logoene på en romferge."

Related logos — Modal Diamond Box in this journal:

Nietzsche, 'law in becoming' and 'play in necessity'

Logos for Philosophers
(Suggested by Modal Logic) —

Nietzsche, 'law in becoming' and 'play in necessity'

Friday, February 2, 2018

For Plato’s Cave

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

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

— From the Occupy Space gallery in Ireland

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

Friday, January 26, 2018

Shadows and Reflections

Filed under: Uncategorized — Tags: — m759 @ 9:27 AM

From the post "For Guy Noir" of Wednesday morning, January 24 —

"as privileged viewers of the shadows and reflections"

Related material —

The death on January 24 of a famed ski film maker,
and the Sun Valley icon below (one of a pair of ski
location icons by Wink, a Minneapolis design firm).

Thursday, January 25, 2018

Our Class

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

See earlier posts now also tagged O.C.D. .

Related material —

Acme Book Shop  and The Philosophy Section .

Beware of Analogical Extension

Filed under: Uncategorized — m759 @ 11:29 AM

"By an archetype  I mean a systematic repertoire
of ideas by means of which a given thinker describes,
by analogical extension , some domain to which
those ideas do not immediately and literally apply."

— Max Black in Models and Metaphors 
    (Cornell, 1962, p. 241)

"Others … spoke of 'ultimate frames of reference' …."

A "frame of reference" for the concept  four quartets

A less reputable analogical extension  of the same
frame of reference

Madeleine L'Engle in A Swiftly Tilting Planet :

"… deep in concentration, bent over the model
they were building of a tesseract:
the square squared, and squared again…."

See also the phrase Galois tesseract .

Wednesday, January 24, 2018

The Pentagram Papers

Filed under: Uncategorized — m759 @ 12:40 PM


From a Log24 post of March 4, 2008 —

"Are Children the Ultimate Literary Critics?"
— Top of the News 29 (Nov. 1972): 32-36.

"Sets forth his own aims in writing for children and laments
'slice of life' and chaos in children's literature. Maintains that
children like good plots, logic, and clarity, and that they
have a concern for 'so-called eternal questions.'"

— An Annotated Listing of Criticism
by Linnea Hendrickson

"She returned the smile, then looked across the room to
her youngest brother, Charles Wallace, and to their father,
who were deep in concentration, bent over the model
they were building of a tesseract: the square squared,
and squared again: a construction of the dimension of time."

— A Swiftly Tilting Planet,
by Madeleine L'Engle

Cover of 'A Swiftly Tilting Planet' and picture of tesseract

For "the dimension of time," see A Fold in TimeTime Fold,
and Diamond Theory in 1937

A Swiftly Tilting Planet  is a fantasy for children 
set partly in Vespugia, a fictional country bordered by
Chile and Argentina.


The pen's point:

Wm. F. Buckley as Archimedes, moving the world with a giant pen as lever. The pen's point is applied to southern South America.
John Trever, Albuquerque Journal, 2/29/08

Note the figure on the cover of National Review  above —

A related figure from Pentagram Design

See, more generally,  Isaac Singer  in this  journal.


Filed under: Uncategorized — Tags: — m759 @ 4:37 AM

The five stages of grief meet
the four stages of design:

For Guy Noir

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

From a search for Limerick in this journal —

"C A V E S  is an exhibition of three large scale works,
each designed to immerse the viewer, and then to
confront the audience with a question regarding how far
they, as privileged viewers of the shadows and reflections
being played out upon the walls, are willing to allow
themselves to believe what they know to be a false reality."

Occupy Space art exhibitions, Limerick, Ireland

Tuesday, January 23, 2018

Le Guin

Filed under: Uncategorized — m759 @ 5:55 PM


Chilean poet Nicanor Parra


Filed under: Uncategorized — m759 @ 4:18 PM

"I need a photo opportunity . . . ." — Paul Simon


Filed under: Uncategorized — Tags: — m759 @ 1:27 PM

For the original Davos icon by Wink-Minneapolis,
see the previous post.  

For related geometry, see posts tagged Barth Art.

Graphic Design

Filed under: Uncategorized — m759 @ 12:00 PM

By Wink-Minneapolis

Monday, January 22, 2018

Hollywood Moment

Filed under: Uncategorized — m759 @ 12:00 PM

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

A death on the date of the above symmetry chat,
Wednesday, August 17, 2016

'Love Story' director dies

An Hispanic Hollywood moment:

Ojo de Dios —

Click for related material.

For further Hispanic entertainment,
see Ben Affleck sing 
"Aquellos Ojos Verdes "
in "Hollywoodland."

Sunday, January 21, 2018

At Which Point

Filed under: Uncategorized — m759 @ 6:06 PM

"In 'Sophistry,' a new play by Jonathan Marc Sherman
at the Playwrights Horizons Studio, a popular tenured
professor stands accused of sexual harassment
by a male student."

— Frank Rich in The New York Times , theater review
on October 12, 1993

"At which point another play, inchoate but arresting,
edges into view." — Rich, ibid.

"Johansson began acting during childhood,
after her mother started taking her to auditions.
She made her professional acting debut
at the age of eight in the off-Broadway production
of 'Sophistry' with Ethan Hawke, at New York's
Playwrights Horizons."

— IMDb Mini Biography by: Pedro Borges 

" 'Suddenly, I was 19 again and I started to remember
all the men I'd known who had taken advantage of
the fact that I was a young woman who didn't yet have
the tools to say no, or to understand the value of
my own self-worth,' the Avengers star described. 
'I had many relationships both personal and professional
where the power dynamic was so off that I had to create
a narrative in which I was the cool girl who could hang in
and hang out, and that sometimes meant compromising
what felt right for me . . . . ' "

— Scarlett Johansson yesterday at the 2018 Women's March
in Los Angeles, as reported in E! News .

Bill Murray and Scarlett Johansson in 'Lost in Translation'

Image in a Log24 post
of March 12, 2009.

Spiritual Memoir

Filed under: Uncategorized — m759 @ 9:09 AM

In her new spiritual memoir . . . .

Armies of the Night —

Armies of the Day —

Cole Porter —

Night and Day —

Saturday, January 20, 2018

Closed Set

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

From "Charmed," a Log24 post of Jan. 13, 2018 :

'The World of A-bar' by A. E. van Vogt, first published as a serial in 1945

The Chaos Symbol of Dan Brown

Filed under: Uncategorized — m759 @ 1:30 AM

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

Related news —

Related symbolism —


A star figure and the Galois quaternion.

The square root of the former is the latter.

Friday, January 19, 2018

The Pentagram Papers

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


Jodie Foster in  a Dec. 15, 2017, sketch  with Stephen Colbert —

"People invest in and take ownership of brands,
and they wonder why the brand didn’t
ask their permission to change."

— Michael Bierut of Pentagram Design
in  a Design Week  article  of Jan. 17, 2018


Filed under: Uncategorized — Tags: — m759 @ 4:04 AM

Thursday, January 18, 2018

A Phrase That Might Have Been

Filed under: Uncategorized — m759 @ 5:12 PM

The online New York Times  reports this afternoon
the death of a production designer on January 9th —

"In addition to the two Oscars Mr. Marsh won
(which he shared with others), he was nominated
for two more: for 'Scrooge' (1970), with Albert Finney and
Alex [sic ] Guinness, and 'Mary, Queen of Scots' (1971),
with Vanessa Redgrave and Glenda Jackson."

" The Little Broomstick  by  Mary Stewart,
illustrated by Shirley Hughes, published Brockhampton 1971.
The story is about Mary, staying at Great-Aunt Charlotte's house,
bored until she meets the black cat Tib and finds the purple flower
fly-by-night that makes the little broomstick fly. In chapter 10
'gay go up and gay go down' Mary hides in Endor College,
the witch school, after hours and finds Tib transformed into a frog
(Madame Mumblechook had taken him from her as her entry fee).
She recites the Master Spell to release him. ' It was a simple,
gay little rhyme, and it ended on a phrase that might have been
(but wasn't) "the dancing ring of days".'  

"Bah, humbug!" — A Christmas Carol

Wednesday, January 17, 2018

Language Game

Filed under: Uncategorized — m759 @ 11:30 AM

Continued from Zen and Language Games
(a post of May 2, 2003, written on March 1, 2002)

From The Harvard Crimson  on St. Andrew's Day 2017 —

See also a larger, clearer view of the titles in the above file photo.

Dialogue suggested by the above Harvard Crimson  line
"I am a book today . . . . I know it all." —

A problem child* of sorts in the 2017 film "Gifted"

Mary- "Maybe this school isn't as great as you think it is."

Mary is returned to the place of her examination.

Professor- "Mary, you knew that the problem was incorrect, 
            why didn't you say anything?"

Mary- "Frank says I'm not supposed to correct older people. 
       Nobody likes a smart-ass."

* "Problem Child" was a working title related to a novel
    Heinlein wrote in 1941, Beyond This Horizon —

“Before Time Began, There Was the Cube”

Filed under: Uncategorized — m759 @ 8:00 AM

See Eightfold Froebel.

The Paradise of Childhood'-- Froebel's Third Gift

At Heaven’s Gate

Filed under: Uncategorized — Tags: — m759 @ 7:30 AM

(Continued from September 12, 2005)

The previous post contrasted the number-triple 11-7-8 below
with number triples 12-9-5 and 12-5-9.

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

A perhaps more logical counterpart of the triple 11-7-8, based
on opposite  locations of star-points or cube-edges, is
the triple 9-12-5. For a theological interpretation, see 9/12/05.

Tuesday, January 16, 2018

An Orison for Ha-Why

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

'Cloud Atlas' book cover illustrating the film

Lines from characters played in the film by Tom Hanks and Halle Berry —

— Cloud Atlas , by David Mitchell (2004).

An orison of sorts from a post on Martin Scorsese's
birthday, Sunday, Nov. 18, 2007 —

BlackBerry with pictures from Log24

Displayed on the BlackBerry are parts
of Log24 posts from October 25, 2007,
and October 24, 2007.

Related pattern geometry 

From a Log24 search for Angleton + Brotherhood:
A photo of Angleton in a post from 12/9/5

The image “http://www.log24.com/log/pix05B/051209-Angleton.jpg” cannot be displayed, because it contains errors.

From a post of 11/7/8


A cryptic note for Dan Brown:

The above dates 11/7/8 and 12/9/5 correspond to the corner-labels
(read clockwise and counter-clockwise) of the two large triangles
in the Finkelstein Talisman

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

Above: More symbology for Tom Hanks from
this morning's post The Pentagram Papers.

The above symbology is perhaps better suited to Hanks in his
role as Forrest Gump than in his current role as Ben Bradlee.

The image “http://www.log24.com/log/pix05B/051211-gump.jpg” cannot be displayed, because it contains errors.

For Hanks as Dan Brown's Harvard symbologist 
Robert Langdon, see the interpretation 12/5/9, rather
than 12/9/5, of the above triangle/cube-corner label.

A Moriarty for Sherlock

Filed under: Uncategorized — m759 @ 10:01 AM

The Pentagram Papers

Filed under: Uncategorized — Tags: — m759 @ 9:16 AM

Other intersection-points-counting material —

The Finkelstein Talisman:

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See also Hanks + Cube in this journal —

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


Filed under: Uncategorized — m759 @ 2:00 AM

"There was a game we used to play . . . ."

— The Cranberries on "Charmed,"
Season 2, Episode 5 (aired Nov.  4, 1999)

Monday, January 15, 2018

IT Strategy

Filed under: Uncategorized — m759 @ 1:06 PM

See also posts tagged Systems Programming.

Boston News

Filed under: Uncategorized — m759 @ 11:14 AM

Related material in this  journal —

The final link in a post of 8:07 AM ET on Friday, June 27, 2008, 
pointed to http://www.gateofheavenparish.com. That 2008 link
now leads to a more recent, quite different, webpage.

The page that the link led to in 2008 is now archived at

Sunday, January 14, 2018


Filed under: Uncategorized — m759 @ 11:24 PM

"Wer gab uns den Schwamm, um den ganzen Horizont wegzuwischen?"

— Nietzsche, "Der Tolle Mensch


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

Ken Yuszkus, Salem News  staff photo

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

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

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

. . . .

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

See also other posts tagged Systems Programming.

Saturday, January 13, 2018


Filed under: Uncategorized — m759 @ 1:00 AM

From an obituary in this morning's online New York Times

"John Tunney seemed to have a charmed political life until 1976,
when at age 42 he lost his Senate seat after just one term
to the unlikeliest of Republican challengers, a former Democrat
named Samuel I. Hayakawa."

Topology punchline —

"Sorry, but A is closed."

For more tasteless mathematical humor, see . . .

'Mathemati-Con: A day of free events open to the public

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