From the Journal of Steven H. Cullinane:
Summer Reading (Aug. 7 - Sept. 22, 2007)
The title is suggested by the New Yorker cover
dated Aug. 20, 2007. (See below.)
The Autumn equinox in 2007 is
September 23 at 5:51 AM EDT.
Saturday, September 22, 2007 6:25 AM
Yom Kippur, Part III:
PA
Lottery
Monolith
Click on image
for soundtrack.
See also
8/09, 9/12.
Saturday, September 22, 2007 6:23 AM
Yom Kippur, Part II:
Retrospect
"It was only in retrospect
that the silliness
became profound."
-- Review of
Faust in Copenhagen
Saturday, September 22, 2007 6:22 AM
Yom Kippur, Part I:
The Magic of
Numbers
"Emphasis will be placed on discovery through conjecture and
experimentation."
-- Elena Mantovan, pre-2007 undated Harvard syllabus for Quantitative Reasoning
28, "The Magic of Numbers"
"The lunatic, the lover, and the poet, said Shakespeare, are of
imagination all compact. He forgot the mathematician.... Those who win
through to the end of The Magic of Numbers will be for the rest
of their lives in touch with the accessible mystery of things."
-- Review, Harvard Magazine, Jan/Feb 2004
"Lear
becomes almost lyrical. 'When thou dost ask me blessing, I'll kneel
down/ And pray, and sing, and tell old tales, and laugh/ At gilded
butterflies, and hear poor rogues/ Talk of court news; and we'll talk
with them too/ Who loses and who wins; who's in, who's out-- And take
upon's the mystery of things/ As if we were God's spies.' That is a
remarkable, haunting passage."
-- Father James V. Schall, Society of Jesus, Georgetown Hoya, undated
column (perhaps, the URL indicates, from All Hallows' Eve, 2006)
Friday, September 21, 2007 8:28 AM
On Dryness:
Word and Object
"We
may recall the ideal of 'dryness' which we associate with the symbolist
movement, with writers such as T. E. Hulme and T. S. Eliot, with Paul
Valery, with Wittgenstein. This 'dryness' (smallness, clearness,
self-containedness) is a nemesis of Romanticism.... The temptation of
art... is to console. The modern writer... attempts to console us by
myths or by stories."
-- Iris Murdoch
"The consolations of form,
the clean crystalline work"
-- Iris Murdoch,
"Against Dryness"
"As a teacher Quine
was carefully organized,
precise, and conscientious,
but somewhat dry
in his classroom style."
-- Harvard Gazette
Word:
Object:
Myth and Story:
The five entries ending
on Jan. 27, 2007
"There is such a thing
as a tesseract."
-- Madeleine L'Engle
Wednesday, September 19, 2007 5:00 AM
Philosophy Wars continued:
Einstein, God, and
the Consolation of Form
"The kind of thing that would make
Einstein gag"
-- Peter Woit, Sept. 18, 2007
"-- ...He did some equations that would make God cry
for the sheer
beauty of them. Take a look at this.... The sonofabitch set out
equations that fit the data. Nobody believes they mean anything. Shit,
when I back off, neither do I. But now and then, just once in a
while...
-- He joined physical and mental events. In a
unified mathematical field.
-- Yeah, that’s what I think he did. But the
bastards in this
department... bunch of goddamned positivists. Proof doesn’t mean a
damned thing to them. Logical rigor, beauty, that damned perfection of
something that works straight out, upside down, or sideways-- they
don’t give a damn."
-- "Nothing Succeeds," in The
Southern Reporter: Stories of John William Corrington, LSU
Press, 1981
"The search for images of order and the loss of them constitute the
meaning of The Southern Reporter."
-- Louisiana State University Press
"By equating reality with the metaphysical abstraction 'contingency'
and explaining his paradigm by reference to simple images of order,
Kermode [but see note below] defines the realist novel not as
one which attempts to get to grips with society or human nature, but
one which, in providing the consolation of form,* makes the occasional
concession to contingency...."
-- Richard
Webster on Frank Kermode's The Sense of an Ending
"We
are here in the
Church of St. Frank."
-- Marjorie
Garber,
Harvard University
* "The consolations of
form" is a phrase Kermode quoted from Iris Murdoch. Webster does not
mention Murdoch. Others have quoted Murdoch's memorable phrase, which
comes from her essay "Against Dryness: A Polemical Sketch," Encounter,
No. 88, January 1961, pp. 16-20. The essay was reprinted in a Penguin
paperback collection of Murdoch's work, Existentialists and Mystics. It was also
reprinted in The Novel Today, ed. Malcolm Bradbury (Manchester,
Manchester U. Press, 1977); in Revisions, ed. S. Hauerwas and
A. MacIntyre (Notre Dame, U. of Notre Dame Press, 1981); and in Iris
Murdoch, ed. H. Bloom (New York, Chelsea House, 1986).
Saturday, September 15, 2007 8:00 PM
Dance for Clarinet and Drums:
|
Professors:
Post Your Syllabi
Professors should post their
course syllabi before move-in,
not after class has started
The Harvard Crimson
Published On Friday, September 14, 2007 12:54 AM
"Classes start in three days, and that means it’s time to... examine
course syllabi-- that is if you can find them...." More
>> |
Classics 101:
The Holy Spook
Prof. Coleman Silk introducing
freshmen to academic values
The Course Begins:
Larry Summers, former president
of Harvard, was recently invited,
then disinvited, to speak at a
politically correct UC campus.
A Guest Lecturer Speaks:
"This
is so pathetic. I used to write long disquisitions on the ethical
dimensions of behavior like this, but years of it can make a girl get
very tired. And that's because this stuff is tiresome, and
boring, and wrong, and pathetic, and so very indicative of the derailed
character of academic life. It's more important to keep punishing
Summers for a comment he made years ago-- and apologized for many times
over, and essentially lost the presidency of Harvard over-- than it is
just to move on and let free exchange happen on campuses. I doubt
Summers would have devoted his time before the Regents to theorizing
gender (not that I would personally care much if he did-- I was not so
mortally wounded by his observations as others were), and he is a
brilliant man with much of value to bring to a visit with the Regents.
But what does that matter when the opportunity to mob a politically
incorrect academic presents itself?" --Erin
O'Connor on Sept. 15, 2007
Illustration of the Theme:
Clarinetist Ken Peplowski
plays "Cry Me a River"
as Nicole Kidman focuses
the students' attention.
A sample Holy Spook,
Kurt Vonnegut, was introduced
by Peplowski on the birthday
this year of Pope Benedict XVI.
"Deeply vulgar"
-- Academic
characterization
of Harvard president Summers
"Do they still call it
the licorice stick?"
-- Kurt Vonnegut
Related Material:
Midnight Drums for Larry
Thursday, September 13, 2007 3:57 AM
Credit Where Credit Is Due:
Scorsese
Is
Kennedy Center
Honoree
"Scorsese,
64, a native New Yorker, thought of being a priest and went to the
seminary after high school. But he changed his mind and built a
catalogue of great films, many of which are considered the best of
their time." -- Washington Post, Sept. 12, 2007
His Life.
My Card.
Columbus Day, 2005
Click on image to enlarge.
Thursday, September 13, 2007 2:02 AM
Battlefield Geometry continued:
Lease Renewed
The New York Times,
Thursday, September 13, 2007--
Burt
Hasen, Artist Inspired
by Maps, Dies at 85
Burt Hasen, a New York painter who drew inspiration
from his experience
working with maps as a military technician during World War II, died on
Friday [September 7, 2007] in Manhattan. He was 85 and lived
in Lower Manhattan....
During
the war he served in the Air Force in the Pacific, where his duties
involved close study of aerial maps, an activity that lastingly
influenced his work. His densely worked canvases often had an overhead
perspective....Toward the end of his life, many of his seemingly
abstract paintings were based directly, and in detail, on maps....
In
2006 Mr. Hasen, his wife and the other tenants of a five-story building
at 7 Dutch Street near the South Street Seaport made news when they
organized against their landlord’s attempt to evict them from the
rent-regulated lofts they had occupied for more than 30 years. They
subsequently had their leases renewed.
"For every kind of vampire,
there is a kind of cross."
-- Gravity's Rainbow
Wednesday, September 12, 2007 5:01 PM
ART WARS continued:
Vector Logic
I learned yesterday from Jonathan Westphal,
a professor of philosophy at Idaho State University, that he and a
colleague, Jim Hardy, have devised another geometric approach to logic:
a system of arrow diagrams that illustrate classical propositional
logic. The diagrams resemble those used to illustrate Euclidean
vector
spaces, and Westphal and Hardy call their approach "a vector system,"
although it does not involve what a mathematician would regard as a
vector space.
Journal of Logic and Computation
15(5) (October, 2005),
pp. 751-765.
Related material:
(2) the quilt pattern
below (click for
the source) --
and
(3) yesterday's entry
"Christ! what are
patterns for?"
Tuesday, September 11, 2007 12:07 AM
Jomini Meets Rommel:
Battlefield
Geometry
"The
general, who wrote the Army's book on counterinsurgency, said he and
his staff were 'trying to do the battlefield geometry right now' as he
prepared his troop-level recommendations."
-- Steven R. Hurst, The
Associated Press, Wednesday, Aug. 15, 2007
"'... we are in the process of doing the battlefield geometry to
determine the way ahead.'"
-- Charles M. Sennott, Boston Globe, Friday,
Sept. 7, 2007
"Based on these considerations, and having worked the battlefield
geometry ... I have recommended a drawdown of the surge forces
from Iraq."
-- United States Army, Monday, Sept. 10, 2007
Related material:
Log24 entries of
June 11 and 12, 2005:
"In the desert you can
remember your name
'Cause there ain't no one
for to give you no pain."
Monday, September 10, 2007 11:07 AM
Beauty Bare: A Poem
The
Story Theory
of Truth --
"I'm a gun for hire,
I'm a saint, I'm a liar,
because there are no facts,
there is no truth,
just data to be manipulated."
-- The Garden of Allah
Data
The data in more poetic form:
To 23,
For 16.
Commentary:
23: See
The Prime Cut Gospel.
16: See
Happy Birthday, Benedict XVI.
Related material:
The remarks yesterday
of Harvard president
Drew G. Faust
to incoming freshmen.
Faust "encouraged
the incoming class
to explore Harvard’s
many opportunities.
'Think of it as
a treasure room
of hidden objects
Harry discovers
at Hogwarts,'
Faust said."
-- Today's Crimson
For a less Faustian approach,
see the Harvard-educated
philosopher Charles Hartshorne
at The Harvard Square Library
and the words of another
Harvard-educated Hartshorne:
"Whenever one
approaches a subject from
two different directions,
there is bound to be
an interesting theorem
expressing their relation."
-- Robin
Hartshorne
Saturday, September 8, 2007 7:11 PM
Saturday Evening:
May 25, 2007:
"Let's give 'em
somethin' to talk about,
A little mystery to figure out"
-- Scarlett Johansson singing on
Saturday Night Live, April 21, 2007
Related material:
Today's previous entry
and the following:
Saturday, September 8, 2007 2:02 PM
Requiem for a Storyteller:
The Intensest
Rendezvous
"There is one story and one story only
That will prove worth your telling....
Dwell on her graciousness, dwell on her smiling,
Do not forget what flowers
The great boar trampled down in ivy time.
Her brow was creamy as the crested wave,
Her sea-blue eyes were wild
But nothing promised that is not performed. "
-- Robert Graves,
To
Juan at the Winter Solstice
The
Devil and Wallace Stevens:
"In a letter to Harriet Monroe, written December 23, 1926, Stevens
refers to the Sapphic fragment that invokes the genius of evening:
'Evening star that bringest back all that lightsome Dawn hath scattered
afar, thou bringest the sheep, thou bringest the goat, thou bringest
the child home to the mother.' Christmas, writes Stevens, 'is like
Sappho's evening: it brings us all home to the fold.' (Letters of
Wallace Stevens, 248)"
-- "The Archangel of Evening," Chapter 5 of Wallace Stevens: The
Intensest Rendezvous, by Barbara M. Fisher, The University Press of Virginia,
1990, pages 72-73
"Evening. Evening of this day. Evening
of the century. Evening of my own life....
At Christmastime my parents held open house on Sunday evenings, and a
dozen or more people gathered around the piano, and the apartment was
full of music, and theology was sung into my heart."
-- Madeleine L'Engle, Bright Evening Star: Mystery of the Incarnation
From the date of
L'Engle's death:
Some enchanted evening...
Friday, September 7, 2007 2:02 PM
Philosophy Wars continued:
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."
-- 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
Thursday, September 6, 2007 11:00 AM
Sunday, September 2, 2007 5:11 PM
Annals of Quantum Geometry
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]...."
Hypercube from the Skotiniotis paper:
Reference:
Friday, August 31, 2007 10:10 PM
String theory:
Being There
"...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,
Serious Numbers,
and...
Balls
of Fury
Wednesday, August 22, 2007 11:00 PM
Serious Numbers, continued:
Wednesday, August 22, 2007 10:31 AM
Concrete Universal, continued:
The Enchanted
Twilight
The Associated Press
Tuesday, August 21, 2007
GENEVA:
British-born author Magdalen Nabb, whose crime novels about a quirky
Italian investigator were acclaimed by her idol Georges Simenon, has
died, her Swiss publishing house said Tuesday. She was 60.
Nabb,
who also wrote stories for children and young adults, died of a stroke
on Saturday [August 18, 2007] in Florence, Italy, where she had lived
and worked since 1975, said Diogenes Verlag AG of Zurich....
Nabb published 13 books for children and young adults,
including "The Enchanted Horse," "Twilight Ghost" and the "Josie Smith" series about a "girl who always has
plenty of ideas."
Tuesday, August 21, 2007 3:29 PM
On the Holy Trinity:
Shell Game
Part I:
Overview of Unix
at pangea.stanford.edu
Last revision August 2, 2004
"The Unix operating environment is
organized into three layers. The innermost level of Unix is the
kernel.
This is the actual operating system, a single large program that always
resides in memory. Sections of the code in this program are executed on
behalf of users to do needed tasks, like access files or terminals.
Strictly speaking, the kernel is Unix.
The next level of the Unix environment
is composed of programs, commands, and utilities.
In Unix, the basic commands like copying or removing files are
implemented not as part of the kernel, but as individual programs, no
different really from any program you could write. What we think of as
the commands and utilities of Unix are simply a set of programs that
have become standardized and distributed. There are hundreds of these,
plus many additional utilities in the public domain that can be
installed.
The final level of the Unix
environment, which stands like an umbrella over the others, is the
shell.
The shell processes your terminal input and starts up the programs that
you request. It also allows you to manipulate the environment in which
those programs will execute in a way that is transparent to the
program. The program can be written to handle standard cases, and then
made to handle unusual cases simply by manipulating its environment,
without having to have a special version of the program." (My
italics.)
Part
II:
Programs
From my paper journal
on the date
"Good Will Hunting"
was released:
|
Friday, December 5, 1997
To: The executive editor, The New York Times
Re: The Front Page/His Girl Friday
Match the speaker with the speech--
|
The Speech--
"The son of a
bitch stole my..." |
|
The Speaker |
Frame of Reference |
| 1. |
rosebud |
A. |
J. Paul Getty |
The front page, N.Y. Times, Monday, 12/1/97 |
| 2. |
clock |
B. |
Joel Silver |
Page 126, The New Yorker, 3/21/94 |
| 3. |
act |
C. |
Blanche DuBois |
The Elysian Fields |
| 4. |
waltz |
D. |
Bob Geldof |
People Weekly 12/8/97 |
| 5. |
temple |
E. |
St. Michael |
Heaven's Gate |
| 6. |
watch |
F. |
Susanna Moore |
In the Cut (pbk., Dec. '96) p. 261 |
| 7. |
line |
G. |
Joseph Lelyveld |
Page A21, The New York Times, 12/1/97 |
| 8. |
chair |
H. |
Kylie Minogue |
Page 69, People Weekly, 12/8/97 |
| 9. |
religion |
I. |
Carol Gilligan |
The Garden of Good and Evil |
| 10. |
wife |
J. |
John Travolta |
"Michael," the movie |
| 11. |
harp |
K. |
Shylock |
Page 40, N.Y. Review of Books, 12/4/97 |
| 12. |
Oscar |
L. |
Stephen King |
The Shining (pbk., 1997), pp. 316, 317 |
Postscript of June 5, 2003:
"...while the scientist sees
everything that happens
in one point of space,
the poet feels
everything that happens
in one point of time...
all forming an
instantaneous and transparent
organism of events...."
-- Vladimir Nabokov
Part III:
The Bourne Shell
"The binary program of the Bourne shell or a compatible
program is located at /bin/sh on most Unix systems, and is
still the default shell for the root superuser on many current Unix implementations."
--Wikipedia
Tuesday, August 21, 2007 8:14 AM
ART WARS
Tuesday, August 21, 2007 8:00 AM
ART WARS, continued:
Compare
and Contrast
Monday, August 20, 2007 8:01 AM
Annals of Journalism:
Sunday, August 19, 2007 8:19 AM
Logos and Epiphany:
Symmetry
and Mirroring
Logo design by Anton Stankowski
"... at the beginning of the thirties... Stankowski began to work as a
typographer and graphic designer in a Zurich advertising agency.
Together with a group of friends-- they were later to be known as the
'Zurich Concretists'-- he explored the possibilities of symmetry and
mirroring in the graphic arts. Stankowski experimented with squares and
diagonals, making them the hallmarks of his art. Of his now
world-famous logo for the Deutsche Bank--
the soaring diagonal in the stable square-- he proudly said in 1974:
'The company logo is a trade-mark that sends out a signal.'"
"Two New York fire fighters were killed
while trying to douse a blaze in the former Deutsche Bank building in
the city.
The
fire broke out on 14th and 15th floors yesterday afternoon and spread
to several floors before it was brought under control about five hours
later.
The building had been heavily damaged during the 11 September, 2001
terrorist attacks.
The
building, which was damaged by falling debris of the twin towers that
had collapsed in 2001 when terrorists flew hijacked planes into them,
was being 'deconstructed' to make way for construction of a new Freedom
Tower."
Related material
SPORTS OF THE TIMES
Restoring the Faith
After Hitting the Bottom
By SELENA ROBERTS
The New York Times
Published: August 1, 2007
What
good is a nadir if it's denied or ignored? What's the value of reaching
the lowest of the low if it can't buy a cheap epiphany? |
When you care enough
to send the very best...
Saturday, August 18, 2007 7:20 PM
Happy Birthday, Robert Redford
"In chapters 19 and 20 of LILA there is a discussion about
the possibility of making Zen and the Art
into a movie. It opens with a scene where Robert Redford, who 'really
would like to have the film rights,' comes to meet and negotiate with
Phaedrus in his New York City hotel room. Phaedrus tells the famous
actor that he can have the rights to the book, but maybe that's just
because he's star-struck and doesn't like to haggle. Under his
excitement, Phaedrus has a bad feeling about it. He tells us that he's
been warned by several different people not to allow such a film to be
made. Even Redford warned him not to do it. So what's the problem? As
it's put at the end of that discussion, 'Films are social media; his
book was largely intellectual. That was the center of the problem.'"
-- David
Buchanan at robertpirsig.org
"The insight is constituted precisely by 'seeing' the idea in the
image, the intelligible in the sensible, the universal in the
particular, the abstract in the concrete."
-- Fr. Brian Cronin's Foundations of Philosophy, Ch. 2, "Identifying
Direct Insights," quoted in Ideas and Art
See also Smiles of a Summer Evening, the current issue of TIME, the time of this entry (7:20:11
PM ET), and Plato, Pegasus, and the Evening Star.
Tuesday, August 14, 2007 12:00 PM
A Writer's Reflections:
Philip K. Dick,
1928 - 1982
on the cover of
a 1987 edition of
his 1959 novel
Time Out of Joint:
Cover art by Barclay Shaw reprinted
from an earlier (1984) edition
Philip K. Dick as a
window wraith (see below)
The above illustration was suggested
by yesterday's quoted New Yorker characterization by Adam
Gopnik of Philip K. Dick--
"...
the kind of guy who can't drink one cup of coffee without drinking six,
and then stays up all night to tell you what Schopenhauer really said
and how it affects your understanding of Hitchcock and what that had to
do with Christopher Marlowe."
-- as well as by the illustrations of Gopnik's
characterization in Kernel of Eternity, and by the following passage
from Gopnik's 2005 novel The King in the Window:
"What's a window wraith?"
"It's
someone who once lived in the ordinary world who lives now in a window,
and makes reflections of the people who pass by and look in."
"You mean you are a ghost?!" Oliver asked, suddenly feeling a
little terrified.
"Just the opposite, actually. You see, ghosts come from another world
and haunt you, but window wraiths are the world. We're the
memory of the world. We're here for good. You're the ones who
come and go like ghosts. You haunt us."
Related material: As noted, Kernel of Eternity, and also John Tierney's piece on simulated reality in last
night's online New York Times.
Whether our everyday reality is merely a simulation has long been a
theme (as in Dick's novel above) of speculative fiction. Interest in
this theme is widespread, perhaps partly because we do exist as
simulations-- in the minds of other people. These simulations may be
accurate or may be-- as is perhaps Gopnik's characterization of Philip
K. Dick-- inaccurate. The accuracy of the simulations is seldom of
interest to the simulator, but often of considerable interest to the
simulatee.
The cover of the Aug. 20 New Yorker
in which the Adam Gopnik essay appears may also be of interest, in view
of the material on diagonals in the Log24 entries of Aug. 1 linked to in yesterday's entry:
"Summer Reading,"
by Joost
Swarte
Monday, August 13, 2007 11:07 AM
Mathematics and Narrative, continued:
Adam Gopnik in
The New Yorker of
August 20, 2007--
On Philip K. Dick:
"...
the kind of guy who can't drink one cup of coffee without drinking six,
and then stays up all night to tell you what Schopenhauer really said
and how it affects your understanding of Hitchcock and what that had to
do with Christopher Marlowe."
Modernity: A Film by
Alfred Hitchcock:
"...
the most thoroughgoing modernist design element in Hitchcock's films
arises out of geometry, as Francois Regnault has argued, identifying 'a
global movement for each one, or a "principal geometric or dynamic
form," which can appear in the pure state in the credits....'"
--Peter J. Hutchings (my italics)
More >>
Sunday, August 12, 2007 9:00 AM
Mathematics and the Ring Saga:
In the context of quantum information theory, the following structure
seems to be of interest--
"... the full two-by-two matrix ring with entries in GF(2), M2(GF(2))--
the unique simple non-commutative ring of order 16 featuring six units
(invertible elements) and ten zero-divisors."
-- "Geometry of Two-Qubits," by Metod Saniga (pdf,
17 pp.), Jan. 25, 2007
This ring is another way of looking at the 16 elements of the affine
space A4(GF(2))
over the 2-element field. (Arrange the four coordinates of each
element-- 1's and 0's-- into a square instead of a straight line, and
regard the resulting squares as matrices.) (For more on A4(GF(2)),
see Finite Relativity and related notes at Finite
Geometry of the Square and Cube.) Using the above ring,
Saniga constructs a system of 35 objects (not unlike the 35 lines of the
finite geometry PG(3,2)) that he calls a "projective line"
over the ring. This system of 35 objects has a subconfiguration
isomorphic to the (2,2) generalized quadrangle W2
(which occurs naturally as a subconfiguration of PG(3,2)-- see Inscapes.)
Saniga concludes:
"We
have demonstrated that the basic properties of a system of two
interacting spin-1/2 particles are uniquely embodied in the
(sub)geometry of a particular projective line, found to be equivalent
to the generalized quadrangle of order two. As such systems are the
simplest ones exhibiting phenomena like quantum entanglement and
quantum non-locality and play, therefore, a crucial role in numerous
applications like quantum cryptography, quantum coding, quantum
cloning/teleportation and/or quantum computing to mention the most
salient ones, our discovery thus
- not only offers a principally new geometrically-underlined
insight into their intrinsic nature,
- but also gives their applications a wholly new perspective
- and opens up rather unexpected vistas for an algebraic
geometrical modelling of their higher-dimensional counterparts."
is not without relevance to
the physics of quantum theory.
Saturday, August 11, 2007 10:00 PM
The Ring Saga continues:
Four Colours
The previous entry
dealt with Plato's myth of the ring of Gyges that conferred
invisibility. Another legendary ring, from Hermann Hesse, with some
background from Carl Jung:
From C. G. Jung, Collected Works (Princeton U. Press), Volume
12-- Psychology and Alchemy (1944)--
Part II-- "Individual Dream Symbolism in Relation to Alchemy"-- Chapter
3, "The Symbolism of the Mandala"-- as quoted in Jung,
Dreams, published by Routledge, 2001-- Page 265--
"...
the dreamer is wandering about in a dark cave, where a battle is going
on between good and evil. But there is also a prince who knows
everything. He gives the dreamer a ring set with a diamond....
Visual impression (waking dream):
The dreamer is falling into the abyss. At the bottom there is a bear
whose eyes gleam alternately in four colours: red, yellow, green, and
blue. Actually it has four eyes that change into four lights. The bear
disappears and the dreamer goes through a long dark tunnel. Light is
shimmering at the far end. A treasure is there, and on top of it the
ring with the diamond. It is said that this ring will lead him on a
long journey to the east."
Hermann Hesse, The Journey to the East (1932):
"'...
Despair is the result of each earnest attempt to go through life with
virtue, justice, and understanding and to fulfil their requirements.
Children live on one side of despair, the awakened on the other side.
Defendant H. is no longer a child and is not yet fully awakened. He is
still in the midst of despair. He will overcome it and thereby go
through his second novitiate. We welcome him anew into the League, the
meaning of which he no longer claims to understand. We give back to him
his lost ring, which the servant Leo has kept for him.'
The
Speaker then brought the ring, kissed me on the cheek and placed the
ring on my finger. Hardly had I looked at the ring, hardly had I felt
its metallic coolness on my fingers, when a thousand things occurred to
me, a thousand inconceivable acts of neglect. Above all, it occurred to
me that the ring had four stones at equal distances apart, and that it
was a rule of the League and part of the vow to turn the ring slowly on
the finger at least once a day, and at each of the four stones to bring
to mind one of the four basic precepts of the vow. I had not only lost
the ring and had not once missed it, but during all those dreadful
years I had also no longer repeated the four basic precepts or thought
of them. Immediately, I tried to say them again inwardly. I had an idea
what they were, they were still within me, they belonged to me as does
a name which one will remember in a moment but at that particular momen
cannot be recalled. No, it remained silent within me, I could not
repeat the rules, I had forgotten the wording. I had forgotten the
rules; for many years I had not repeated them, for many years I had not
observed them and held them sacred-- and yet I had considered myself a
loyal League brother.
The Speaker patted my arm kindly when he observed my dismay and deep
shame."
Friday, August 10, 2007 10:31 AM
Puppet Magic:
The Ring of Gyges
10:31:32 AM ET
Commentary by Richard Wilhelm
on I Ching Hexagram 32:
"Duration
is... not a state of rest, for mere standstill is regression. Duration
is rather the self-contained and therefore self-renewing movement of an
organized, firmly integrated whole, taking place in accordance with
immutable laws and beginning anew at every ending."
Related material
Jung and the Imago Dei
"Not Being There,"
by Christopher Caldwell,
from next Sunday's
New York Times Magazine:
|
"The
chance to try on fresh identities was the great boon that life online
was supposed to afford us. Multiuser role-playing games and discussion
groups would be venues for living out fantasies. Shielded by anonymity,
everyone could now pass a 'second life' online as Thor the Motorcycle
Sex God or the Sage of Wherever. Some warned, though, that there were
other possibilities. The Stanford Internet expert Lawrence
Lessig
likened online anonymity to the ring of invisibility that surrounds the
shepherd Gyges in one of Plato's dialogues. Under such circumstances,
Plato feared, no one is 'of such an iron nature that he would stand
fast in justice.'
Time, along with a string of sock-puppet scandals, has proved Lessig
and Plato right." |
"The Boy Who Lived,"
by Christopher Hitchens,
from next Sunday's
New York Times Book Review:
On the conclusion of the Harry Potter series:
"The toys have been put firmly back in the box, the wand has been
folded up, and the conjuror is discreetly accepting payment while the
children clamor for fresh entertainments. (I recommend that they
graduate to Philip Pullman, whose daemon scheme is finer than any patronus.)"
|
I, on the other hand,
recommend Tolkien...
or, for those who are
already familiar with
Tolkien, Plato-- to whom
"
The Ring of Gyges" may
serve as an introduction.
"It's all in Plato, all in Plato:
bless me, what do they
teach them at these schools!"
-- C. S. Lewis
Thursday, August 9, 2007 12:00 PM
Amalfi Conjecture:
Bulletin of the American Mathematical Society,
Volume 31, Number 1, July 1994, Pages 1-14
Selberg's Conjectures
and Artin L-Functions (pdf)
M. Ram Murty
Introduction
In its comprehensive form, an identity between an automorphic L-function
and a "motivic" L-function
is called a reciprocity law. The celebrated Artin reciprocity law is
perhaps the fundamental example. The conjecture of Shimura-Taniyama
that every elliptic curve over Q is "modular" is certainly the
most intriguing reciprocity conjecture of our time. The "Himalayan
peaks" that hold the secrets of these nonabelian reciprocity laws
challenge humanity, and, with the visionary Langlands
program,
we have mapped out before us one means of ascent to those lofty peaks.
The recent work of Wiles suggests that an important case (the
semistable case) of the Shimura-Taniyama conjecture is on the horizon
and perhaps this is another means of ascent. In either case, a long
journey is predicted.... At the 1989 Amalfi meeting,
Selberg [S]
announced a series of conjectures which looks like another approach to
the summit. Alas, neither path seems the easier climb....
[S] A. Selberg, Old and new
conjectures and results
about a class of Dirichlet series,
Collected
Papers, Volume II,
Springer-Verlag, 1991, pp. 47-63.
Zentralblatt MATH Database on the above Selberg paper:
"These are notes of lectures presented at the Amalfi Conference on
Number Theory,
1989.... There are various stimulating conjectures (which are related
to several other conjectures like the Sato-Tate conjecture, Langlands
conjectures, Riemann conjecture...).... Concluding remark of the
author: 'A more complete account with proofs is under preparation and
will in time appear elsewhere.'"
Related material: Previous entry.
Tuesday, August 7, 2007 6:25 PM
Three church scenes
In memory of
Atle Selberg, mathematician,
dead at 90 on August 6, 2007
According to the
American Mathematical Society,
Selberg died, like
André Weil, on
the Feast of the Metamorphosis.
Endgame
Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye.
-- Steven H. Cullinane, Nov. 7, 1986
Read more.
For further views of
the Amalfi coast, site of
the above Escher scene,
see the film "
A Good Woman"
(made in 2004, released in 2006)
starring Scarlett Johansson--
Scene from "A Good Woman"
-- and the following from
Collegiate Church of
St. Mary Magdalene,
Atrani, Amalfi Coast, Italy:
"An interior made exterior"
-- Wallace Stevens
