Or: The Naked Blackboard Jungle
|
"…it would be quite a long walk
Swiftly Mrs. Who brought her hands… together.
"Now, you see," Mrs. Whatsit said,
– A Wrinkle in Time , |
Related material: Machete Math and…
Starring the late Eleanor Parker as Swiftly Mrs. Who.
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—
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—
This figure is relevant because of a
tesseract sculpture by Peter Forakis—
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
"And take upon's
the mystery of things
as if we were God's spies"
— King Lear
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:
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 —
Related material:
Beckinsale in another film
(See At the Crossroads,
Log24, Dec. 8, 2006):
"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 —
"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
170
even one micro-second she would have what she had |
"The page numbers
are generally reliable."
The New York Times online,
Friday, Sept. 7, 2007:
Madeleine L’Engle,
Children’s Writer,
Is Dead
Her death, of natural causes, was announced today by her publisher, Farrar, Straus and Giroux."
Related material:
Log24 entries of
August 31—
"That is how we travel."
— 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
On Spekkens’ toy system and finite geometry
Background–
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:
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]…."
Hypercube from the Skotiniotis paper:
Reference:
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.)
"…it would be quite
a long walk
for him if he had to
walk straight across."
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."
— A Wrinkle in Time,
Chapter 5,
"The Tesseract"
Related material:
To Measure the Changes,
and…
 |
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.'"
Day Without Logic
(March 8, 2007)
and
The Geometry of Logic
(March 10, 2007):
"There is such a thing
as a tesseract."
— Madeleine L'Engle,
A Wrinkle in Time
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."
"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
Day Without Logic,
Introduction to Logic,
The Geometry of Logic,
Structure and Logic,
Spider-Man and Fan:
"There is such a thing
as a tesseract."
— A Wrinkle in Time
"… 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."
For the meaning of multispeech,
see the entries of
All Hallows' Eve, 2005:
"There is such a thing
as a tesseract."
— A Wrinkle in Time
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!”
“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.”
— Freeman Dyson,
New York Review of Books,
issue dated May 28, 1998
"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."
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 |
Senior Honors
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.'"
From The Catholic Encyclopedia:
"It is sufficient for true knowledge that it affirm as real that which is truly real."
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.
Kate Beckinsale, adapted from
poster for Underworld: Evolution
(DVD release date 6/6/6)
"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.'"
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 nevertheless does
"announce a faith."
"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"
"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 "faith" announced by
the above lottery numbers
on All Hallows' Eve is
perhaps that of the artist
Madeleine L'Engle:
"Does the word 'tesseract'
mean anything to you?"
— Robert A. Heinlein in
The Number of the Beast
(1980)
My reply–
Part I:
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:
"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
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.
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.
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