Tuesday, December 31, 2013

Objects of Beauty

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


"I am a town." — Mary Chapin Carpenter

"A town, huh?" — Sydney Prosser

Related material — "Put on your red dress, baby."

Christmas Ornaments

Filed under: General,Geometry — Tags: , , — m759 @ 12:25 AM

Continued from December 25

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

A link from Sunday afternoon to Nov. 26, 2012,
suggests a review of one of the above structures.

The Dreaming Jewels  cover at left is taken from a review
by Jo Walton at Tor.com—

"This is a book that it’s clearly been difficult
for publishers to market. The covers have been
generally pretty awful, and also very different.
I own a 1975 Corgi SF Collectors Library
paperback that I bought new for 40p in the later
seventies. It’s purple, and it has a slightly grainy
cover, and it matches my editions of The Menace
From Earth
  and A Canticle for Leibowitz .
(Dear old Corgi SF Collectors Editions with their
very seventies fonts! How I imprinted on them at
an early age!) I mention this, however, because
the (uncredited) illustration actually represents and
illustrates the book much better than any of the other
cover pictures I’ve seen. It shows a hexagon with an
attempt at facets, a man, a woman, hands, a snake,
and stars, all in shades of green. It isn’t attractive,
but it wouldn’t put off people who’d enjoy what’s inside

The "hexagon with an attempt at facets" is actually
an icosahedron, as the above diagram shows.
(The geometric part of the diagram is from a Euclid webpage.)

For Plato's dream about these jewels, see his Timaeus.

Monday, December 30, 2013

A Wilderness of Mirrors

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

A link to a Nov. 22 post on Arcade Fire was added today
to yesterday's "Dating an OS" post. 

That Nov. 22 post suggests a review related to a new film —

"If the spy wars of the later 20th century were fought
in 'a wilderness of mirrors,' beset by paradox and
moral uncertainty— evil done in the name of good—
then John le Carré, or, rather, the narrative voice that
went by the name John le Carré, was the perfect
choice to polish those mirrors. It was the voice of the
urbane, upper-class Englishman: courteous, opaque
and chilly, with a ruthless, penetrative intellect and
razor wit for the delivery of its insights."

— Alan Furst in The New York Times Sunday
      Book Review 
 on October 12, 2008

For other material on mirrors, see all posts tagged Arcade Fire.

Sunday, December 29, 2013

Good Question

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

Amy Adams in the new film “Her” —

“You’re dating an OS?  What is that like?”

— Question quoted in a Hollywood Reporter
story on the film’s second trailer

From the same story, by Philiana Ng —

” The trailer is set to Arcade Fire’s
mid-tempo ballad ‘Supersymmetry.’ “

Parts of an answer for Amy —

Nov. 26, 2012, as well as

July 19, 2008,

Dec. 18, 2013,

Dec. 24, 2013, and

Dec. 27, 2013.

The Hollywood Reporter  story is from Dec. 3, 2013.
See also that date in this  journal.

Friday, December 27, 2013

Dreigroschen Trifft Vierfarben

Filed under: General — m759 @ 8:28 PM

See also Pop Meets Hochkultur in a post of Dec. 18, 2013.

Some background for that post— July 19, 2008.

Space Epiphany

Filed under: General — m759 @ 12:00 PM

For posts related to the title, click here.

Jodie Foster in 'Contact'

Occupy Space

Filed under: General — m759 @ 11:00 AM


Many people enter the merry- go-round.
Here and there one catches a phrase —
"Room for one more on the hippo's back"….

— Adapted from the prologue to
     Liliom , by Ferenc Molnár

Click Elysium for a related image.

Thursday, December 26, 2013


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

For fans of Hunger Games  and Elysium —

Roberta Smith in this evening's* online New York Times

"Especially with the gap between the wealthiest
and everyone else so wide, it is dicey
for a major museum to celebrate the often frivolous
objects on which the rich spend their ever increasing
surplus income. Such a show must be beyond reproach
in every way: transparent in organization, impeccable
in exhibition design, illuminating in catalog and labeling
and, most of all, self-evidently excellent in the quality of
the objects on display."

Da capo:  "I've heard of affairs that are strictly Platonic."

* 5:08 PM ET

How It Works

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


“Design is how it works.” — Steve Jobs

“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”

— “Block Designs,” by Andries E. Brouwer (Ch. 14 (pp. 693-746),
Section 16 (p. 716) of Handbook of Combinatorics, Vol. I ,
MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel,
and László Lovász)

For some background on that Steiner system, see the footnote to
yesterday’s Christmas post.

Boxing Day

Filed under: General — m759 @ 10:00 AM

See "Glory Road" + "Black Box."

Wednesday, December 25, 2013

Rotating the Facets

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

Previous post

“… her mind rotated the facts….”

Related material— hypercube rotation,* in the context
of rotational symmetries of the Platonic solids:

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

“I’ve heard of affairs that are strictly Platonic”

Song lyric by Leo Robin

* Footnote added on Dec. 26, 2013 —

 See Arnold Emch, “Triple and Multiple Systems, Their Geometric
Configurations and Groups
,” Trans. Amer. Math. Soc.  31 (1929),
No. 1, 25–42.

 On page 42, Emch describes the above method of rotating a
hypercube’s 8 facets (i.e., three-dimensional cubes) to count
rotational symmetries —

See also Diamond Theory in 1937.

Also on p. 42, Emch mentions work of Carmichael on a
Steiner system with the Mathieu group M11 as automorphism
group, and poses the problem of finding such systems and
groups that are larger. This may have inspired the 1931
discovery by Carmichael of the Steiner system S(5, 8, 24),
which has as automorphisms the Mathieu group M24 .

Rotating the Facts

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

IMAGE- 'American Hustle' and Art Cube

"She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test."

— Steve Martin, An Object of Beauty

"So you should not feel so all alone…"
— Adapted song lyric

A Midnight Clear

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

Click image for a meditation.

Tuesday, December 24, 2013

Through a Mirror, Darkly

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

Review of a book first published in 1989—

Reality's Mirror: Exploring the Mathematics of Symmetry —

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

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

IMAGE- Daily Princetonian, Dec. 23, 2013

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

"Always with a little humor." — Yen Lo

Monday, December 23, 2013


Filed under: General — m759 @ 1:00 PM

In memory of Mikhail Kalashnikov, who reportedly died today at 94:

Integrity, Craftsmanship, Tradition .

See also an SNL tracking shot

A Yahrzeit for Scaccia

Filed under: General — m759 @ 12:00 PM

Bat Signal

Filed under: General — m759 @ 11:30 AM

From the Bacardi website

"Hamilton, Bermuda, December 13, 2012 —
Bacardi Limited caps off the yearlong celebration
of its 150th anniversary with the creation of a
commemorative time capsule…."

See also this journal on that date.

Paradise Alley

Filed under: General — m759 @ 3:00 AM

From The Iceman Cometh  (1946, set in 1912) —

HOPE— (calls effusively) Hey there, Larry! Come over
and get paralyzed! What the hell you doing, sitting there?
(Then as Larry doesn't reply he immediately forgets him
and turns to the party. They are all very drunk now, just a
few drinks ahead of the passing-out stage, and hilariously
happy about it.) Bejees, let's sing! Let's celebrate! It's my
birthday party! Bejees, I'm oreyeyed! I want to sing! (He
starts the chorus of "She's the Sunshine of Paradise Alley,"
and instantly they all burst into song. But not the same song.
Each starts the chorus of his or her choice….)

From Paradise Alley  (1978, set in 1946) —

Sunday, December 22, 2013

In Memoriam

Filed under: General — m759 @ 7:00 PM

The image “http://www.log24.com/log/pix05/050522-Jack.jpg” cannot be displayed, because it contains errors.


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

From a prequel to The Shining , by Stephen King—

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

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

See also Steam

For one answer to the riddle, click here.

The Bronfman Catechism

Filed under: General — m759 @ 10:21 AM


Log24 on Sunday, October 5, 2008

Theologian James Edwin Loder:

“In a game of chess, the knight’s move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a ‘knight’s move’ in intelligence.”

Related material:

Terence McKenna:

“Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey ‘haunts time like a ghost.’”

Anonymous author:

“‘Knight’s move thinking’ is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia.”

Related journalism

IMAGE- Scene from a blackboard jungle

"What's the 'S'  stand for?" — Amy Adams

House of Seagram’s

Filed under: General — m759 @ 2:01 AM

See also the life of Joseph E. Seagram.

Saturday, December 21, 2013

House of Secrets*

Filed under: General,Geometry — m759 @ 6:01 PM

The title is taken from a book for ages 8-12 published
on Shakespeare's birthday, April 23, 2013.

Also from that date, a note for older readers—

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

Half a dozen of the other —

For further context, see all  posts for the cruelest month of this past year.

* Secrets :  A sometimes dangerous word.

Logic and Poetry

Filed under: General — m759 @ 12:00 PM

Headline on an avant-garde-theater piece in
The New York Times  that was the subject of
a Log24 post on December 15  (Julie Taymor's birthday):

"To Thine Own Algorithm Be True"

Today is the feast of St. Peter Canisius.

Click on Canisius for material related to the Times
story, and on the feast for a more traditional tale.


Filed under: General — m759 @ 11:01 AM

"It's going to be accomplished in steps,
this establishment of the Talented
in the scheme of things."

— To Ride Pegasus ,
     by Anne McCaffrey (Radcliffe '47),
    quoted here on December 1, 2013

"Twenty-one days is enough time to build trust
and decimate it several times over, and long enough
for someone to drop their pretensions altogether.
So while 'Dude, You’re Screwed' is about a person
at war with himself, 'Naked and Afraid' is about
people at war with each other. The elements may
get you down, but hell is other people."

Jon Caramanica in The New York Times
    (page C1 of today's New York print edition)

Ephemera for the Solstice

Filed under: General — m759 @ 10:01 AM

Miami Link

Filed under: General,Geometry — m759 @ 2:14 AM

The Miami-Dade County Public Schools math webpage
​now has a link to the Diamond 16 Puzzle.

Friday, December 20, 2013

For Emil Artin

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

(On His Dies Natalis )

An Exceptional Isomorphism Between Geometric and
Combinatorial Steiner Triple Systems Underlies 
the Octads of the M24 Steiner System S(5, 8, 24).

This is asserted in an excerpt from… 

"The smallest non-rank 3 strongly regular graphs
​which satisfy the 4-vertex condition"
by Mikhail Klin, Mariusz Meszka, Sven Reichard, and Alex Rosa,

(Click for clearer image)

Note that Theorem 46 of Klin et al.  describes the role
of the Galois tesseract  in the Miracle Octad Generator
of R. T. Curtis (original 1976 version). The tesseract
(a 4×4 array) supplies the geometric  part of the above
exceptional geometric-combinatorial isomorphism.

Thursday, December 19, 2013


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

For Josefine Lyche, artist of High White Noon —

Thursday, October 10, 2013

Mr. Noon

Filed under: Uncategorized — m759 @ 12:00 PM 

Excerpt from 'Mr. Noon,' by D.H. Lawrence

See also "Finishing Up at Noon," "S in a Diamond," and "Beyond: Two Souls."



Annals of Literature

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

(This morning's Text and Pretext, continued)

"… a reality that only my notes can provide."
    — Kinbote in Nabokov's novel Pale Fire

Click the above remarks on screws for another perspective on reality.

Text and Pretext

Filed under: General — Tags: — m759 @ 10:35 AM

IMAGE- NY Times lead obituary, Thursday morning, Dec. 19, 2013, with phrase 'without the slightest pretext'

The above image is a pre-text. For details, see the text .

Wednesday, December 18, 2013

Gute Frage

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

A scene from the 2002 film Max

(Click for a video on the film.)

Related material— This journal, posts of Sept. 8-9, 2013.

Some backstory— Outsider Art, and an obituary for Günther Förg 
in tonight's online New York Times

"Günther Förg, a German painter, sculptor and
photographer whose work exemplified, toyed with,
tweaked and commented on— sometimes all at
once— the broad artistic movement known as
modernism, died at his home in Freiburg, Germany,
on Dec. 5, his 61st birthday." 

The Log24 posts of that date, Dec. 5, are not without relevance.

Bing Bang Theory

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

Microsoft in 2009 on its new search engine name—

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

A search on Bing today —

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

A colorful tale —

IMAGE- The Diamond 16 Puzzle, with commentary

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

A Hand for the Band

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

"How about another hand for the band?
They work real hard for it.
The Cherokee Cowboys, ladies and gentlemen."

— Ray Price, video, "Danny Boy Mid 80's Live"

Other deathly hallows suggested by today's NY Times

Click the above image for posts from December 14.

That image mentions a death on August 5, 2005, in
"entertainment Mecca" Branson, Missouri.

Another note from August 5, 2005, reposted here
on Monday

IMAGE- Aug. 5, 2005- Galois tesseract, Shakespeherian Rag, Sir Alec Guinness

Happy birthday, Keith Richards.

Monday, December 16, 2013

Questions of Faith

Filed under: General — m759 @ 11:00 PM

"Mr. Nissenson took years to create alternative worlds
in pursuing questions of faith in books like 'The Tree
of Life
.'" — NY Times  obituaries index this evening

"O fearful meditation!" — William Shakespeare
in this journal (see posts on Ray Price).

The Seventh Square

Filed under: General,Geometry — m759 @ 10:00 PM

The above image is from Geometry of the 4×4 Square.

(The link "Visible Mathematics" in today's previous post, Quartet,
led to a post linked to that page, among others.)

Note that the seventh square above, at top right of the array of 35,
is the same as the image in Quartet.

Related reading


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

IMAGE- Four quadrants of a Galois tesseract, and a figure from 'Lawrence of Arabia'

Happy Beethoven's Birthday.

Related material:  Abel 2005 and, more generally, Abel.

See also Visible Mathematics.

Sunday, December 15, 2013

Knowing Brooklyn

Filed under: General — m759 @ 7:01 PM

The New York Times  this evening has a story
on "A Piece of Work," an avant-garde production
at Brooklyn Academy of Music (BAM) that is to open

A background check on Annie Dorsen, the production's 
author-director, yields the following remarks on a video
promoting a show titled "Magical"—

"This video is sent us by the company for promotion
of their show in Bergen the 15. and 16. of April 2011.
Excerpt from the program:

Do magic and feminism go together? Anne Juren, the
French choreographer living in Vienna, and Annie
Dorsen, the New York based director, attempt to prove
that it can: it’s alchemical, it’s political and it works."

Related material:  This journal eight years ago today, and
the Log24 posts from the dates, April 15-16, 2011, of the
"Magical" production in Bergen, Norway.

Happy birthday, Julie Taymor.

A Life

Filed under: General — m759 @ 5:01 PM

A+ with garlands.


Filed under: General,Geometry — m759 @ 11:00 AM

Odin's Jewel

Jim Holt, the author of remarks in yesterday's
Saturday evening post

"It turns out that the Kyoto school of Buddhism
makes Heidegger seem like Rush Limbaugh—
it’s so rarified, I’ve never been able to
understand it at all. I’ve been knocking my head
against it for years."

Vanity Fair Daily , July 16, 2012

Backstory Odin + Jewel in this journal.

See also Odin on the Kyoto school —

For another version of Odin's jewel, see Log24
on the date— July 16, 2012— that Holt's Vanity Fair
remarks were published. Scroll to the bottom of the
"Mapping Problem continued" post for an instance of
the Galois tesseract —

IMAGE- The Galois tesseract as a four-dimensional vector space, from a diagram by Conway and Sloane in 'Sphere Packings, Lattices, and Groups'

Saturday, December 14, 2013

Beautiful Mathematics

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

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

Some material relevant to the title adjective:

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

Some relevant links—

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

Update of March 9, 2014 —

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

Bend Sinister

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

I Ching hexagram 14, box style

Click image for background.
See also related posts.

American Beauty

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

Or: Blackboard Jungle, Continued

  Click image for
  a related story.

Sacred and Profane

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

(Continued from yesterday afternoon)

This journal on December 12th, 2009

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

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

Compare and contrast with Frenkel at the Fields Institute

Friday, December 13, 2013

Outsider Art

Filed under: General — m759 @ 1:23 PM

(Continued from yesterday afternoon)

From yesterday's online New York Times  (5:59 PM ET)—

A Tension Between the Sacred and the Profane

What exactly are we looking at? Is it the real thing, or is it the promotion of a famous brand gussied up in spectacular, pseudo-sacramental style? Gold or fool’s gold?

This sort of confusion pervades today’s art world, where, so often, the sales pitch comes in the form of quasi-religious rhetoric. It’s a big reason the tribal arts of Africa and other lands — as well as the putatively purely authentic creations of folk artists and so-called outsiders — are held in such high esteem.

— Ken Johnson, review of two exhibitions,
    of tribal African art and of Brancusi

"Tenser, said the tensor…"

Unscientific Postscript

Filed under: General — m759 @ 12:25 PM

" What you mean 'we' ? "

Thursday, December 12, 2013

Communion of Saints

Filed under: General — Tags: — m759 @ 11:59 PM

For Hugh Jackman,  St. Gall,  and Delmore Schwartz

IMAGE- Logan and bear in 'The Wolverine' (2013)

"All the saints have powers."

Outsider Art

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

"… Galois was a mathematical outsider…."

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

Related art: 

(Click for a larger image.)

IMAGE- Google search for 'Diamond Space' + Galois

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


Filed under: General — m759 @ 1:27 PM

The late Colin Wilson appears at the head
of this afternoon's New York Times  obituaries —

Margalit Fox's description this afternoon of 
Wilson's first book, from 1956—

"The Outsider  had an aim no less ambitious
than its scope: to delineate the meaning of
human existence."

This suggests a review of Log24 posts on "The Zero Theorem"
that yields—

IMAGE- Barry Mazur: 'A good story is an end in itself.'

See also Log24 on the date of Wilson's death.

Related material: Devil's Night, 2011.

Wednesday, December 11, 2013

Howl (continued)

Filed under: General — Tags: — m759 @ 12:31 PM

See the Telegraph  obituary of Jim Hall
and a post on Charlie Christian (and others).

The inclusion of D. H. Lawrence in that post
suggests a review of posts tagged Howl.

"The werewolves are here to save us."
— Simon in "The Mortal Instruments: City of Bones."

The Well-Tempered Monolith

Filed under: General — m759 @ 12:00 PM

IMAGE- The Cullinane frequency matrix

"My God, it's full of numbers!"

Tuesday, December 10, 2013

Blue Note

Filed under: General — m759 @ 10:25 PM

For the late Jim Hall

Backstory:   Icon, 1:44 PM ET today.

Update of 11 PM ET Dec. 10, 2013 — 

For all  the notes, see Da Capo  (11 AM today)
and the Cullinane frequency matrix (12×12).

IMAGE- Matrix used to illustrate the well-tempered scale. The integer frequency-ratio values are only approximate in such a scale.

Matrix used to illustrate the well-tempered
scale. The integer frequency-ratio values
are only approximate in such a scale.

Wittgenstein’s Tesseract

Filed under: General,Geometry — m759 @ 5:14 PM

See also last night's "Pink Champagne on Ice" post.
The "ice" in that post's title refers to the white lines
forming a tesseract in the book cover's background—
"icy white and crystalline," as Johnny Mercer put it.
(A Tune for Josefine, Nov. 25.)

See also the tag Diamond Theory tesseract in this journal.


Filed under: General — m759 @ 1:44 PM

"Let’s love, and kill like 17 now."
— AFI song, soundtrack of "City of Bones"

See also Comic Strip Dead and
Llewyn Davis in this journal.

Da Capo*

Filed under: General — m759 @ 11:00 AM

An upload date —

Related material — 

* The title is a musical term

IMAGE- Music by Bach in 'The Mortal Instruments: City of Bones' (at 1:04:14)

Pink Champagne on Ice

Filed under: General — m759 @ 1:00 AM

The title refers to a post of April 26, 2009.

U. of California edition of Wittgenstein's 'Zettel'-- pink cover, white tesseract in background

Mirrors, Mirrors

Filed under: General — m759 @ 12:24 AM

For Blancanieves, Elizabeth Taylor, and Lily Collins.

IMAGE- Lily Collins and the Seven Dwarfs dance in 'Mirror Mirror'

See also this journal on the above upload date— June 21, 2012.

Monday, December 9, 2013

Being There

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

Or: The Naked Blackboard Jungle

"…it would be quite a long walk
for him if he had to walk straight across."

The image “http://www.log24.com/log/pix07A/070831-Ant1.gif” cannot be displayed, because it contains errors.

Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

The image “http://www.log24.com/log/pix07A/070831-Ant2.gif” cannot be displayed, because it contains errors.

– A Wrinkle in Time 
Chapter 5, "The Tesseract"

Related material: Machete Math and

Starring the late Eleanor Parker as Swiftly Mrs. Who.

Heaven Descending

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

An I Ching  study quoted in Waiting for Ogdoad (St. Andrew’s Day, 2013)—

(Click for clearer image.)

The author of the above I Ching  study calls his lattice “Arising Heaven.”

The following lattice might, therefore, be called “Heaven Descending.”

IMAGE- Construction of 'Heaven Descending' lattice

Click for the source, mentioned in Anatomy of a Cube (Sept. 18, 2011).

Sunday, December 8, 2013

Honors Night

Filed under: General — m759 @ 10:00 PM

Tonight was Honors Night at the Kennedy Center.

"For every kind of vampire,
there is a kind of cross." — Pynchon

From "Colin Wilson: The Persistence of Meaning"

"At a literary conference at SUNY New Paltz three years ago, among people who I thought would be positively disposed to Wilson, my mentioning of his name resulted in any number of arched eyebrows and suavely disparaging remarks. Now this might itself be, not an affirmation of justified oblivion, as one could easily assume, but rather a kind of indirect evidence for intrinsic merit. I stress the academic  character of the event and the self-assured oiliness of the dismissal. In context, the reference seemed to carry a distinctly un-PC valence so that the reaction to it, as I picture it in retrospect, resembled that of a patrician vampire to garlic."

—  Thomas F. Bertonneau on Thursday,
      May 7, 2009, in The Brussels Journal 

Black Mass*

Filed under: General — Tags: — m759 @ 2:29 PM

IMAGE- 'The Pyx' (1973), starring Karen Black and Christopher Plummer, in a post from the date of Black's death

* The title refers to the film illustrated above, and also
(with a different meaning) to this morning's 11 AM post,
as well as to topics that may interest fans of the authors  
in this afternoon's previous post.

Ad Altare

Filed under: General — m759 @ 1:04 PM

Update of 2:02 PM ET:

From this journal on the day of Wilson's death

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

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

These two quotations, intended for Stephen King fans,
may also appeal to Colin Wilson fans.


Filed under: General — m759 @ 11:00 AM

Click to enlarge. See also All About Eve (Dec. 31, 2009).

 Backstory (update of 11:45 AM ET Dec. 8):

Saturday, December 7, 2013

For the X-Men of St Andrews…

Filed under: General — m759 @ 10:00 PM

… and Little Colva

Two links on a Jewish approach to such matters:
Bee Season and, more generally, Kabbalah.

My Way

Filed under: General — m759 @ 12:25 PM

IMAGE- Battleship (2012): 'My way is much more simple.'

"My way is much more simple."

Comic Strip Dead

Filed under: General — m759 @ 10:30 AM

"So it's the laughter we will remember…." —Streisand

IMAGE- 'Comedy Club Owner Dies at 73'

Speak for yourself, Barbra.
Wachs reportedly died on Monday, December 2, 2013.


Memory Study

Filed under: General — m759 @ 2:45 AM

"What's too painful to remember…" — Streisand
"So set 'em up, Joe…" — Sinatra

I've got a little story you oughta know .

Shadow of a Lie

Filed under: General — m759 @ 1:20 AM

A recent addition to Barry Mazur's home page

"December 1, 2013: Here are rough notes for
a short talk entitled The Faces of Evidence
(in Mathematics)
([PDF]) to be given at the
Cambridge Scientific Club, Dec. 5 2013."

The PDF link does not work, but some earlier remarks by
Mazur on this topic have been published elsewhere:

IMAGE- 'Shadows of Evidence,' by Barry Mazur

Related material:

The Proof and the Lie (St. Andrew's Day, 2003), and
a recent repetition of the lie in Wikipedia:

"Around 1955, Japanese mathematicians Goro Shimura 
Yutaka Taniyama observed a possible link between
two apparently completely distinct, branches of mathematics, 

elliptic curves and modular forms."

This statement, from the article on Algebraic number theory,
was added on Oct. 22, 2013 by one "Brirush," apparently a
Temple University postdoctoral researcher, in what he rightly
called a "terrible history summary."

Friday, December 6, 2013

Raiders of the Lost Script

Filed under: General — m759 @ 5:31 PM

Happy Feast of Saint Nicholas.

Thursday, December 5, 2013

Blackboard Jungle

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

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

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

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

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

Research Contributions

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

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

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

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

— John Tate in Oslo on May 25, 2010.

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


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

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

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

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

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

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

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

(Click for a larger image.)

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

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

Wednesday, December 4, 2013

The Mirror’s Faces*

Filed under: General — m759 @ 2:00 PM

See the previous post, the remarks of Roger Kimball
on Frank Stella's lecture at Harvard on Oct. 12, 1983,
and "Study of O" in this journal, with my own images
of space from October 1983.

* The title refers to a 1996 film.
   Happy birthday to Jeff Bridges.

Space According to Stella

Filed under: General — m759 @ 1:06 PM

IMAGE- 'The aim of art is to create space.'- Frank Stella

Related remarks: yesterday's post at this hour.

Bear and Bull

Filed under: General — m759 @ 12:00 PM

Excerpt from a poem by Johanna Skibsrud
(Toronto Quarterly , April 2, 2011)—

No, I could not love a human being if they 
could not leave a mark.

Even if I was a bear 
and I ate you, you would 
move right through me. 

Even if you were a bear 
and you ate me, I would 
move right through you.

But I am not a bear. And will not eat you. 
If I said I could, I could not.

And you are not a bear. And will not eat me.

And that is why I could not love you. 

Related material: Into the Bereshit.

See also the remarks on space in Skibsrud's
January 2012 doctoral thesis at the University
of Montreal—

" 'The nothing that is': An Ethics of Absence
    Within the Poetry of Wallace Stevens."

— as well as Bull Run I and Bull Run II.

Tuesday, December 3, 2013

Diamond Space

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

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

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

Monday, December 2, 2013

Finite-Geometry Notes

Filed under: General,Geometry — m759 @ 8:30 PM

See my Google Sites page if you would like to
download a zipped copy (31 MB) of my
Finite-Geometry Notes  site
(not zipped, at finitegeometry.org/sc/map.html).
Or you can of course use a website downloader.

(Suggested by a recent NY Times  piece on
a company, Citia, that splits books into pieces 
for easier electronic access. The large zipped
file referred to above is sort of a reverse of this

Sunday, December 1, 2013


Filed under: General — m759 @ 11:00 AM

IMAGE- 'To Ride Pegasus,' 1973 1st ed., by Anne McCaffrey

First edition, 1973, cover art by Gene Szafran

"It's going to be accomplished in steps,
this establishment of the Talented
in the scheme of things."

To Ride Pegasus ,
     by Anne McCaffrey (Radcliffe '47)


Filed under: General — m759 @ 10:16 AM

Click for clearer image.

From Willard Van Orman Quine Guest Book Volume 1

"May 7, 1997 'McX and Wyman' — In his essay 'On What There Is', Willard Quine introduces two fictional philosophers who put forward certain ontological doctrines: McX and Wyman. It would be interesting to know whether Quine was thereby alluding to some real philosophers. My guess for McX would be Hugh MacColl, but I have no idea who Wyman might stand for. Thanks for considering the question! from Dr. Kai F. Wehmeier — Email: Kai.Wehmeier (at) math.uni-muenster.de Web Page: http://wwwmath.uni-muenster.de/math/users/wehmeier/"

"I spoke with Prof Quine last night regarding your question which he found interesting. He says his intention was to create some fictional philosophers ('X' and 'Y') to illustrate some of his concerns. There may also have been a 'Z' man. These fictional philosophers were not designed to represent any particular philosophers although their viewpoints may happen [to] reflect those of actual philosophers. – Doug” [Douglas Boynton Quine]

Related material: 

The X-Men Tree (Nov. 12),
X-Men Tree continued (Nov. 17),
Waiting for Ogdoad (Oct. 30),
Interpenetrative Ogdoad (Oct. 31),
Waiting for Ogdoad continued (Nov. 30),
For Sean Connery on St. Andrew's Day (Nov. 30).

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