From the journal of Steven H. Cullinane...
2007 August 01-15
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 moment 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
Tuesday, August 7, 2007 8:00 AM
Annals of Communication:
The Horse Whisperer
Scarlett Johansson and friend
in "The Horse Whisperer" (1998)
Thanks to
University Diaries (Aug. 6) for the following:
"'The
University of Sydney
has ordered an independent review into allegations that the dean of the
Conservatorium of Music hired a horse whisperer to conduct management
workshops.'
[Are you, like UD,
a bit vague on exactly what a horse whisperer is? And are you having
trouble figuring out what a horse whisperer would have to offer a
management workshop? But then, what exactly is a management workshop? Read on.]"
For some background on horse whispering and management workshops, see
IABC Steal Sheet, March 2004.
Related material:
The recent Log24 entries
Putting Descartes
Before Dehors
"Descartes déclare que
c'est en moi, non hors de moi,
en moi, non dans le monde,
que je pourrais voir
si quelque chose existe
hors de moi."
-- ATRIUM, Philosophie
For further details,
see ART WARS.
|
Monday, August 6, 2007 8:00 AM
Philosophy Wars continued:
|
The Place of the Lion, by Charles
Williams, 1931, Chapter Eight:
"Besides,
if this fellow were right, what harm would the Divine Universals do us?
I mean, aren't the angels supposed to be rather gentle and helpful and
all that?"
"You're doing what Marcellus warned you
against... judging them by English pictures. All nightgowns and body
and a kind of flacculent sweetness. As in cemeteries, with broken bits
of marble. These are Angels-- not a bit the same thing. These are the
principles of the tiger and the volcano and the flaming suns of space."
Under the Volcano, Chapter Two:
"But
if you look at that sunlight there, then perhaps you'll get the answer,
see, look at the way it falls through the window: what beauty can
compare to that of a cantina in the early morning? Your volcanoes
outside? Your stars-- Ras Algethi? Antares raging south southeast?
Forgive me, no."
A Spanish-English dictionary:
lucero m.
morning or evening star:
any bright star....
hole in a window panel
for the admission of light....
Look at the way it
falls through the window....
-- Malcolm Lowry
How art thou fallen from heaven,
O Lucifer, son of the morning!
-- Isaiah 14:12
For more on Spanish
and the evening star,
see Plato, Pegasus, and
the Evening Star.
|
Symmetry axes
of the square:
(See Damnation Morning.)
From the cover of the
Martin Cruz Smith novel
Stallion Gate:
"That old Jew
gave me this here."
-- Dialogue from the
Robert Stone novel
A Flag for Sunrise.
Related material:
A Mass for Lucero,
Log24, Sept. 13, 2006--
-- and this morning's online
New York Times obituaries:
The above image contains summary obituaries for Cardinal
Lustiger, Archbishop of Paris, 1981-2005, and for Sal Mosca,
jazz pianist and teacher. In memory of the former, see all of the
remarks preceding the image above. In memory of the latter, the remarks
of a character in Martin Cruz Smith's Stallion Gate on jazz piano may have
some relevance:
"I
hate arguments. I'm a coward. Arguments are full of words, and each
person is sure he's the only one who knows what the words mean. Each
word is a basket of eels, as far as I'm concerned. Everybody gets to
grab just one eel and that's his interpretation and he'll fight to the
death for it.... Which is why I love music. You hit a C and it's a C
and that's all it is. Like speaking clearly for the first time. Like
being intelligent. Like understanding. A Mozart or an Art Tatum sits at
the piano and picks out the undeniable truth."
Sunday, August 5, 2007 7:00 PM
Smiles of a Summer Evening:
Lucero
"What
have I got out of my life? Contacts with famous men... The occasion
Einstein asked me the time, for instance. That summer evening....
smiles when I say I don't know. And yet asked me. Yes: the great Jew,
who has upset the whole world's notions of time and space, once leaned
down... to ask me... ragged freshman... at the first approach of the
evening star, the time. And smiled again when I pointed out the clock
neither of us had noticed."
To
Ride Pegasus, by Anne
McCaffrey, 1973:
"Mary-Molly
luv, it's going to be accomplished in steps, this establishment of the
Talented in the scheme of things. Not society, mind you, for we're the
original nonconformists.... and Society will never permit us to
integrate. That's okay!" He consigned Society to
insignificance with a
flick of his fingers. "The Talented form their own society and that's
as it should be: birds of a feather. No, not birds. Winged
horses! Ha!
Yes, indeed. Pegasus... the poetic winged horse of flights of fancy. A
bloody good symbol for us. You'd see a lot from the back of a winged
horse..."
From Holt Spanish and English Dictionary, 1955:
lucero m Venus
(as morning or evening star);
bright star...
star (in forehead of animal)....
Scarlett Johansson and friend
in "The Horse Whisperer" (1998)
Sunday, August 5, 2007 9:00 AM
MySpace and...
Saturday, August 4, 2007 8:00 AM
Annals of...
Law and Poetry
Robert Duvall and John Travolta
This entry is in memory of Robert E. Keeton, a "judge's judge" who
is the subject of an obituary in today's New York Times. Judge
Keeton died, according to the Times, on July 1. According
to Harvard Law School, the University of Texas Law School, and The Boston Globe, he died on July 2. Such
details can sometimes be important.
Friday, August 3, 2007 10:09 PM
Cheap Epiphany, continued...
From August 1 --
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? |
The following image
represents an epiphany
of sorts:
It contains the
"double cross" symbol
of Fritz Leiber's
Changewar stories;
the "double cross" is
also the traditional
eight-ray symbol of
the evening star--
the planet Venus.
Epiphanies due to Venus
are indeed sometimes
cheap... but not always.
For further details, see
and
Friday, August 3, 2007 2:02 PM
The Long Hello
Friday, August 3, 2007 8:09 AM
Final Arrangements, continued:
Every Picture
Tells a Story
New York Times online, August 3, 2007
As does
Kevin Cullen --
"Tommy Makem was
an Irish soul singer,
and souls don't die."
Cullen's statement
in picture form:
E is
for Everlast
Scene from "Million
Dollar Baby"
Log24
on July 30, 2005
Wednesday, August 1, 2007 9:29 PM
A Little Mystery:
"Let's give 'em somethin' to
talk about,
A little mystery to figure out"
(Scarlett Johansson singing on
Saturday Night Live, April 21, 2007)
A Midrash for Sid
Scene from "
Scoop" (2006)
Clues:
Today's previous entries,
Show Business
according to Fritz Leiber:
"Sid thinks you're ready for
some of the smaller parts,"
April 22, 2007, 11:09 AM:
Teaching a Brick to Sing,
April 22, 2007, 8:31 PM:
Welcome to the Cave,
and, in conclusion...
Shadows in the Cave--
Today's Pennsylvania lottery
and a midrash on
today's lottery:
527 --
5/27, 2005:
Drama of the Diagonal,
Part
Deux
and 168 --
December 25, 2005:
The Beauty of Klein's
Simple Group
(of order 168).
Wednesday, August 1, 2007 6:19 PM
Detail, continued:
Wednesday, August 1, 2007 8:00 AM
Annals of Prose Style
August First,
8:00:14 AM:
Cheap Epiphany
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? |
Pennsylvania
Lottery
on the Feast of
St. Ignatius Loyola:
|
 |
 |
Restoring the Booze:
A Look at the 50's-
Another Epiphany:
Box-style
I Ching, January 6, 1989
(Click on image for background.)
Detail:
Related material:
Logos
and Logic
and
Diagon Alley.
"What a swell
party
this is."
-- adapted from
Cole Porter
