Log24

Thursday, December 21, 2017

Wrinkles

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

TIME magazine, issue of December 25th, 2017 —

" In 2003, Hand worked with Disney to produce a made-for-TV movie.
Thanks to budget constraints, among other issues, the adaptation
turned out bland and uninspiring. It disappointed audiences,
L’Engle and Hand. 'This is not the dream,' Hand recalls telling herself.
'I’m sure there were people at Disney that wished I would go away.' "

Not the dream?  It was, however, the nightmare, presenting very well
the encounter in Camazotz of Charles Wallace with the Tempter.

From a trailer for the latest version —

Detail:

From the 1962 book —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Monday, October 17, 2016

A Wrinkle in Space

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

"There is  such a thing as a counting-pattern."

— Saying adapted from a young-adult novel

See also the previous post and

Friday, September 11, 2015

Omega Wrinkle:

Filed under: Uncategorized — m759 @ 9:42 PM

A Phrase That Haunts

From this journal on August 23, 2013

Illustration from New York Times  review 
of the novel Point Omega —

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

From the print version of The New York Times Sunday Book Review
dated Sept. 13, 2015 —

The online version, dated Sept. 11, 2015 —

From the conclusion of the online version —

On the above print  headline, "Wrinkles in Time,"
that vanished in the online version —

"Now you see it, now you don't"
is not a motto one likes to see demonstrated
by a reputable news firm.

Related material:  Jews Telling Stories.

Tuesday, August 18, 2015

A Wrinkle in Terms

Filed under: Uncategorized — m759 @ 8:23 AM

The phrase “the permutation group Sn” refers to a
particular  group of permutations that act on an
-element set N— namely, all  of them. For a given n ,
there are, in general, many  permutation groups that
act on N.  All but one are smaller than S.

In other words, the phrase “the permutation group Sn
does not  imply that “Sn ” is a symbol for a structure
associated with n  called “the  permutation group.”
It is instead a symbol for “the symmetric  group,” the largest
of (in general) many permutation groups that act on N.

This point seems to have escaped John Baez.

For two misuses by Baez of the phrase “permutation group” at the
n-Category Café, see “A Wrinkle in the Mathematical Universe”
and “Re: A Wrinkle…” —

“There is  such a thing as a permutation group.”
— Adapted from A Wrinkle in Time , by Madeleine L’Engle

Monday, August 4, 2014

A Wrinkle in Space

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

"There is  such a thing as a tesseract." — Madeleine L'Engle

An approach via the Omega Matrix:

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

See, too, Rosenhain and Göpel as The Shadow Guests .

Thursday, May 8, 2014

Wrinkles in Time

Filed under: Uncategorized — Tags: — m759 @ 2:25 PM

Rivka Galchen, in a piece mentioned here in June 2010

On Borges:  Imagining the Unwritten Book 

"Think of it this way: there is a vast unwritten book that the heart reacts to, that it races and skips in response to, that it believes in. But it’s the heart’s belief in that vast unwritten book that brought the book into existence; what appears to be exclusively a response (the heart responding to the book) is, in fact, also a conjuring (the heart inventing the book to which it so desperately wishes to respond)."

Related fictions

Galchen's "The Region of Unlikeness" (New Yorker , March 24, 2008)

Ted Chiang's "Story of Your Life." A film adaptation is to star Amy Adams.

… and non-fiction

"There is  such a thing as a 4-set." — January 31, 2012

Wednesday, November 18, 2009

A Wrinkle in Dimensions…

Filed under: Uncategorized — m759 @ 9:29 AM

Continued from Monday:

An educated consumer
is our best customer!

Bernie Madoff at work

Acme Klein Bottles — where
yesterday’s future is here today!”

Monday, November 16, 2009

A Wrinkle in Dimensions

Filed under: Uncategorized — m759 @ 9:00 PM

Clifford Pickover now seems to be trying to catch up with Christian fantasists Madeleine L’Engle and Charles Williams. Click on the images below for further details.

Cover of 'Jews in Hyperspace,' by Clifford Pickover

http://www.log24.com/log09/saved/091116-SidKibbitzMusic.JPG

Saturday, August 4, 2018

Manifestations of Exquisite Geometry

Filed under: Uncategorized — m759 @ 1:23 PM

An alleged manifestation in physics, from Scientific American  —

http://www.log24.com/log/pix18/180804-Exquisite_Geometry-subhead-Sciam-500w.jpg

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

Counting symmetries with the orbit-stabilizer theorem

For some entertaining literary  manifestations, see Wrinkle.

Sunday, June 10, 2018

Pieces of April

Filed under: Uncategorized — Tags: — m759 @ 12:25 AM

This journal on April 16, 2018 —

Happy birthday to Pope Emeritus Benedict XVI.

Related material from another weblog in a post also dated April 16, 2018 —

"As I write this, it’s April 5, midway through the eight-day
festival of Passover. During this holiday, we Jews air our
grievances against the ancient Pharaoh who enslaved
and oppressed us, and celebrate the feats of strength
with which the Almighty delivered us from bondage —
wait a minute, I think I’m mixing up Passover with Festivus."
. . . .

"Next month: Time and Tesseracts."

From that next post, dated May 16, 2018 —

"The tesseract entered popular culture through
Madeleine L’Engle’s 'A Wrinkle in Time' . . . ."

The post's author, James Propp, notes that

" L’Engle caused some of her readers confusion
when one of the characters … the prodigy
Charles Wallace Murray [sic ] , declared 'Well, the fifth
dimension’s a tesseract.' "

Propp is not unfamiliar with prodigies:

"When I was a kid living in the Long Island suburbs,
I sometimes got called a math genius. I didn’t think
the label was apt, but I didn’t mind it; being put in
the genius box came with some pretty good perks."

— "The Genius Box," a post dated March 16, 2018

To me, Propp seems less like Charles Wallace
and more like the Prime Coordinator —

For further details, see the following synchronicity checks:

Propp March 16     Log24 March 16

Propp April 16        Log24 April 16

Propp May 16        Log24 May 16 .

Thursday, May 31, 2018

Quantum Suffering

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

See as well, in this  journal, Koestler and Darkness at Noon .

Wednesday, May 16, 2018

Same Old Story

Filed under: Uncategorized — Tags: , — m759 @ 9:00 AM

. . . as time goes by.

Wednesday, May 9, 2018

On April 2, 2005 . . .

Filed under: Uncategorized — m759 @ 11:19 AM

Nostalgie de la Boue

 "Odd-numbered (recto) pages
read from the gutter (inside margin)
towards the fore-edge;
even-numbered (verso) pages
read towards the gutter."

— From The Golden Compasses 
     "Appendix 8: Impositions and
     Folding Schemes" (page 526).

For Wrinkle in Time  fans —

Enthusiasts of la boue  may consult Log24 posts about the above date.

From a Log24 post of April 2, 2005

Thursday, April 19, 2018

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.

Sunday, March 11, 2018

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.

Thursday, March 8, 2018

Thanking the Academy…

Filed under: Uncategorized — m759 @ 9:11 PM

Continues.

Thursday, March 1, 2018

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:

Monday, January 8, 2018

Raiders of the Lost Theorem

Filed under: Uncategorized — Tags: — m759 @ 11:15 PM
 

The Quantum Tesseract Theorem 

 


 

Raiders —

A Wrinkle in Time
starring Storm Reid,
Reese Witherspoon,
Oprah Winfrey &
Mindy Kaling

 

Time Magazine  December 25, 2017 – January 1, 2018

Saturday, December 30, 2017

About IT

Filed under: Uncategorized — Tags: — m759 @ 12:06 AM

Goodreads review of 'Systems Programming,' a book by John J. Donovan

Background: See Wrinkle  in this journal and a post,
Field of Manifestation, from the above 2015 date.

See as well the Goodreads page below.

The six books reviewed by this user were written or
co-written by the author in the review shown above.
Each review gave the highest rating, five stars.

Friday, December 22, 2017

IT

Filed under: Geometry — Tags: — m759 @ 4:08 PM

Movie marquee on Camazotz, from the 2003 film of 'A Wrinkle in Time'

From a Log24 post of October 10, 2017

Koen Thas, 'Unextendible Mututally Unbiased Bases' (Sept. 2016)

Related material from May 25, 2016 —

Friday, July 7, 2017

Psycho History

Filed under: Uncategorized — m759 @ 6:00 PM

The title was suggested by the term "psychohistory" in
the Foundation  novels of Isaac Asimov. See the previous post.

See also a 2010 New York Times  review of
DeLillo's novel Point Omega . The review is titled,
without any other reference to L'Engle's classic tale
of the same name, "A Wrinkle in Time."

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

Related material: The Crosswicks Curse.

Sunday, June 4, 2017

In Memory of the Time Cube Page*

Filed under: Uncategorized — m759 @ 10:00 PM

From this journal on August 18, 2015, "A Wrinkle in Terms" —

For two misuses by John Baez of the phrase “permutation group”
at the n-Category Café, see “A Wrinkle in the Mathematical Universe
and “Re: A Wrinkle” —

“There is  such a thing as a permutation group.”
— Adapted from A Wrinkle in Time , by Madeleine L’Engle

* See RIP, Time Cube at gizmodo.com (September 1, 2015).

Thursday, January 26, 2017

Split

Filed under: Uncategorized — Tags: — m759 @ 11:09 AM

(Continued from Tuesday, Jan. 24, 2017)

"We have reached peak polarization."

— Olga Khazan in the online Atlantic  today,
     as quoted in the Muck Rack image below.

Perhaps not yet.

Consider the headline below,

"Why Trump Supporters Lie About the Inauguration Photo."

Consider also Olga's "Brain Bro" below in the context of 
the film "Limitless" and of the book A Wrinkle in Time .

See also all posts now tagged "Split."

Saturday, April 16, 2016

Matinee (continued)

Filed under: Uncategorized — m759 @ 2:15 PM

Today is Kelli O'Hara's last Saturday matinee in "The King and I."

A show that some may prefer —

Related to the plot of Dante's film

"…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"

Tuesday, April 12, 2016

For Non-Charlatans

Filed under: Uncategorized — m759 @ 12:45 PM

The previous post, Charlatans 101, was on a book whose author
is associated rather closely with an Alabama institution called
"Samford University" (not to be confused with Stanford University).

A photo from Samford

Related material for non-charlatans, not  from Samford —

See as well A Wrinkle in Terms in this journal.

Friday, January 29, 2016

Excellent Adventure*

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

(Continued from Dec. 9, 2013)

"…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"

From a media weblog yesterday, a quote from the video below —

"At 12:03 PM Eastern Standard Time, January 12th, 2016…."

This  weblog on the previous day (January 11th, 2016) —

"There is  such a thing as harmonic analysis of switching functions."

— Saying adapted from a young-adult novel

* For some backstory, see a Caltech page.

Thursday, September 17, 2015

A Word to the Wise:

Filed under: Uncategorized — m759 @ 12:00 PM

Symplectic.

Related material:

From the website of the American Mathematical Society today,
a column by John Baez that was falsely backdated to Sept. 1, 2015 —

Compare and contrast this Baez column 
with the posts in the above
Log24 search for "Symplectic."

Updates after 9 PM ET Sept. 17, 2015 —

Related wrinkles in time: 

Baez's preceding Visual Insight  post, titled 
"Tutte-Coxeter Graph," was dated Aug. 15, 2015.
This seems to contradict the AMS home page headline
of Sept. 5, 2015, that linked to Baez's still earlier post
"Heawood Graph," dated Aug. 1. Also, note the 
reference in "Tutte-Coxeter Graph" to Baez's related 
essay — dated August 17, 2015 — 

Friday, June 19, 2015

Footnote

Filed under: Uncategorized — m759 @ 9:29 PM

There is  such a thing as geometry.*

* Proposition adapted from A Wrinkle in Time , by Madeleine L'Engle.

Monday, September 1, 2014

Mathematics, Not Theology

Filed under: Uncategorized — m759 @ 5:00 PM

(Continued)

“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

— Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
 , Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

“There is  such a thing as a three-set.”
— Saying adapted from a novel by Madeleine L’Engle

Friday, May 9, 2014

Borges on the I Ching

Filed under: Uncategorized — m759 @ 12:00 PM

Para una Versión del I King
por Jorge Luis Borges

El porvenir es tan irrevocable
como el rígido ayer. No hay una cosa
que no sea una letra silenciosa
de la eterna escritura indescifrable
cuyo libro es el tiempo. Quien se aleja
de su casa ya ha vuelto. Nuestra vida
es la senda futura y recorrida.
Nada nos dice adiós. Nada nos deja.
No te rindas. La ergástula es oscura,
la firme trama es de incesante hierro,
pero en algún recodo de tu encierro
puede haber un descuido, una hendidura.
El camino es fatal como la flecha
pero en las grietas está Dios, que acecha.

— La Moneda de Hierro  (1976)

For a translation, see a Dickinson College page.

See also Wrinkles in Time and Models of Everything.

Friday, March 14, 2014

The Search for Charles Wallace

Filed under: Uncategorized — Tags: — m759 @ 2:19 PM

The search in the previous post for the source of a quotation from Poincaré yielded, as a serendipitous benefit, information on an interesting psychoanalyst named Wilfred Bion (see the Poincaré  quotation at a webpage on Bion). This in turn suggested a search for the source of the name of author Madeleine L'Engle's son Bion, who may have partly inspired L'Engle's fictional character Charles Wallace.  Cynthia Zarin wrote about Bion in The New Yorker  of April 12, 2004 that

"According to the family, he is the person for whom L’Engle’s insistence on blurring fiction and reality had the most disastrous consequences."

Also from that article, material related to the name Bion and to what this journal has called "the Crosswicks Curse"*—

"Madeleine L’Engle Camp was born in 1918 in New York City, the only child of Madeleine Hall Barnett, of Jacksonville, Florida, and Charles Wadsworth Camp, a Princeton man and First World War veteran, whose family had a big country place in New Jersey, called Crosswicks. In Jacksonville society, the Barnett family was legendary: Madeleine’s grandfather, Bion Barnett, the chairman of the board of Jacksonville’s Barnett Bank, had run off with a woman to the South of France, leaving behind a note on the mantel. Her grandmother, Caroline Hallows L’Engle, never recovered from the blow. ….

… The summer after Hugh and Madeleine were married, they bought a dilapidated farmhouse in Goshen, in northwest Connecticut. Josephine, born in 1947, was three years old when they moved permanently to the house, which they called Crosswicks. Bion was born just over a year later."

* "There is  such a thing as a tesseract."

Monday, December 9, 2013

Being There

Filed under: Uncategorized — 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.

Wednesday, October 23, 2013

24 Hour Psycho…

Filed under: Uncategorized — m759 @ 4:07 PM

Continues.

"24 Hour Psycho" at the Museum of Modern Art in the novel
Point Omega  is illustrated in New York Times  review

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

Related material — Today's 1 PM post and 

IMAGE- From a Lawrence Block mystery 'A Stab in the Dark'- 'There was a problem in long division worked out in yellow chalk on the blackboard.'

See also yesterday's  1 PM post.

Wednesday, September 11, 2013

Language Game

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

In which Plato continues to thank the Academy.

From the Academy, a lead balloon for 9/11 —
continued from March First, 2002.

A search today for the name Eisenman
(see previous post) yields the following :

"We need a cameo from Plato, a safecracker,
a wrinkle or two to be ironed out, some ice,
some diamonds, and, above all, laughter
for this irony of ironies."

Jeffrey Kipnis, "Twisting the Separatrix,"
Assemblage  No. 14, April 1991, MIT Press

Friday, August 23, 2013

Vacant Space

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

A passage from Wallace Stevens

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

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

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

The rest of the film is not recommended.

Related material—

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

Illustration from a New York Times  review

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

Tuesday, July 16, 2013

Tag (Part II)

Filed under: Uncategorized — Tags: — m759 @ 9:29 AM

(Continued from yesterday evening)

Madeleine L'Engle in The Irrational Season
(1977), Chapter 9:

"After A Wrinkle in Time  was finally published,
it was pointed out to me that the villain, a naked
disembodied brain, was called 'It' because It
stands for Intellectual truth as opposed to a truth
which involves the whole of us, heart as well as
mind.  That acronym had never occurred to me. 
I chose the name It intuitively, because an IT
does not have a heart or soul.  And I did not
understand consciously at the time of writing
that the intellect, when it is not informed by
the heart, is evil."

You're…  IT.

Related material: Mathematics as a Post-Communist Activity.

Sunday, April 21, 2013

Sermon

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

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

Adapted from a novel

Tuesday, April 9, 2013

Kountry Korn Kandy

Filed under: Uncategorized — m759 @ 9:00 PM

For the first two words of the title, 
see the previous post.

For the third word, see a review of the recent film "Hitchcock"
about the director and Janet Leigh during the filming of "Psycho"—

Hopkins' Hitchcock more or less eats out of Janet's hand
when she feeds him candy corn during a drive together
(the reference is to the candy Norman Bates is devouring
when he's interviewed by Martin Balsam's detective).

A story that demands the blended talents of Hitchcock and of
Mel Brooks to do it justice:

See also a 2010 New York Times  review of
DeLillo's novel Point Omega . The review is titled,
without any other reference to L'Engle's classic tale
of the same name, "A Wrinkle in Time."

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

Related material: The Crosswicks Curse.

Thursday, March 28, 2013

Woman at the Well

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

For some images related to this rather biblical topic,

see Hillman + Dream in this journal.

“She was dazzled by light and shade, by the confusing
duplication of reflections and of frames. All coming from
too many directions for the mind to take account of.
The various images bounced against each other
until she felt a desperate vertigo….”

Cold Mountain

Summary image:

IMAGE- Quilt blocks- Devil's Claws and Yankee Puzzle

“… Margaret Murry, wrapped in an old patchwork quilt, sat on the foot of her bed….”

A Wrinkle in Time

Saturday, March 16, 2013

The Crosswicks Curse

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

Continues.

From the prologue to the new Joyce Carol Oates
novel Accursed

"This journey I undertake with such anticipation
is not one of geographical space but one of Time—
for it is the year 1905 that is my destination.

1905!—the very year of the Curse."

Today's previous post supplied a fanciful link
between the Crosswicks Curse of Oates and
the Crosswicks tesseract  of Madeleine L'Engle.

The Crosswicks Curse according to L'Engle
in her classic 1962 novel A Wrinkle in Time —

"There is  such a thing as a tesseract."

A tesseract is a 4-dimensional hypercube that
(as pointed out by Coxeter in 1950) may also 
be viewed as a 4×4 array (with opposite edges
identified).

Meanwhile, back in 1905

For more details, see how the Rosenhain and Göpel tetrads occur naturally
in the diamond theorem model of the 35 lines of the 15-point projective
Galois space PG(3,2).

See also Conwell in this journal and George Macfeely Conwell in the
honors list of the Princeton Class of 1905.

Thursday, February 21, 2013

Galois Space

Filed under: Uncategorized — Tags: — m759 @ 6:00 PM

(Continued)

The previous post suggests two sayings:

"There is  such a thing as a Galois space."

— Adapted from Madeleine L'Engle

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

Thomas Pynchon

Illustrations—

(Click to enlarge.)

Thursday, November 22, 2012

Putting the “I” in “IT”

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

Jennifer Scott at IT Pro , Feb. 16, 2012, on Autonomy

Mike Lynch, founder of Autonomy  and vice president
of information management at HP, took to the stage
at his new parent company’s global partner conference
to impart his philosophy to the 3,000 partners gathered.

'It is no longer about the data but about the meaning
of that data,' he said. 'There is a fundamental revolution
going on in information and the industry is now about
the "I" not the "T" in IT.'"

Click on the logo below for the source.

See also today's previous post and…

Madeleine L'Engle in
The Irrational Season
(1977), Chapter 9:

"After A Wrinkle in Time  was finally published,
it was pointed out to me that the villain,
a naked disembodied brain, was called 'It'
because It stands for Intellectual truth
as opposed to a truth which involves the whole of us,
heart as well as mind.  That acronym had never
occurred to me.  I chose the name It intuitively,
because an IT does not have a heart or soul. 
And I did not understand consciously
at the time of writing that the intellect,
when it is not informed by the heart, is evil."

Friday, November 2, 2012

For All Souls’ Day

Filed under: Uncategorized — m759 @ 9:48 AM

From this journal yesterday (All Saints' Day)—

"But, I asked, is there a difference
between fiction and nonfiction?
'Not much,' she said, shrugging."

New Yorker  profile of tesseract
author Madeleine L'Engle

For a discussion of this issue in greater depth—

"Truth and fact are not the same thing."

— see a 1998 award acceptance speech by L'Engle.

See also a Log24 post of March 1st, 2008, on the soul.

Smart News

Filed under: Uncategorized — m759 @ 4:04 AM

The late Arthur R. Jensen was an expert on IQ testing.

From a Log24 post on Oct. 22, 2012, the reported date of his death—

IMAGE- Smithsonian 'Smart News' reports the death of Paul Kurtz

Related material — "IT" in A Wrinkle in Time .

Time and Chance (continued)

Filed under: Uncategorized — m759 @ 1:20 AM

For clergymen who embrace Trudeau's
"Story Theory of Truth" (see last evening's
7:20 PM post on geometry and A Wrinkle in Time )

Here are two meditations suggested by
yesterday evening's New York Lottery :

1.  Page 141 in Philosophies of India

2.  Post 4658 in this journal— A Wrinkle in Dimensions.

Thursday, November 1, 2012

Theories of Truth

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

A review of two theories of truth described
by a clergyman, Richard J. Trudeau, in
The Non-Euclidean Revolution

The Story Theory of Truth:

"But, I asked, is there a difference
between fiction and nonfiction?
'Not much,' she said, shrugging."

New Yorker  profile of tesseract
     author Madeleine L'Engle

The Diamond Theory of Truth:

(Click image for some background.)

Spaces as Hypercubes

See also the links on a webpage at finitegeometry.org.

Wednesday, October 31, 2012

The Malfunctioning TARDIS

Filed under: Uncategorized — m759 @ 11:01 AM

(Continued from previous TARDIS posts)

Summary: A review of some  posts from last August is suggested by the death,
reportedly during the dark hours early on October 30, of artist Lebbeus Woods.

An (initially unauthorized) appearance of his work in the 1995 film
Twelve Monkeys 

 … suggests a review of three posts from last August.

Wednesday, August 1, 2012

Defining Form

Filed under: Uncategorized — m759 @ 11:01 AM 

Continued from July 29 in memory of filmmaker Chris Marker,
who reportedly* died on that date at 91 at his home in Paris.

See Slides and Chantingand Where Madness Lies.

See also Sherrill Grace on Malcolm Lowry.

Washington PostOther sources say Marker died on July 30.

 These notably occur in Marker's masterpiece
     La Jetée  (review with spoilers).

 

Wednesday, August 1, 2012

Triple Feature

Filed under: Uncategorized — m759 @ 11:11 PM

IMAGE- Triple Feature: 'Twelve Monkeys,' Reagan National Airport on July 31, 2012, and 'Die Hard 2'

For related material, see this morning's post Defining Form.

 

Sunday, August 12, 2012

Doctor Who

Filed under: Uncategorized — m759 @ 2:00 PM

On Robert A. Heinlein's novel Glory Road

"Glory Road  (1963) included the foldbox , a hyperdimensional packing case that was bigger inside than outside. It is unclear if Glory Road  was influenced by the debut of the science fiction television series Doctor Who  on the BBC that same year. In Doctor Who , the main character pilots a time machine called a TARDIS, which is built with technology which makes it 'dimensionally transcendental,' that is, bigger inside than out."

— Todd, Tesseract article at exampleproblems.com

From the same exampleproblems.com article—

"The connection pattern of the tesseract's vertices is the same as that of a 4×4 square array drawn on a torus; each cell (representing a vertex of the tesseract) is adjacent to exactly four other cells. See geometry of the 4×4 square."

For further details, see today's new page on vertex adjacency at finitegeometry.org.

 

"It was a dark and stormy night."— A Wrinkle in Time

Friday, August 31, 2012

Translation

Filed under: Uncategorized — Tags: — m759 @ 6:08 AM

"Translation in the direction
conceptual -> concrete and symbolic
is much easier than
translation in the reverse direction…."

The late William P. Thurston

(See also "Atlas to the Text," Harvard Crimson , March 8, 2011).

Related cinematic imagery

Conceptual  (thanks to Don DeLillo and The New York Times )—

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

Concrete and symbolic (thanks to Amy Adams and Emily Blunt, as well as
Frederick Seidel in the September 3, 2012, New Yorker )

"Biddies still cleaned the student rooms."

IMAGE- Shower wall in 'Sunshine Cleaning'

Tuesday, August 28, 2012

Dark and Stormy

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

It  was a  dark and stormy night.

A Wrinkle in Time  (brought  up to date)

Monday, February 13, 2012

Why Now?

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

From the 2011 film "Hanna"—

Marissa: Why now, Erik? 
Erik: Kids grow up. 

From the 50th Anniversary Edition
(January 31, 2012) of A Wrinkle in Time

(Click to enlarge.)

IMAGE- Charles Wallace and Calvin O'Keefe discuss sports.

Monday, January 30, 2012

Enda’s Game*

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

The following passage by Tolkien was suggested by a copy of next Sunday's New York Times Book Review  that arrived in the mail today. (See Orson Scott Card's remarks on page 26— "Uncle Orson"— and the Review 's concluding essay "Grand Allusion.")

"Lastly, tengwesta  [system or code of signs] has also become an impediment. It is in Incarnates clearer and more precise than their direct reception of thought. By it also they can communicate easily with others, when no strength is added to their thought: as, for example, when strangers first meet. And, as we have seen, the use of 'language' soon becomes habitual, so that the practice of ósanwe  (interchange of thought) is neglected and becomes more difficult. Thus we see that the Incarnate tend more and more to use or to endeavour to use ósanwe  only in great need and urgency, and especially when lambe  is unavailing. As when the voice cannot be heard, which comes most often because of distance. For distance in itself offers no impediment whatever to ósanwe . But those who by affinity might well use ósanwe  will use lambe  when in proximity, by habit or preference. Yet we may mark also how the 'affine' may more quickly understand the lambe  that they use between them, and indeed all that they would say is not put into words. With fewer words they come swifter to a better understanding. There can be no doubt that here ósanwe  is also often taking place; for the will to converse in lambe  is a will to communicate thought, and lays the minds open. It may be, of course, that the two that converse know already part of the matter and the thought of the other upon it, so that only allusions dark to the stranger need be made; but this is not always so. The affine** will reach an understanding more swiftly than strangers upon matters that neither have before discussed, and they will more quickly perceive the import of words that, however numerous, well-chosen, and precise, must remain inadequate."

* "If a poem catches a student's interest at all, he or she should damned well be able to look up an unfamiliar word in the dictionary…."

   — Elizabeth Bishop, quoted in the essay "Grand Allusion" mentioned above. For a brief dictionary of most of the unfamiliar words in this post's title and in the above passage, see Vinyar Tengwar  39 (July 1998). This is copyrighted but freely available on the Web.

** The word "affine" has connotations not intended by Tolkien. See that word in this journal. See also page 5 of next Sunday's Times Book Review , which contains a full-page ad for the 50th anniversary edition of A Wrinkle in Time . "There is  such a thing as a tesseract."

Thursday, November 3, 2011

Ockham’s Bubbles–

Filed under: Uncategorized — m759 @ 10:30 AM

Mathematics and Narrative, continued

"… a vision invisible, even ineffable, as ineffable as the Angels and the Universal Souls"

— Tom Wolfe, The Painted Word , 1975, quoted here on October 30th

"… our laughable abstractions, our wryly ironic po-mo angels dancing on the heads of so many mis-imagined quantum pins."

— Dan Conover on September 1st, 2011

"Recently I happened to be talking to a prominent California geologist, and she told me: 'When I first went into geology, we all thought that in science you create a solid layer of findings, through experiment and careful investigation, and then you add a second layer, like a second layer of bricks, all very carefully, and so on. Occasionally some adventurous scientist stacks the bricks up in towers, and these towers turn out to be insubstantial and they get torn down, and you proceed again with the careful layers. But we now realize that the very first layers aren't even resting on solid ground. They are balanced on bubbles, on concepts that are full of air, and those bubbles are being burst today, one after the other.'

I suddenly had a picture of the entire astonishing edifice collapsing and modern man plunging headlong back into the primordial ooze. He's floundering, sloshing about, gulping for air, frantically treading ooze, when he feels something huge and smooth swim beneath him and boost him up, like some almighty dolphin. He can't see it, but he's much impressed. He names it God."

— Tom Wolfe, "Sorry, but Your Soul Just Died," Forbes , 1996

"… Ockham's idea implies that we probably have the ability to do something now such that if we were to do it, then the past would have been different…"

Stanford Encyclopedia of Philosophy

"Today is February 28, 2008, and we are privileged to begin a conversation with Mr. Tom Wolfe."

— Interviewer for the National Association of Scholars

From that conversation—

Wolfe : "People in academia should start insisting on objective scholarship, insisting  on it, relentlessly, driving the point home, ramming it down the gullets of the politically correct, making noise! naming names! citing egregious examples! showing contempt to the brink of brutality!"

As for "mis-imagined quantum pins"…
This 
journal on the date of the above interview— February 28, 2008

http://www.log24.com/log/pix08/080228-Wooters2.jpg

Illustration from a Perimeter Institute talk given on July 20, 2005

The date of Conover's "quantum pins" remark above (together with Ockham's remark above and the above image) suggests a story by  Conover, "The Last Epiphany," and four posts from September 1st, 2011—

BoundaryHow It WorksFor Thor's Day,  and The Galois Tesseract.

Those four posts may be viewed as either an exploration or a parody of the boundary between mathematics and narrative.

"There is  such a thing as a tesseract." —A Wrinkle in Time

Sunday, September 11, 2011

First Lady

Filed under: Uncategorized — m759 @ 7:59 AM

Betty Skelton, "the First Lady of Firsts," died on the last day of August.

http://www.log24.com/log/pix11B/110911-NYTobitsSm.jpg

From this  journal on August thirty-first—

"The Tesseract was the jewel of Odin's treasure room."

http://www.log24.com/log/pix11B/110831-JohannSchmidt.jpg

Hugo Weaving also played Agent Smith
in The Matrix Trilogy .

For Cynthia Zarin, biographer of Madeleine L'Engle

"There is  such a thing as a tesseract."
A Wrinkle in Time

Thursday, September 1, 2011

Boundary (continued*)

Filed under: Uncategorized — m759 @ 12:00 AM

It is now midnight. Yesterday was Odin's Day. Today is Thor's Day.

From a weblog post on Captain America and Thor

"While all this [Captain America] is happening an SS officer, Johann Schmidt (Hugo Weaving), has found a religious artefact called the Tesseract which Schmidt describes as 'the jewel of Odin’s treasure room,' linking it in with the Thor storyline."

That's Entertainment  weblog, August 14, 2011

From Wallace Stevens, "An Ordinary Evening in New Haven," Canto III—

The point of vision and desire are the same.
It is to the hero of midnight that we pray
On a hill of stones to make beau mont thereof.

Captain America opened in the United States on Friday, July 22, 2011.

Thor opened in the United States on Friday, May 6, 2011.

"There is  such a thing as a tesseract." —A Wrinkle in Time

* Continued from August 30.

Sunday, February 20, 2011

Sunday Dinner

Filed under: Uncategorized — m759 @ 2:00 PM

Judith Shulevitz at The New York Times
on Sunday, July 18, 2010 —

"What would an organic Christian Sabbath look like today?
For James Carroll, an ex-priest and dissenting Catholic
in Boston (he is the author of Practicing Catholic ,
published in 2009), it would look like the Sunday dinners
of his childhood. These were big formal meals,
held at 2 p.m. every Sunday….

'If Jesus were to visit us, it would have been
the Sunday dinner he would have insisted on
being a part of, not the worship service at the church.'"

Possible Table Topics

Arts & Letters Daily (20 Feb 2011)

Sat Feb 19, 2011 23:00

Nobody likes a grammar scold, but it must be said:
Ambiguity has a death grip on our syntax.
The principles of effective speech are in tatters.
Verbal chaos reigns… more

How did the armies of Mordor cope with defeat?
A retelling of The Lord of the Rings
is more complicated and less sentimental
than the original… more

Is philosophy of science an obsolete
pseudo-discipline? Stephen Hawking thinks so.
But his work relies on the very sort of speculations
that philosophers invented… more

Some background for the discussion —

A book said to have received 15,480 reviews—

http://www.log24.com/log/pix11/110220-UserRatings.jpg

Monday, June 21, 2010

Test

Filed under: Uncategorized — Tags: — m759 @ 11:30 PM

From a post by Ivars Peterson, Director
of Publications and Communications at
the Mathematical Association of America,
at 19:19 UTC on June 19, 2010—

Exterior panels and detail of panel,
Michener Gallery at Blanton Museum
in Austin, Texas—

http://www.log24.com/log/pix10A/100621-MichenerGalleryPanel.jpg

Peterson associates the four-diamond figure
with the Pythagorean theorem.

A more relevant association is the
four-diamond view of a tesseract shown here
on June 19 (the same date as Peterson's post)
in the "Imago Creationis" post—

Image-- The Four-Diamond Tesseract

This figure is relevant because of a
tesseract sculpture by Peter Forakis—

http://www.log24.com/log/pix09A/091220-ForakisHypercube.jpg

This sculpture was apparently shown in the above
building— the Blanton Museum's Michener gallery—
as part of the "Reimagining Space" exhibition,
September 28, 2008-January 18, 2009.

The exhibition was organized by
Linda Dalrymple Henderson, Centennial Professor
in Art History at the University of Texas at Austin
and author of The Fourth Dimension and
Non-Euclidean Geometry in Modern Art
(Princeton University Press, 1983;
new ed., MIT Press, 2009).

For the sculptor Forakis in this journal,
see "The Test" (December 20, 2009).

"There is  such a thing
as a tesseract."
A Wrinkle in TIme   

Monday, April 12, 2010

Mathematics and Narrative, continued

Filed under: Uncategorized — m759 @ 8:00 PM

Saturday's post quoted a mathematical narrative with the following opening sentence–

"Let G  be a finite, primitive subgroup of GL(V) = GL(n,D),
where V  is an n-dimensional vector space over the division ring D."

If that narrative were a novel, its opening might win a Bulwer-Lytton prize.

As might the opening of another nonfiction narrative

"What are we are doing?"

A partial answer to this profound metaphysical question
for fans of the classic film "Dark City"
(which was written in part by one "Lem Dobbs")–

Part I — Fiction —

Wednesday August 4, 2004

Filed under: Uncategorized — m759 @ 12:29 AM

Shell Beach

“It was a dark and stormy night….”

– Opening of A Wrinkle in Time, a classic novel by Madeleine L’Engle.

For those who seek religious significance in the name of Hurricane Alex:

Alex Proyas directs this futuristic thriller about a man waking up to find he is wanted for brutal murders he doesn’t remember. Haunted by mysterious beings who stop time and alter reality, he seeks to unravel the riddle of his identity.”

– Description of the 1998 film Dark City

[See also June 14, 2005.]


Part II — Nonfiction —

http://www.log24.com/log/pix10/100412-ShellBeachInn.jpg

http://www.shellbeachinn.com/

Part III — Fiction —

"The bench on which Dobbs was sitting
was not so good."

— B. Traven, opening sentence
of The Treasure of the Sierra Madre

Monday, February 1, 2010

Frame by Frame

Filed under: Uncategorized — m759 @ 7:26 PM

From "Time's Breakdown," September 17, 2003

“… even if we can break down time into component Walsh functions, what would it achieve?”

– The Professor, in “Passing in Silence,” by Oliver Humpage

“Being is not a steady state but an occulting one: we are all of us a succession of stillness blurring into motion on the wheel of action, and it is in those spaces of black between the pictures that we find the heart of mystery in which we are never allowed to rest. The flickering of a film interrupts the intolerable continuity of apparent world; subliminally it gives us those in-between spaces of black that we crave.”

Gösta Kraken, Perception Perceived: an Unfinished Memoir (p. 9 in Fremder, a novel by Russell Hoban)

This flashback was suggested by

  1. A review in next Sunday's New York Times Book Review of a new novel, Point Omega, by Don DeLillo. The review's title (for which the reviewer, Geoff Dyer, should not be blamed) is "A Wrinkle in Time." The review and the book are indeed concerned with time, but the only apparent connection to the 1962 novel of Madeleine L'Engle also titled A Wrinkle in Time is rather indirect– via the Walsh functions mentioned above.
  2. A phrase in the Times's review, "frame by frame," also appeared in this jounal on Saturday. It formed part of the title of a current exhibition at Harvard's Carpenter Center for the Visual Arts.
  3. The Carpenter Center exhibition will have an opening reception on February 4.
  4. February 4 is also the birthday of the above Russell Hoban, who will turn 85. See a British web page devoted to that event.

DeLillo is a major novelist, but the work of Hoban seems more relevant to the phrase "frame by frame."

Sunday, December 20, 2009

The Test

Filed under: Uncategorized — m759 @ 11:00 AM

Dies Natalis of
Emil Artin

From the September 1953 Bulletin of the American Mathematical Society

Emil Artin, in a review of Éléments de mathématique, by N. Bourbaki, Book II, Algebra, Chaps. I-VII–

"We all believe that mathematics is an art. The author of a book, the lecturer in a classroom tries to convey the structural beauty of mathematics to his readers, to his listeners. In this attempt he must always fail. Mathematics is logical to be sure; each conclusion is drawn from previously derived statements. Yet the whole of it, the real piece of art, is not linear; worse than that its perception should be instantaneous. We all have experienced on some rare occasions the feeling of elation in realizing that we have enabled our listeners to see at a moment's glance the whole architecture and all its ramifications. How can this be achieved? Clinging stubbornly to the logical sequence inhibits the visualization of the whole, and yet this logical structure must predominate or chaos would result."

Art Versus Chaos

http://www.log24.com/log/pix09A/091220-ForakisHypercube.jpg
From an exhibit,
"Reimagining Space
"

The above tesseract (4-D hypercube)
sculpted in 1967 by Peter Forakis
provides an example of what Artin
called "the visualization of the whole."

For related mathematical details see
Diamond Theory in 1937.

"'The test?' I faltered, staring at the thing.
'Yes, to determine whether you can live
in the fourth dimension or only die in it.'"
Fritz Leiber, 1959

See also the Log24 entry for
Nov. 26,  2009, the date that
Forakis died.

"There is such a thing
as a tesseract."
Madeleine L'Engle, 1962

Monday, September 21, 2009

Monday September 21, 2009

Filed under: Uncategorized — Tags: , , — m759 @ 2:56 AM
Keys

A Google search for "Das Scheinen," a very rough translation into Heidegger's German of "The Shining," leads to a song. A search for the English version of the song leads to a site with a sidebar advertising Pearl Jam's new (Sept. 20) album "Backspacer."
 

Packaging:

Pearl Jam 'Backspacer' album released Sept. 20, 2009

Happy birthday,
 Stephen King.

Background:

Yesterday's entries
and the plot of
L'Engle's classic
A Wrinkle in Time.
(See this journal's entries
for March 2008.)

The Pearl Jam album cover art
is of particular interest in light
of King's story "Apt Pupil" and
of Katherine Neville's remark
"Nine is a very powerful
Nordic number.
"

Those who prefer more sophisticated
aesthetic theory may click on the
following keys:

Back Space key from manual typewriter, linking to Babich on Music, Nietzsche, and Heidegger
Shift Lock key from manual typewriter, linking to Levin's 'The Philosopher's Gaze'

Saturday, November 29, 2008

Saturday November 29, 2008

Filed under: Uncategorized — m759 @ 1:06 PM
The Messier Brand

Virginia Heffernan on the film version of A Wrinkle in Time:

“… the film is also sad, and soaring. It recalls the hippie days when a perverse, hubristic originality was a quality to be cultivated, not medicated. Told not from an aloof remove– through the eyes of a wise Yoda or Peter Jackson– the movie glitters irregularly, woven through with the sparkling fibers of a righteous child’s tormented imagination. Steven Spielberg also attempted, with the same ambiguous but moving results, this messier brand of science fiction in ‘A.I.'”

Log24 on
 Jan. 21, 2007:

California Dreamin’, Part II

Spielberg, A.I., and Robot Wisdom

Related material:

An entry of
Dec. 29, 2006,
and entries of
Jan. 20, 2007.

See also today’s
 previous entries.

Happy birthday,
Denny Doherty.

Saturday November 29, 2008

Filed under: Uncategorized — m759 @ 11:29 AM
An Astrophysicist
Goes Missing,
And His Children
Search the Stars

Related material:

Happy birthday, C. S. Lewis.

Monday, May 5, 2008

Monday May 5, 2008

Filed under: Uncategorized — Tags: , — m759 @ 11:07 AM
Lottery Sermon

"And take upon's
the mystery of things
 as if we were God's spies"
King Lear  

PA Lottery Sunday, May 4, 2008: mid-day 170, evening 144

From Log24 on Aug. 19, 2003
and on Ash Wednesday, 2004:
a reviewer on
An Instance of the Fingerpost::

"Perhaps we are meant to
see the story as a cubist
   retelling of the crucifixion."

From Log24 on
Michaelmas 2007:

Kate Beckinsale (in 'Pearl Harbor') pointing to an instance of the number 144

Google searches suggested by
Sunday's PA lottery numbers
(mid-day 170, evening 144)
and by the above
figure of Kate Beckinsale
pointing to an instance of
the number 144 —

Click to enlarge:

Search for the meaning of 170 and 144, the PA lottery numbers of Sunday, May 4, 2008

Related material:

Beckinsale in another film
(See At the Crossroads,
Log24, Dec. 8, 2006):

"For every kind of vampire,
there is a kind of cross."
Gravity's Rainbow  
 
Kate Beckinsale in Underworld: Evolution

 

Kate Beckinsale, adapted from
poster for Underworld: Evolution
(DVD release date 6/6/6)
 
There is such a thing
as a tesseract.

"It was only in retrospect
that the silliness
became profound."

— Review of  
Faust in Copenhagen

From the conclusion of
Joan Didion's 1970 novel
  Play It As It Lays

Cover of 'Play It As It Lays'

"I know what 'nothing' means,
and keep on playing."

From Play It As It Lays,
the paperback edition of 1990
  (Farrar, Straus and Giroux) —

Page 170:

"By the end of a week she was thinking constantly
about where her body stopped and the air began,
about the exact point in space and time that was the
difference between Maria and other. She had the sense
that if she could get that in her mind and hold it for

170  

even one micro-second she would have what she had
come to get."

"The page numbers
are generally reliable."

Michaelmas 2007   

Wednesday, March 5, 2008

Wednesday March 5, 2008

Filed under: Uncategorized — m759 @ 1:09 PM
(Context: March 2-4)

For CENTRAL
Central Intelligence:

“God does not play dice.”
— Paraphrase of a remark
by Albert Einstein

Another Nobel Prize winner,
Isaac Bashevis Singer

“a God who speaks in deeds,
not in words, and whose
vocabulary is the Cosmos”

From “The Escapist:
The Reality of Fantasy Games
“–

Platonic solids as Dungeons & Dragons dice
Dungeons & Dragons Dice

From today’s New York Times:

NY Times obituaries online, March 5, 2008: Gary Gygax, Wm. F. Buckley, Kaddish ad by Hadassah

A Kaddish for Gygax:


“I was reading Durant’s section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)”


Related material:

For more on the word
“phantasmagoria,” see
Log24 on Dec. 12, 2004
and on Sept. 23, 2006.

For phantasmagoria in action,
see Dungeons & Dragons
and Singer’s (and others’)
Jewish fiction.

For non-phantasmagoria,
see (for instance) the Elements
of Euclid, which culminates
in the construction of the
Platonic solids illustrated above.

See also Geometry for Jews.

Monday, March 3, 2008

Monday March 3, 2008

Filed under: Uncategorized — Tags: — m759 @ 11:09 AM
CENTRAL Central Intelligence
 
A Wrinkle in Time:

"Holding hands, they crossed the square. The huge CENTRAL Central Intelligence Building had only one door, but it was an enormous one, at least two stories high and wider than a room, made of a dull, bronzelike material.

'Do we just knock?' Meg giggled."

Tom Raum story on Obama vs. Clinton with associated Miami Herald CIA ad

Detail:

Detail of Tom Raum Obama-Clinton story and associated Miami Herald CIA ad

"Do we just knock?"

"Click PLAY."
_______________________

Related material:

Der Einsatz

 

Friday, September 7, 2007

Friday September 7, 2007

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

The New York Times online,
Friday, Sept. 7, 2007:

Madeleine L’Engle,
Children’s Writer,
Is Dead

"Madeleine L’Engle, who in writing more than 60 books, including childhood fables, religious meditations and science fiction, weaved emotional tapestries transcending genre and generation, died Thursday [Sept. 6, 2007] in Connecticut. She was 88.

Her death, of natural causes, was announced today by her publisher, Farrar, Straus and Giroux."

More >>

Related material:

Log24 entries of
August 31

"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"

— and of 
September 2
(with update of
 September 5)–

"There is such a thing
as a tesseract."
A Wrinkle in Time  

Sunday, September 2, 2007

Sunday September 2, 2007

Filed under: Uncategorized — Tags: — m759 @ 5:11 PM

Comment at the
n-Category Cafe

Re: This Week’s Finds in Mathematical Physics (Week 251)

On Spekkens’ toy system and finite geometry

Background–

  • In “Week 251” (May 5, 2007), John wrote:
    “Since Spekkens’ toy system resembles a qubit, he calls it a “toy bit”. He goes on to study systems of several toy bits – and the charming combinatorial geometry I just described gets even more interesting. Alas, I don’t really understand it well: I feel there must be some mathematically elegant way to describe it all, but I don’t know what it is…. All this is fascinating. It would be nice to find the mathematical structure that underlies this toy theory, much as the category of Hilbert spaces underlies honest quantum mechanics.”
  • In the n-Category Cafe ( May 12, 2007, 12:26 AM, ) Matt Leifer wrote:
    “It’s crucial to Spekkens’ constructions, and particularly to the analog of superposition, that the state-space is discrete. Finding a good mathematical formalism for his theory (I suspect finite fields may be the way to go) and placing it within a comprehensive framework for generalized theories would be very interesting.”
  • In the n-category Cafe ( May 12, 2007, 6:25 AM) John Baez wrote:
    “Spekkens and I spent an afternoon trying to think about his theory as quantum mechanics over some finite field, but failed — we almost came close to proving it couldnt’ work.”

On finite geometry:

The actions of permutations on a 4 × 4 square in Spekkens’ paper (quant-ph/0401052), and Leifer’s suggestion of the need for a “generalized framework,” suggest that finite geometry might supply such a framework. The geometry in the webpage John cited is that of the affine 4-space over the two-element field.

Related material:

Update of
Sept. 5, 2007

See also arXiv:0707.0074v1 [quant-ph], June 30, 2007:

A fully epistemic model for a local hidden variable emulation of quantum dynamics,

by Michael Skotiniotis, Aidan Roy, and Barry C. Sanders, Institute for Quantum Information Science, University of Calgary. Abstract: "In this article we consider an augmentation of Spekkens’ toy model for the epistemic view of quantum states [1]…."
 

Skotiniotis et al. note that the group actions on the 4×4 square described in Spekkens' paper [1] may be viewed (as in Geometry of the 4×4 Square and Geometry of Logic) in the context of a hypercube, or tesseract, a structure in which adjacency is isomorphic to adjacency in the 4 × 4 square (on a torus).

Hypercube from the Skotiniotis paper:

Hypercube

Reference:

[1] Robert W. Spekkens, Phys. Rev. A 75, 032110 (2007),

Evidence for the epistemic view of quantum states: A toy theory
,

Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada N2L 2Y5 (Received 11 October 2005; revised 2 November 2006; published 19 March 2007.)

"There is such a thing
as a tesseract."
A Wrinkle in Time  
 

Friday, August 31, 2007

Friday August 31, 2007

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

"…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:


To Measure the Changes
,

Serious Numbers,

and…

 
The image “http://www.log24.com/log/pix06A/061017-Gump2A.jpg” cannot be displayed, because it contains errors.

Balls of Fury
 

Tuesday, August 21, 2007

Tuesday August 21, 2007

Filed under: Uncategorized — Tags: — m759 @ 8:14 AM
In the Details

I Ching hexagram 14, box style

Symbol from the
box-style I Ching

Related material:
The five Log24 entries
ending on August 1

Lou Beach, Science and Magic, New York Times 8/21/07

Illustration by Lou Beach
in today's New York Times
article on science and magic

Related material:
A Wrinkle in Time 

Monday, May 21, 2007

Monday May 21, 2007

Filed under: Uncategorized — Tags: — m759 @ 4:00 PM
No Royal Roads
Illustration from a
1980 article at JSTOR:

Coxeter as King of Geometry

A more recent royal reference:

"'Yau wants to be the king of geometry,' Michael Anderson, a geometer at Stony Brook, said. 'He believes that everything should issue from him, that he should have oversight. He doesn't like people encroaching on his territory.'" –Sylvia Nasar and David Gruber in The New Yorker, issue dated Aug. 28, 2006

Wikipedia, Cultural references to the Royal Road:

"Euclid is said to have replied to King Ptolemy's request for an easier way of learning mathematics that 'there is no royal road to geometry.' Charles S. Peirce, in his 'How to Make Our Ideas Clear' (1878), says 'There is no royal road to logic, and really valuable ideas can only be had at the price of close attention.'"

Related material:

Day Without Logic
(March 8, 2007)

and
The Geometry of Logic
(March 10, 2007)
:

The image “http://www.log24.com/log/pix07/070521-Tesseract.gif” cannot be displayed, because it contains errors.

There may be
no royal roads to
geometry or logic,
but…

"There is such a thing
as a tesseract."
— Madeleine L'Engle, 
A Wrinkle in Time

Monday, May 14, 2007

Monday May 14, 2007

Filed under: Uncategorized — Tags: — m759 @ 3:09 AM

Crossing Point

From Log24's
"Footprints for Baudrillard"–

"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?

— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"

"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time,
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,

"The Tesseract"

From Log24's
Xanga footprints,
3:00 AM today:

 

Texas /431103703/item.html 5/14/2007 3:00 AM

The link leads to a Jan. 23, 2006 entry
on what one philosopher has claimed is
"exactly that crossing point
of constraint and freedom
which is the very essence
of man's nature."

Thursday, May 3, 2007

Thursday May 3, 2007

Filed under: Uncategorized — Tags: — m759 @ 3:00 PM
A Web
of Links

"Some postmodern theorists like to talk about the relationship between 'intertextuality' and 'hypertextuality'; intertextuality makes each text a 'mosaic of quotations' [Kristeva, Desire in Language, Columbia U. Pr., 1980, 66] and part of a larger mosaic of texts, just as each hypertext can be a web of links and part of the whole World-Wide Web." —Wikipedia
 

The image “http://www.log24.com/log/pix07/070503-Tiffany.jpg” cannot be displayed, because it contains errors.

Related material

Day Without Logic,
Introduction to Logic,
The Geometry of Logic,
Structure and Logic,
Spider-Man and Fan:

The image “http://www.log24.com/log/pix07/070503-Devillers.jpg” cannot be displayed, because it contains errors.

"There is such a thing
as a tesseract."
A Wrinkle in Time  
 

Friday, April 20, 2007

Friday April 20, 2007

Filed under: Uncategorized — Tags: — m759 @ 10:31 PM
Speech

In Grand Rapids today

"… Bush spoke and answered audience questions for nearly 90 minutes inside East Grand Rapids High School in suburban Grand Rapids….

After leaving the school, Bush's motorcade stopped at the Gerald R. Ford Presidential Museum in downtown Grand Rapids, where he stood silently for a few moments after placing a bouquet of white roses at Ford's burial site on the museum grounds. The 38th president, who grew up in Grand Rapids, died Dec. 26 at age 93."

Multispeech

Mich. Lottery Apr. 20, 2007: Day 019, Night 001

 

For the meaning of the lottery icons
above, see this morning's entry and
an entry that it links to —
Time's Labyrinth continued
of March 8, 2007.

For the meaning of multispeech,
see the entries of
All Hallows' Eve, 2005:

Tesseract on the cover of The Gameplayers of Zan
 
"There is such a thing
as a tesseract."
A Wrinkle in Time 
 

Tuesday, April 3, 2007

Tuesday April 3, 2007

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

Mathematics Awareness Month

 
Related material:

"But what is it?"
Calvin demanded.
"We know that it's evil,
but what is it?"

"Yyouu hhave ssaidd itt!"
Mrs. Which's voice rang out.
"Itt iss Eevill. Itt iss thee
Ppowers of Ddarrkknesss!"

A Wrinkle in Time

AMS Notices cover, April 2007

"After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called 'It' because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil."

See also
"Darkness Visible"
in ART WARS.
 
"When all is said and done,
science is about things and
theology is about words."
— Freeman Dyson,
New York Review of Books,
issue dated May 28, 1998

"Does the word 'tesseract'
mean anything to you?"
 

Monday, March 19, 2007

Monday March 19, 2007

Filed under: Uncategorized — Tags: — m759 @ 10:31 AM
The Naked Brain

The cover (pdf) of the Notices of the American Mathematical Society for April 2007 (Mathematics Awareness Month) features a naked disembodied brain (Log24, March 16), courtesy of researchers at the Catholic University of Louvain.
 

Related material:

 

Log24, Jan. 26

"… at last she realized
what the Thing on the dais was.
IT was a brain.
A disembodied brain…."
 
A Wrinkle in Time, by Madeleine L'Engle
"There could not be an objective test
that distinguished a clever robot
from a really conscious person."
 
— Daniel Dennett in TIME magazine,
Daniel Dennett in his office

Daniel Dennett, Professor of Philosophy
and Director of the
Center for Cognitive Studies
at Tufts University,
in his office on campus.
(Boston Globe, Jan. 29, 2006.
Photo © Rick Friedman.)

 

Related recommended
reading and viewing:

Tom Wolfe's essay
"Sorry, But Your Soul Just Died,"
and a video of an interview
 with Wolfe.
 

Friday, March 16, 2007

Friday March 16, 2007

Filed under: Uncategorized — Tags: — m759 @ 10:48 AM
"Geometry,
 Theology,
 and Politics:

 
Context and Consequences of 

the Hobbes-Wallis Dispute"
(pdf)

 

by Douglas M. Jesseph
Dept. of Philosophy and Religion
North Carolina State University

Excerpt:

"We are left to conclude that there was something significant in Hobbes's philosophy that motivated Wallis to engage in the lengthy and vitriolic denunciation of all things Hobbesian.

In point of fact, Wallis made no great secret of his motivations for attacking Hobbes's geometry, and the presence of theological and political motives is well attested in a 1659 letter to Huygens. He wrote:

But regarding the very harsh diatribe against Hobbes, the necessity of the case, and not my manners, led to it. For you see, as I believe, from other of my writings how peacefully I can differ with others and bear those with whom I differ. But this was provoked by our Leviathan (as can be easily gathered fro his other writings, principally those in English), when he attacks with all his might and destroys our universities (and not only ours, but all, both old and new), and especially the clergy and all institutions and all religion. As if the Christian world knew nothing sound or nothing that was not ridiculous in philosophy or religion; and as if it has not understood religion because it does not understand philosophy, nor philosophy because it does not understand mathematics. And so it seemed necessary that now some mathematician, proceeding in the opposite direction, should show how little he understand this mathematics (from which he takes his courage). Nor should we be deterred from this by his arrogance, which we know will vomit poison and filth against us. (Wallis to Huygens, 11 January, 1659; Huygens 1888-1950,* 2: 296-7)

The threats that Hobbes supposedly posed to the universities, the clergy, and all religion are a consequence of his political and theological doctrines. Hobbes's political theory requires that the power of the civil sovereign be absolute and undivided. As a consequence, such institutions as universities and the clergy must submit to the dictates of the sovereign in all matters. This extends, ironically enough, to geometry, since Hobbes notoriously claimed that the sovereign could ban the teaching of the subject and order 'the burning of all books of Geometry' if he should judge geometric principles 'a thing contrary to [his] right of dominion, or to the interest of men that have dominion' (Leviathan (1651) 1.11, 50; English Works** 3: 91). In the area of church government, Hobbes's doctrines are a decisive rejection of the claims of Presbyterianism, which holds that questions of theological doctrine is [sic] to be decided by the elders of the church– the presbytery– without reference to the claims of the sovereign. As a Presbyterian minister, a doctor of divinity, and professor of geometry at Oxford, Wallis found abundant reason to reject this political theory."

* Huygens, Christiaan. 1888-1950. Les oeuvres complètes de Chrisiaan Huygens. Ed. La Société Hollandaise des Sciences. 22 vols. The Hague: Martinus Nijhoff.

** Hobbes, Thomas. [1839-45] 1966. The English Works of Thomas Hobbes of Malmesbury, now First Collected and Edited by Sir William Molesworth. Edited by William Molesworth. 11 vols. Reprint. Aalen, Germany: Scientia Verlag.

 

Related material:

"But what is it?"
Calvin demanded.
"We know that it's evil,
but what is it?"

"Yyouu hhave ssaidd itt!"
Mrs. Which's voice rang out.
"Itt iss Eevill. Itt iss thee
Ppowers of Ddarrkknesss!"

A Wrinkle in Time

The image “http://www.log24.com/log/pix07/070316-AMScover.jpg” cannot be displayed, because it contains errors.

"After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called 'It' because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil."

 

See also
"Darkness Visible"
in ART WARS.
 

Saturday, March 10, 2007

Saturday March 10, 2007

Filed under: Uncategorized — m759 @ 2:00 AM
Tesseract

A new page at finitegeometry.org,
The Geometry of Logic,
includes the following figure:

The 16 binary connectives arranged in a tesseract

There is such a thing
as a tesseract.

— Madeleine L’Engle
 

Wednesday, March 7, 2007

Wednesday March 7, 2007

Filed under: Uncategorized — Tags: — m759 @ 8:35 AM
Footprints for
Baudrillard

The image “http://www.log24.com/log/pix07/070307-Baudrillard.jpg” cannot be displayed, because it contains errors.

"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?

 

— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"

 

"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time,
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,
"The Tesseract"

In memory of the French philosopher Jean Baudrillard, who died yesterday, Tuesday, March 6, 2007. 

The following Xanga footprints may be regarded as illustrating Log24 remarks of Dec. 10, 2006 on the Library of Congress, geometry, and bullshit, as well as remarks of Aug. 28, 2006 on the temporal, the eternal, and St. Augustine.

From the District of Columbia–
Xanga footprints in reverse
chronological order from
the noon hour on Tuesday,
March 6, 2007, the date
of Baudrillard's death:

District of Columbia
/499111929/item.html
Beijing String
3/6/2007
12:04 PM
District of Columbia
/497993036/item.html
Spellbound
3/6/2007
12:03 PM
District of Columbia
/443606342/item.html
About God, Life, Death
3/6/2007
12:03 PM
District of Columbia
/494421586/item.html
A Library of Congress Reading
3/6/2007
12:03 PM
District of Columbia
/500434851/item.html
Binary Geometry
3/6/2007
12:03 PM
District of Columbia
/404038913/item.html
Prequel on St. Cecelia's Day
3/6/2007
12:03 PM

Thursday, March 1, 2007

Thursday March 1, 2007

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

Senior Honors

Notes in Memory of
a Father, a Son, and a Holy Ghost

From the obituary in today's New York Times of historian Arthur M. Schlesinger Jr.–

"Mr. Schlesinger, partly through his appreciation of history, fully realized his good fortune. 'I have lived through interesting times and had the luck of knowing some interesting people,' he wrote.

A huge part of his luck was his father, who guided much of his early research, and even suggested the topic for his [Harvard] senior honors: Orestes A. Brownson, a 19th-century journalist, novelist and theologian. It was published by Little, Brown in 1938 as 'Orestes A. Brownson: A Pilgrim's Progress.'"

Douglas Martin

From The Catholic Encyclopedia:

"It is sufficient for true knowledge that it affirm as real that which is truly real."

Article on Ontologism

From The Diamond Theory of Truth:

"Was there really a cherubim waiting at the star-watching rock…?
Was he real?
What is real?

— Madeleine L'Engle, A Wind in the Door, Farrar, Straus and Giroux, 1973, conclusion of Chapter Three, "The Man in the Night"

"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time, Farrar, Straus and Giroux, 1962, conclusion of Chapter Five, "The Tesseract"

Related material: Yesterday's first annual "Tell Your Story Day" at Harvard and yesterday's entry on Euclid.

Saturday, January 27, 2007

Saturday January 27, 2007

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM
Art and the
Holy Spirit

Madeleine L'Engle in The Irrational Season (1977), beginning of Chapter 9 (on Pentecost):

"The Holy Spirit, the third person of the Trinity, is the easiest of this not-at-all-easy concept for me to understand.  Any artist, great or small, knows moments when something more than he takes over, and he moves into a kind of 'overdrive,' where he works as ordinarily he cannot work.  When he is through, there is a sense of exhilaration, exhaustion, and joy.  All our best work comes in this fashion, and it is humbling and exciting.

After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called 'It' because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil."
 

Friday, January 26, 2007

Friday January 26, 2007

Filed under: Uncategorized — Tags: — m759 @ 2:48 PM
 
IT
 
"… at last she realized
what the Thing on the dais was.
IT was a brain.
A disembodied brain…."
 
A Wrinkle in Time, by Madeleine L'Engle

"There could not be an objective test
that distinguished a clever robot
from a really conscious person."

— Daniel Dennett in TIME magazine,
issue dated Mon., Jan. 29, 2007

 

Daniel Dennett in his office

 

Daniel Dennett, Professor of Philosophy
and Director of the
Center for Cognitive Studies
at Tufts University,
in his office on campus.
(Boston Globe, Jan. 29, 2006.
Photo © Rick Friedman.)

Hexagram 39:
Obstruction

I Ching, Hexagram 39

The Judgment

Obstruction. The southwest furthers.
(See Zenna Henderson.) 
The northeast does not further.
 (See Daniel Dennett.)
It furthers one to see the great man.
 (See Alan Turing.)
Perseverance brings good fortune.

"If telepathy is admitted
it will be necessary
to tighten our test up."
 
Alan Turing, 1950
 
Amen.

Friday, December 8, 2006

Friday December 8, 2006

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM
An Instance
of the Fingerpost
The image “http://www.log24.com/log/pix06B/061208-Date.jpg” cannot be displayed, because it contains errors.
 
"CRUCIAL (from Lat. crux, a cross),
that which has the form of a cross…
 From Francis Bacon's expression
instantia crucis (taken, as he says, from
the finger-post or crux at cross-roads)"
 
Encyclopaedia Britannica,
the classic 11th edition (1911)
 
"For every kind of vampire,
there is a kind of cross."
Gravity's Rainbow  
 
The image “http://www.log24.com/log/pix06A/060614-EvolutionBegins2.jpg” cannot be displayed, because it contains errors.

Kate Beckinsale, adapted from
poster for Underworld: Evolution
(DVD release date 6/6/6)

 
There is such a thing
as a tesseract.
A Wrinkle in Time  
 
Related material:
 
The tesseract on the cover of
The Gameplayers of Zan
(All Hallows' Eve, 2005), and
 
A Last Stitch in Time…or
A Map of the Map
of Kierkegaard's World:

"Appropriating the Button-molder's
words to Peer Gynt, he would say,
'We'll meet at the next crossroads…
and then we'll see–
I won't say more.'"

Monday, November 13, 2006

Monday November 13, 2006

Filed under: Uncategorized — m759 @ 8:23 PM
Cognitive Blend:

Casino Royale
and
Time in the Rock

PA lottery Nov. 13, 2006: Mid-day 726, Evening 329
 
In today’s cognitive blend,
the role of Casino Royale
is played by the
Pennsylvania Lottery,
which points to 7/26,
Venus at St. Anne’s
(title of the closing chapter
of That Hideous Strength).

The role of
Time in the Rock
is played by a
Log24 entry of 3/29,
Diamond Theory in 1937.

There is such a thing
as a tesseract.

Tuesday, October 31, 2006

Tuesday October 31, 2006

Filed under: Uncategorized — Tags: , , — m759 @ 11:00 PM
To Announce a Faith

From 7/07, an art review from The New York Times:

Endgame Art?
It's Borrow, Sample and Multiply
in an Exhibition at Bard College

"The show has an endgame, end-time mood….

I would call all these strategies fear of form…. the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.

Fear of form above all means fear of compression– of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

— Roberta Smith

It is doubtful that Smith
 would consider the
following "found" art an
example of originality.

It nevertheless does
"announce a faith."


The image “http://www.log24.com/log/pix06A/061031-PAlottery2.jpg” cannot be displayed, because it contains errors.


"First for yourself"

Today's mid-day
Pennsylvania number:
707

See Log24 on 7/07
and the above review.
 

"Second, perhaps,
for the rest of us"

Today's evening
Pennsylvania number:
384

This number is an
example of what the
reviewer calls "compression"–

"an artistic focus that condenses
 experiences, ideas and feelings
into something
whole, committed
 and visually comprehensible."

"Experiences"

See (for instance)

Joan Didion's writings
(1160 pages, 2.35 pounds)
on "the shifting phantasmagoria
which is our actual experience."

"Ideas"

See Plato.

"Feelings"

See A Wrinkle in Time.

"Whole"

The automorphisms
of the tesseract
form a group
of order 384.

"Committed"

See the discussions of
groups of degree 16 in
R. D. Carmichael's classic
Introduction to the Theory
of Groups of Finite Order
.

"Visually comprehensible"

See "Diamond Theory in 1937,"
an excerpt from which
is shown below.

The image “http://www.log24.com/theory/images/Carmichael440abbrev.gif” cannot be displayed, because it contains errors.

The "faith" announced by
the above lottery numbers
on All Hallows' Eve is
perhaps that of the artist
Madeleine L'Engle:

"There is such a thing
as a tesseract.
"

Friday, May 12, 2006

Friday May 12, 2006

Filed under: Uncategorized — Tags: — m759 @ 3:00 AM
Tesseract

"Does the word 'tesseract'
mean anything to you?"
— Robert A. Heinlein in
The Number of the Beast
(1980)

My reply–

Part I:

The image “http://www.log24.com/log/pix06A/WrinkleInTime1A.jpg” cannot be displayed, because it contains errors.

A Wrinkle in Time, by
Madeleine L'Engle
(first published in 1962)

Part II:

Diamond Theory in 1937
and
Geometry of the 4×4 Square

Part III:

Catholic Schools Sermon

Conclusion:
 

"Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy."

— Charles Williams, Witchcraft, Faber and Faber, London, 1941

Related material:

A New Yorker profile of Madeleine L'Engle from April 2004, which I found tonight online for the first time.  For a related reflection on truth, stories, and values, see Saint's Day.  For a wider context, see the Log24 entries of February 1-15, 2003 and February 1-15, 2006.
 

Wednesday, March 29, 2006

Wednesday March 29, 2006

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

The image “http://www.log24.com/theory/images/Carmichael440.gif” cannot be displayed, because it contains errors.
Note: Carmichael's reference is to
A. Emch, "Triple and multiple systems, their geometric configurations and groups," Trans. Amer. Math. Soc. 31 (1929), 25–42.

"There is such a thing as a tesseract."
A Wrinkle in Time

Sunday, March 26, 2006

Sunday March 26, 2006

Filed under: Uncategorized — m759 @ 2:02 PM
‘Nauts

(continued from
Life of the Party, March 24)

Exhibit A —

From (presumably) a Princeton student
(see Activity, March 24):

The image “http://www.log24.com/log/pix06/060324-Activity.jpg” cannot be displayed, because it contains errors.

Exhibit B —

From today’s Sunday comics:

The image “http://www.log24.com/log/pix06/060326-Blondie2.gif” cannot be displayed, because it contains errors.

Exhibit C —

From a Smith student with the
same name as the Princeton student
(i.e., Dagwood’s “Twisterooni” twin):

The image “http://www.log24.com/log/pix06/060326-Smith.jpg” cannot be displayed, because it contains errors.

Related illustrations
(“Visual Stimuli“) from
the Smith student’s game —

The image “http://www.log24.com/log/pix06/060326-Psychonauts1.jpg” cannot be displayed, because it contains errors.

Literary Exercise:

Continuing the Smith student’s
Psychonauts theme,
compare and contrast
two novels dealing with
similar topics:

A Wrinkle in Time,
by the Christian author
Madeleine L’Engle,
and
Psychoshop,
by the secular authors
Alfred Bester and
Roger Zelazny.

Presumably the Princeton student
would prefer the Christian fantasy,
the Smith student the secular.

Those who prefer reality to fantasy —
not as numerous as one might think —
may examine what both 4×4 arrays
illustrated above have in common:
their structure.

Both Princeton and Smith might benefit
from an application of Plato’s dictum:

The image “http://www.log24.com/theory/images/motto2.jpg” cannot be displayed, because it contains errors.

Friday, December 2, 2005

Friday December 2, 2005

Filed under: Uncategorized — m759 @ 5:55 AM

Proof 101

From a course description:

“This module aims to introduce the student to rigorous university level mathematics….
    Syllabus: The idea of and need for mathematical statements and proofs…. proof by contradiction… proof by induction…. the infinite number of primes….”

In the December Notices of the American Mathematical Society, Brian (E. B.) Davies, a professor of mathematics at King’s College London, questions the consistency of Peano Arithmetic (PA), which has the following axioms:

From BookRags.com

Axiom 1. 0 is a number.

Axiom 2. The successor of any number is a number.

Axiom 3. If a and b are numbers and if their successors are equal, then a and b are equal.

Axiom 4. 0 is not the successor of any number.

Axiom 5. If S is a set of numbers containing 0 and if the successor of any number in S is also in S, then S contains all the numbers.

It should be noted that the word “number” as used in the Peano axioms means “non-negative integer.”  The fifth axiom deserves special comment.  It is the first formal statement of what we now call the “induction axiom” or “the principle of mathematical induction.”

Peano’s fifth axiom particularly troubles Davies, who writes elsewhere:

I contend that our understanding of number should be placed in an historical context, and that the number system is a human invention.  Elementary arithmetic enables one to determine the number of primes less than twenty as certainly as anything we know.  On the other hand Peano arithmetic is a formal system, and its internal consistency is not provable, except within set-theoretic contexts which essentially already assume it, in which case their consistency is also not provable.  The proof that there exists an infinite number of primes does not depend upon counting, but upon the law of induction, which is an abstraction from our everyday experience…. 
… Geometry was a well developed mathematical discipline based upon explicit axioms over one and a half millennia before the law of induction was first formulated.  Even today many university students who have been taught the principle of induction prefer to avoid its use, because they do not feel that it is as natural or as certain as a purely algebraic or geometric proof, if they can find one.  The feelings of university students may not settle questions about what is truly fundamental, but they do give some insight into our native intuitions.

E. B. Davies in
   “Counting in the real world,”
    March 2003 (word format),
    To appear in revised form in
    Brit. J. Phil. Sci. as
   “Some remarks on
    the foundations
    of quantum mechanics”

Exercise:

Discuss Davies’s claim that

The proof that there exists an infinite number of primes does not depend upon counting, but upon the law of induction.

Cite the following passage in your discussion.

It will be clear by now that, if we are to have any chance of making progress, I must produce examples of “real” mathematical theorems, theorems which every mathematician will admit to be first-rate. 

… I can hardly do better than go back to the Greeks.  I will state and prove two of the famous theorems of Greek mathematics.  They are “simple” theorems, simple both in idea and in execution, but there is no doubt at all about their being theorems of the highest class.  Each is as fresh and significant as when it was discovered– two thousand years have not written a wrinkle on either of them.  Finally, both the statements and the proofs can be mastered in an hour by any intelligent reader, however slender his mathematical equipment.

I. The first is Euclid’s proof of the existence of an infinity of prime numbers.

The prime numbers or primes are the numbers

   (A)   2, 3, 5, 7, 11, 13, 17, 19, 23, 29, … 

which cannot be resolved into smaller factors.  Thus 37 and 317 are prime.  The primes are the material out of which all numbers are built up by multiplication: thus

    666 = 2 . 3 . 3 . 37. 

Every number which is not prime itself is divisible by at least one prime (usually, of course, by several).   We have to prove that there are infinitely many primes, i.e. that the series (A) never comes to an end.

Let us suppose that it does, and that

   2, 3, 5, . . . , P
 
is the complete series (so that P is the largest prime); and let us, on this hypothesis, consider the number

   Q = (2 . 3 . 5 . . . . . P) + 1.

It is plain that Q is not divisible by any of

   2, 3, 5, …, P;

for it leaves the remainder 1 when divided by any one of these numbers.  But, if not itself prime, it is divisible by some prime, and therefore there is a prime (which may be Q itself) greater than any of them.   This contradicts our hypothesis, that there is no prime greater than P; and therefore this hypothesis is false.

The proof is by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons.  It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

— G. H. Hardy,
   A Mathematician’s Apology,
   quoted in the online guide for
   Clear and Simple as the Truth:
   Writing Classic Prose, by
   Francis-Noël Thomas
   and Mark Turner,
   Princeton University Press

In discussing Davies’s claim that the above proof is by induction, you may want to refer to Davies’s statement that

Geometry was a well developed mathematical discipline based upon explicit axioms over one and a half millennia before the law of induction was first formulated

and to Hardy’s statement that the above proof is due to Euclid.

Saturday, June 11, 2005

Saturday June 11, 2005

Filed under: Uncategorized — Tags: — m759 @ 2:25 PM

Evil

Some academics may feel that a denunciation of an essay by one of their fellow academics as "evil" (see this morning's entry The Last Word) goes too far.

Here is a followup to that entry.

From the Riviera Presbyterian Church, a sermon quoting Madeleine L’Engle's classic A Wrinkle in Time:
 

For a moment there was the darkness of space, then another planet. The outlines of this planet were not clean and clear. It seemed to be covered with a smoky haze. Through the haze Meg thought she could make out the familiar outlines of continents like pictures in her Social Studies books. "Is it because of our atmosphere that we can't see properly?" she asked anxiously. "No, Meg, yyou know thattt itt iss nnott tthee attmosspheeere," Mrs. Which said. "Yyou mmusstt bee brrave."

"It's the Thing!" Charles Wallace cried. "It's the Dark Thing we saw… when we were riding on Mrs. Whatsit's back!" "Did it just come?" Meg asked in agony, unable to take her eyes from the sickness of the shadow which darkened the beauty of the earth. Mrs. Whatsit sighed. "No, Meg. It hasn't just come. It has been there for a great many years. That is why your planet is such a troubled one." "I hate it!" Charles Wallace cried passionately. "I hate the Dark Thing!" Mrs. Whatsit nodded. "Yes, Charles dear. We all do." "But what is it?" Calvin demanded. "We know that it's evil, but what is it?" "Yyouu hhave ssaidd itt!" Mrs. Which's voice rang out. "Itt iss Eevill. Itt iss thee Ppowers of Ddarrkknessss!" "But what's going to happen?" Meg's voice trembled. "Oh, please, Mrs. Which, tell us what's going to happen!" "We will continue tto ffight!" Something in Mrs. Which's voice made all three of the children stand straighter, throwing back their shoulders with determination, looking at the glimmer that was Mrs. Which with pride and confidence. "And we're not alone, you know, children," came Mrs. Whatsit, the comforter. "All through the universe it's being fought, all through the cosmos… and some of our very best fighters have come right from your own planet, and it's a little planet, dears, out on the edge of a little galaxy." 

"Who have some of our fighters been?" Calvin asked. "Oh, you must know them dear," Mrs. Whatsit said. Mrs. Who's spectacles shone out at them triumphantly, "And the light shineth in darkness, and the darkness comprehended it not." "Jesus!" Charles Wallace said. "Why, of course, Jesus!" "Go on, Charles, love. There were others. All your great artists. They've been lights for us to see by." "Leonardo da Vinci?" Calvin suggested tentatively. "And Michelangelo?" "And Shakespeare," Charles Wallace called out, "and Bach! And Pasteur and Madame Curie and Einstein!" Now Calvin's voice rang with confidence. "And Schweitzer and Gandhi and Buddha and Beethoven and Rembrandt and St. Francis!" "Watch!" the Medium told them. The earth with its fearful covering of dark shadow swam out of view and they moved rapidly through the Milky Way. And there was the Thing again. Suddenly there was a great burst of light through the Darkness. The light spread out and where it touched the Darkness the Darkness disappeared. The light spread until the patch of Dark Thing had vanished, and there was only a gentle shining, and through the shining came the stars, clear and pure. No shadows. No fear. Only the stars and the clear darkness of space, quite different from the fearful darkness of the Thing. "You see!" the Medium cried, smiling happily. "It can be overcome! It is being overcome all the time!"

And it is. Lift up your hearts, lift up your heads, catch the ball, practice Advent, see in the dark. You are a city set on a hill, whose light cannot be hid. said Jesus, and he believed it.

 

Amen.

Wednesday, August 4, 2004

Wednesday August 4, 2004

Filed under: Uncategorized — m759 @ 12:29 AM

Shell Beach

“It was a dark and stormy night….”

— Opening of A Wrinkle in Time, a classic novel by Madeleine L’Engle.

For those who seek religious significance in the name of Hurricane Alex:

Alex Proyas directs this futuristic thriller about a man waking up to find he is wanted for brutal murders he doesn’t remember. Haunted by mysterious beings who stop time and alter reality, he seeks to unravel the riddle of his identity.”

— Description of the 1998 film Dark City

See also ART WARS of June 19, 2002.

Wednesday, March 31, 2004

Wednesday March 31, 2004

Filed under: Uncategorized — Tags: — m759 @ 3:33 PM

Presbyterian Poets Society

The Wrinkle in Time link in my previous entry led to a sermon for St. Andrew’s day, 2003, at the Riviera Presbyterian Church in Miami.

I belong to no church, but have a vague recollection of being confirmed in the Presbyterian church in early adolescence.  That ceremony meant nothing to me then, and means nothing to me now.  It was the culmination of fitful attendance at Presbyterian Sunday School, which I recall, reluctantly, only as a course of training in ugliness, lies, and stupidity.

There seems, however, to be a paradox here.  The same religion I so detested seems to have inspired in others works of beauty, truth, and intelligence.

To wit, three poets, each with a Presbyterian background:

Robinson Jeffers

Wallace Stevens

Marianne Moore.

It may be that I am becoming reconciled to the religion that was urged upon me in my youth… becoming, at last, a Riviera Presbyterian.

For more details,
click on the above picture.

Wednesday March 31, 2004

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

Literary Archaeology

“Mrs. Who’s spectacles shone out
at them triumphantly,
‘And the light shineth in darkness;
and the darkness
comprehended it not.’ ”
A Wrinkle in Time

See, too,

Shining Forth and

 The Shining of May 29.

Friday, March 19, 2004

Friday March 19, 2004

Filed under: Uncategorized — m759 @ 2:35 PM

Geometry of the 4×4 Square:

http://log24.com/theory/geometry.html

“There is such a thing as a tesseract.”
A Wrinkle in Time

Friday, October 10, 2003

Friday October 10, 2003

Filed under: Uncategorized — m759 @ 4:44 PM

Storyline

To hear a story, or to read it straight through from start to finish, is to travel along a one-dimensional line.  A well-structured story has, however, more than one dimension.

Juxtaposing scenes shows that details that seem to be far apart in the telling (or the living) of a story may in fact be closely related.

Here is an example from the film “Contact,” in which a young girl’s drawing and a vision of paradise are no longer separated by the time it takes to tell (or live) the story:

(See my entry of Michaelmas 2002.)

For details of how time is “folded”
by artists and poets, see the following:

A Wrinkle in Time, by Madeleine L’Engle,

and Time Fold, by S. H. Cullinane.

Tuesday, May 13, 2003

Tuesday May 13, 2003

Filed under: Uncategorized — m759 @ 12:06 PM

Cubist Catechism

For the birthday of Georges Braque

From A Wrinkle in Time, by Madeleine L’Engle:

“Now we will tesser, we will wrinkle again. Do you understand?”

“No,” Meg said flatly….

“Oh, dear,” Meg sighed. “I guess I am a moron. I just don’t get it.”

“That is because you think of space only in three dimensions,” Mrs. Whatsit told her….

Meg sighed. “Just explain it to me.”

“Okay,” Charles said. “What is the first dimension?”

“Well — a line.”

“Okay. And the second dimension?”

“Well, you’d square the line. A flat square would be in the second dimension.”

“And the third?”

“Well, you’d square the second dimension. Then the square wouldn’t be flat any more. It would have a bottom, and sides, and a top.”

“And the fourth?”

“Well, I guess if you want to put it into mathematical terms you’d square the square. But you can’t take a pencil and draw it the way you can the first three.”


Braque

Wednesday, March 19, 2003

Wednesday March 19, 2003

Filed under: Uncategorized — m759 @ 4:04 AM


Aptheker

  A Look at the Rat

In memory of Herbert Aptheker, theoretician of the American Communist Party, who died on St. Patrick’s Day, 2003 —

From The New Yorker, issue dated March 24, 2003, Louis Menand on Edmund Wilson’s To the Finland Station:

“Wilson did know what was going on in the Soviet Union in the nineteen-thirties, as his pages on Stalin in To the Finland Station make clear. The problem wasn’t with Stalin; the problem was with Lenin, the book’s ideal type of the intellectual as man of action. Wilson admitted that he had relied on publications controlled by the Party for his portrait of Lenin. (Critical accounts were available; for example, the English translation of the émigré Mark Landau-Aldanov’s Lenin was published, by Dutton, in 1922.) Lenin could create an impression of selfless humanitarianism; he was also a savage and ruthless politician—a ‘pail of milk of human kindness with a dead rat at the bottom,’ as Vladimir Nabokov put it to Wilson in 1940, after reading To the Finland Station.  In the introduction to the 1972 edition, Wilson provided a look at the rat. He did not go on to explain in that introduction that the most notorious features of Stalin’s regime—the use of terror, the show trials, and the concentration camps—had all been inaugurated by Lenin. To the Finland Station begins with Napoleon’s betrayal of the principles of the French Revolution; it should have ended with Lenin’s betrayal of European socialism.” 

From Herbert Aptheker, “More Comments on Howard Fast“:

“We observe that in the list of teachers whom Howard Fast names as most influential in his own life there occur the names of fourteen individuals from Jefferson to Bernard Shaw, Upton Sinclair to Marx, Douglass to Engels, but there is no room for Lenin.
   He is, I think, an important teacher, too; indeed, in my view, Lenin is the greatest figure in the whole galaxy of world revolutionary leaders. He is, certainly, the greatest analyzer of and fighter against imperialism.”

For more on Howard Fast, see my entry
“Death Knell” of March 13, 2003

For a look at the pail of milk, see
the New Yorker cover in Geometry for Jews.

For a more cheerful look at geometry
on this St. Joseph’s Day, see
Harry J. Smith’s

Tesseract Site.

“There is such a thing as a tesseract.”
A Wrinkle in Time

Friday, November 29, 2002

Friday November 29, 2002

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

A Logocentric Archetype

Today we examine the relativist, nominalist, leftist, nihilist, despairing, depressing, absurd, and abominable work of Samuel Beckett, darling of the postmodernists.

One lens through which to view Beckett is an essay by Jennifer Martin, "Beckettian Drama as Protest: A Postmodern Examination of the 'Delogocentering' of Language." Martin begins her essay with two quotations: one from the contemptible French twerp Jacques Derrida, and one from Beckett's masterpiece of stupidity, Molloy. For a logocentric deconstruction of Derrida, see my note, "The Shining of May 29," which demonstrates how Derrida attempts to convert a rather important mathematical result to his brand of nauseating and pretentious nonsense, and of course gets it wrong. For a logocentric deconstruction of Molloy, consider the following passage:

"I took advantage of being at the seaside to lay in a store of sucking-stones. They were pebbles but I call them stones…. I distributed them equally among my four pockets, and sucked them turn and turn about. This raised a problem which I first solved in the following way. I had say sixteen stones, four in each of my four pockets these being the two pockets of my trousers and the two pockets of my greatcoat. Taking a stone from the right pocket of my greatcoat, and putting it in my mouth, I replaced it in the right pocket of my greatcoat by a stone from the right pocket of my trousers, which I replaced by a stone from the left pocket of my trousers, which I replaced by a stone from the left pocket of my greatcoat, which I replaced by the stone which was in my mouth, as soon as I had finished sucking it. Thus there were still four stones in each of my four pockets, but not quite the same stones….But this solution did not satisfy me fully. For it did not escape me that, by an extraordinary hazard, the four stones circulating thus might always be the same four."

Beckett is describing, in great detail, how a damned moron might approach the extraordinarily beautiful mathematical discipline known as group theory, founded by the French anticleric and leftist Evariste Galois. Disciples of Derrida may play at mimicking the politics of Galois, but will never come close to imitating his genius. For a worthwhile discussion of permutation groups acting on a set of 16 elements, see R. D. Carmichael's masterly work, Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937, reprinted by Dover, New York, 1956.

There are at least two ways of approaching permutations on 16 elements in what Pascal calls "l'esprit géométrique." My website Diamond Theory discusses the action of the affine group in a four-dimensional finite geometry of 16 points. For a four-dimensional euclidean hypercube, or tesseract, with 16 vertices, see the highly logocentric movable illustration by Harry J. Smith. The concept of a tesseract was made famous, though seen through a glass darkly, by the Christian writer Madeleine L'Engle in her novel for children and young adults, A Wrinkle in Tme.

This tesseract may serve as an archetype for what Pascal, Simone Weil (see my earlier notes), Harry J. Smith, and Madeleine L'Engle might, borrowing their enemies' language, call their "logocentric" philosophy.

For a more literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill.

For a discussion of the full range of meaning of the word "logos," which has rational as well as religious connotations, click here.

Friday, August 30, 2002

Friday August 30, 2002

Filed under: Uncategorized — Tags: , — m759 @ 2:30 AM

For Mary Shelley, on her birthday: A Chain of Links The creator of Frankenstein might appreciate the following chain of thought. Lucifer.com Lucifer Media Corporation Lucifer Media Sites The Extropy Institute: International Transhumanist Solutions Why Super-Human Intelligence Would Be Equivalent To Precognition, by Marc Geddes:

"Consider the geometry of multiple dimensions as an analogy for mental abilities… …if there is a 4th dimension of intelligence, to us ordinary humans stuck with 3 dimensional reasoning, this 4th dimension would be indistinguishable from precognition. Post-humans would appear to us ordinary humans as beings which could predict the future in ways which would be inexplicable to us. We should label post-humans as 'Pre-Cogs.'

In the Steven Speilberg [sic]  film Minority Report, we encounter genetically engineered humans with precisely the abilities described above."

Internet Movie Database page on "Minority Report"

IMDb page on "Minority Report" author Philip K. Dick

IMDb biography of Philip K. Dick, where our chain of links ends.  Here Dick says that

"The basic tool for the manipulation of reality is the manipulation of words. If you can control the meaning of words, you can control the people who must use the words."

On the other hand, Dick also says here that

"Reality is that which, when you stop believing in it, doesn't go away."

These two quotations summarize, on the one hand, the cynical, relativistic nominalism of the postmodernists and, on the other hand, the hard-nosed realism of the Platonists.

What does all this have to do with "the geometry of multiple dimensions"?

Consider the famous story for adolescents, A Wrinkle in Time, by Madeleine L'Engle.   The author, a well-meaning Christian, tries, like all storytellers,  to control her readers by controlling the meaning of words.   The key word in this book is "tesseract," a term from multi-dimensional geometry.   She insists that a tesseract has mystic properties and cannot be visualized.  She is wrong (at least about the visualizing).

See The Tesseract: A look into 4-dimensional space, by Harry J. Smith.

See also the many revealing comments in Harry J. Smith's Guestbook.

One of Smith's guests remarks, apropos of Smith's comments on St. Joseph, that he has his own connection with St. Augustine.

For a adult-level discussion of Augustine, time, eternity, and Platonism, see the website Time as a Psalm in St. Augustine, by A. M. Johnston.

See also the remark headlining Maureen Dowd's New York Times column of August 28, 2002, Saint Augustine's Day:

"I'm with Dick."

Whether the realist Dick or the nominalist Dick, she does not say.

As for precognition, see my series of journal notes below, which leads up to two intriguing errors in an Amazon.com site on the "Forbidden Planet" soundtrack.   The first two audio samples from this soundtrack are (wrongly) entitled "Birdland" and "Flamingo."  See also the West Wing episode rebroadcast on Wednesday, August 28, 2002,

The Black Vera Wang

C. J. Cregg (Allison Janney), who models a black Vera Wang dress in that episode, has the Secret Service codename Flamingo.

"…that woman in black She's a mystery She's everything a woman should be Woman in black got a hold on me"

(Foreigner 4 in my August 28 note below)

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