Log24

Wednesday, December 19, 2007

Wednesday December 19, 2007

Filed under: General — Tags: — m759 @ 9:00 am
Tutelary Figures

An entry in memory of
Dr. Joseph L. Henderson,
Jungian analyst, who died
on Nov. 17 at 104

(An obituary appears in
today’s New York Times.)


Some remarks by Dr. Henderson
:

The myth of the hero is the most common and the best known myth in the world… classical mythology… Greece and Rome… Middle Ages… Far East… contemporary primitive tribes. It also appears in dreams… obvious dramatic… profound… importance. P. 101

… structurally very similar… universal pattern… over and over again… a tale of… miraculous… humble birth… early proof of superhuman strength… rapid rise to prominence… triumphant struggle with the forces of evil… fallibility to the sin of pride (hybris)… and his fall through betrayal or a “heroic” sacrifice that ends in his death. P. 101

… another important characteristic… provides a clue… the early weakness… is balanced by… strong “tutelary” figures… who enable him to perform the superhuman tasks that he cannot accomplish unaided. Theseus had Poseidon… Perseus had Athena… Achilles had Cheiron… the wise centaur, as his tutor. P. 101 

And Stan Carlisle had
Dr. Lilith Ritter
:

http://www.log24.com/log/pix07A/071219-StanLilith.jpg

See also the noir entry on
“Nightmare Alley” for
Winter Solstice 2002,
as well as a solstice-related
commentary on I Ching
Hexagram 41, Decrease.

Related material:

http://www.log24.com/log/pix07A/071219-Authors2.jpg

Dr. Dyane N. Sherwood and
Dr. Joseph L. Henderson, authors
of Transformation of the Psyche
(Routledge, Nov. 7, 2003)

Dr. Henderson is said to
have been, in his youth,
a student of Thornton Wilder
as well as of Dr. Jung.

Sunday, December 16, 2007

Sunday December 16, 2007

Filed under: General — Tags: , , — m759 @ 1:09 pm
 
Mad Phaedrus
Meets Mad Ezra

"Plato's Good was a fixed and eternal and unmoving Idea, whereas for the rhetoricians it was not an Idea at all. The Good was not a form of reality. It was reality itself, ever changing, ultimately unknowable in any kind of fixed, rigid way." –Phaedrus in Zen and the Art of Motorcycle Maintenance

This apparent conflict between eternity and time, fixity and motion, permanence and change, is resolved by the philosophy of the I Ching and by the Imagism of Ezra Pound.  Consider, for example, the image of The Well

as discussed here on All Saints' Day 2003 and in the previous entry.

As background, consider the following remarks of James Hillman in "Egalitarian Typologies Versus the Perception of the Unique," Part  III: Persons as Images

"To conceive images as static is to forget that they are numens that move.  Charles Olson, a later poet in this tradition, said:  'One perception must immediately and directly lead to a further perception… always, always one perception must must must move instanter, on another.' 80  Remember Lavater and his insistence on instantaneity for reading the facial image.  This is a kind of movement that is not narrational, and the Imagists had no place for narrative.  'Indeed the great poems to come after the Imagist period– Eliot’s The Waste Land and Four Quartets; Pound’s Cantos; Williams’s Paterson– contain no defining narrative.' 81  The kind of movement Olson urges is an inward deepening of the image, an in-sighting of the superimposed levels of significance within it. 82  This is the very mode that Jung suggested for grasping dreams– not as a sequence in time, but as revolving around a nodal complex.  If dreams, then why not the dreamers.  We too are not only a sequence in time, a process of individuation. We are also each an image of individuality."

   80  The New American Poetry (D. M. Allen, ed.) N.Y.: Evergreen, Grove, 1960, pp. 387-88. from Jones, p. 42.

81  Jones,* p. 40.

82  H. D. later turned narration itself into image by writing a novel in which the stories were "compounded like faces seen one on top of another," or as she says "superimposed on one another like a stack of photographic negatives" (Jones, p. 42).  Cf. Berry,** p. 63: "An image is simultaneous. No part precedes or causes another part, although all parts are involved with each other… We might imagine the dream as a series of superimpositions, each event adding texture and thickening to the rest."

    * Imagist Poetry (Peter Jones, ed.) London: Penguin, 1972

    ** The contrast between image simultaneity and narrative succession, and the different psychological effects of the two modes, is developed by Patricia Berry, "An Approach to the Dream," Spring 1974 (N. Y./Zürich: Spring Publ.), pp. 63, 68-71

Hillman also says that

"Jung’s 'complex' and Pound's definition of Image and Lavater's 'whole heap of images, thoughts, sensations, all at once' are all remarkably similar.  Pound calls an Image, 'that which presents an intellectual and emotional complex in an instant of time'… 'the Image is more than an Idea.  It is a vortex or cluster of fused ideas and is endowed with energy'… 'a Vortex, from which and through which, and into which, ideas are constantly rushing.' 79 Thus the movement, the dynamics, are within the complex and not only between complexes, as tensions of opposites told about in narrational sequences, stories that require arbitrary syntactical connectives which are unnecessary for reading an image where all is given at once."

79  These definitions of Image by Pound come from his various writings and can all be found in Jones, pp. 32-41.  Further on complex and image, see J. B. Harmer, Victory in Limbo: Imagism 1908-17, London: Secker & Warburg, 1975, pp. 164-68.

These remarks may help the reader to identify with Ada during her well-viewing in Cold Mountain (previous entry):

"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…."

If such complexity can be suggested by Hexagram 48, The Well, alone, consider the effect of the "cluster of fused ideas… endowed with energy" that is the entire 64-hexagram I Ching.
 

Related material: St. Augustine's Day 2006

Wednesday, October 31, 2007

Wednesday October 31, 2007

Filed under: General — m759 @ 8:28 pm
On Time


Anthony Hopkins on time:

"For me time is God, God is time…. I'm fascinated by the fact that we can't grasp anything about time. The magical, supernatural force that is with us every second is time." —Cinema Blend

"For me time is God, God is time. It's an equation, like an Einstein equation." —Washington Square News

A Marxist on time:

"God demands scrutiny beyond his menacingly comic aspects. Primarily, the [Saramago] Gospel 's God is time, and not truth, the other attribute he asserts. Saramago, a Marxist (an eccentric one), and not a Christian, subverts St. Augustine on the theodicy of time. If time is God, then God can be forgiven nothing, and who would desire to forgive him anyway?"

Harold Bloom on José Saramago's The Gospel According to Jesus Christ  (1991). Saramago was awarded the Nobel Prize in Literature in 1998.

Related material:

Augustine's Theodicy
and Joyce's Aesthetics,

Today's Sinner
(St. Augustine's Day, 2006),

Happy Halloween.

Monday, October 29, 2007

Monday October 29, 2007

Filed under: General — m759 @ 7:20 am
Home from Home

On Anthony Hopkins’s new film:

“At one point during ‘Slipstream,’ Hopkins’s character stumbles upon a Dolly Parton impersonator while Parton’s wonderful song, ‘Coat of Many Colors,’ plays on the soundtrack.  I told Hopkins that I thought he used the tune– which is about a multi-hued coat that little Dolly’s grandmother made for her out of random pieces of cloth when the future superstar’s family was dirt poor– as a sort of commentary on the patchwork structure of ‘Slipstream’ itself.  Hopkins smiled broadly and his eyes lit up.  Yes, he said, that’s exactly what he was doing.  He said he even tried to get Parton to appear in the movie, but she was booked and couldn’t do it.”

—  Paul Tatara, Oct. 22, 2007

Anthony Hopkins:

“Our existence is beyond understanding.  Nobody has an answer.  I sense that life is such a mystery.  To me, God is time.”

Related material:

“Have you ever worried about your memory, because it doesn’t seem to recall exactly the same past from one day to the next? Have you ever thought that the whole universe might be a crazy, mixed-up dream? If you have, then you’ve had hints of the Change War…

Spider and Snake on cover of Fritz Leiber's novel Big Time

It’s been going on for a billion years and it will last another billion or so. Up and down the timeline, the two sides– ‘Spiders’ and ‘Snakes’– battle endlessly to change the future and the past. Our lives, our memories, are their battleground. And in the midst of the war is the Place, outside space and time, where Greta Forzane and the other Entertainers provide solace and r-&-r for tired time warriors.”

— Publisher’s description of Fritz Leiber’s Big Time.

Dialogue from “Slipstream”

“My God, this place must be
a million years old!”

Anthony Hopkins at Dolly's Little Diner in Slipstream

“Dolly’s Little Diner–
Home from Home”

Meanwhile…

Country Star
Porter Wagoner, 80, Dies

Wallace Stevens,
“Country Words”–

“What is it that my feeling seeks?
I know from all the things it touched
And left beside and left behind.
It wants the diamond pivot bright.”

Wednesday, October 24, 2007

Wednesday October 24, 2007

Filed under: General,Geometry — Tags: , , , — m759 @ 11:11 pm
Descartes’s Twelfth Step

An earlier entry today (“Hollywood Midrash continued“) on a father and son suggests we might look for an appropriate holy ghost. In that context…

Descartes

A search for further background on Emmanuel Levinas, a favorite philosopher of the late R. B. Kitaj (previous two entries), led (somewhat indirectly) to the following figures of Descartes:

The color-analogy figures of Descartes
This trinity of figures is taken from Descartes’ Rule Twelve in Rules for the Direction of the Mind. It seems to be meant to suggest an analogy between superposition of colors and superposition of shapes.Note that the first figure is made up of vertical lines, the second of vertical and horizontal lines, and the third of vertical, horizontal, and diagonal lines. Leon R. Kass recently suggested that the Descartes figures might be replaced by a more modern concept– colors as wavelengths. (Commentary, April 2007). This in turn suggests an analogy to Fourier series decomposition of a waveform in harmonic analysis. See the Kass essay for a discussion of the Descartes figures in the context of (pdf) Science, Religion, and the Human Future (not to be confused with Life, the Universe, and Everything).

Compare and contrast:

The harmonic-analysis analogy suggests a review of an earlier entry’s
link today to 4/30–  Structure and Logic— as well as
re-examination of Symmetry and a Trinity


(Dec. 4, 2002).

See also —

A Four-Color Theorem,
The Diamond Theorem, and
The Most Violent Poem,

Emma Thompson in 'Wit'

from Mike Nichols’s birthday, 2003.

Friday, October 12, 2007

Friday October 12, 2007

Filed under: General — Tags: — m759 @ 9:10 am
From
A Harvard Education
in a Sentence:

“At times, bullshit can
only be countered
with superior bullshit.”

Norman Mailer,
Harvard ’43

Illustration from
today’s Crimson:

Nobel Laureate Morrison
Reads at Opening Event

Friday, October 12, 2007 3:17 AM

From the reserved elegance of Memorial Church to the sweeping grandeur of Sanders Theatre, the Harvard community honored 28th University President Drew G. Faust with two festive events on the eve of her inauguration.

Thursday, October 11, 2007

Thursday October 11, 2007

Filed under: General — Tags: , — m759 @ 9:26 pm
Words and Music
suggested by the recent
Princeton symposium
"Deep Beauty"

The image “http://www.log24.com/log/pix07A/071011-vonNeumann.jpg” cannot be displayed, because it contains errors.

1. From my childhood:

"You remind me of a man."
"What man?"
"The man with the power."
"What power?"
"The power of hoodoo."
"Hoodoo?"
"You do."
"Do what?
"Remind me of a man…."

— Dialogue from
"The Bachelor and the
Bobby-Soxer" (1947)

2.  From later years:

"When I was a little boy,
(when I was just a boy)
and the Devil would
call my name
(when I was just a boy)
I'd say 'now who do,
who do you think
you're fooling?'"

Paul Simon, 1973 

"At times, bullshit can
only be countered
with superior bullshit."
— Norman Mailer

(See A Harvard Education
in a Sentence.)

From Plato's Cave:

A description of caveman life
translated from German

John von
 Neumann

"Soon Freud, soon mourning,
Soon Fried, soon fight.
Nevertheless who know this language?"

(Language courtesy of
Google's translation software)

Picture of von Neumann courtesy of
Princeton University Library

More from Rhymin' Simon–

"one funny mofo"–

"Oh, my mama loves,
she loves me,
she get down on her knees
and hug me
like she loves me
like a rock.
She rocks me
like the rock of ages"

Related material:

The previous Log24 entries
of Oct. 7-11, 2007, and
the five Log24 entries
ending with "Toy Soldiers"
(Valentine's Day, 2003).

See also

"Taking Christ to the Movies,"
by Anna Megill, Princeton '06
.

Sunday, September 2, 2007

Sunday September 2, 2007

Filed under: General,Geometry — 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  
 

Tuesday, August 21, 2007

Tuesday August 21, 2007

Filed under: General — Tags: — m759 @ 3:29 pm
Shell Game

The Bourne Ultimatum, starring Matt Damon” cannot be displayed, because it contains errors.

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

Afterword:

See also
the recent comments
of root@matrix.net in
Peter Woit’s weblog.

“Hey, Carrie-Anne,
what’s your game now….”

— The Hollies, 1967   

Tuesday, July 24, 2007

Tuesday July 24, 2007

Filed under: General — m759 @ 7:11 am
The Church of St. Frank

See yesterday’s entries for
some relevant quotations
from Wallace Stevens.

Further quotations for what
Marjorie Garber, replying to
a book review by
Frank Kermode, has called
the Church of St. Frank“–

Frank Kermode on

Harold Bloom:

“He has… a great, almost
selfish passion for poetry,
and he interprets difficult
texts as if there were no
more important activity
in the world, which may
be right.”

Page 348 of Wallace Stevens:
The Poems of Our Climate
,
by Harold Bloom
(1977, Cornell U. Press):

“The fiction of the leaves is now Stevens’ fiction…. Spring, summer, and autumn adorn the rock of reality even as a woman is adorned, the principle being the Platonic one of copying the sun as source of all images….

… They are more than leaves
              that cover the barren rock….

They bear their fruit    
             so that the year is known….

If they are more than leaves, then they are no longer language, and the leaves have ceased to be tropes or poems and have become magic or mysticism, a Will-to-Power over nature rather than over the anteriority of poetic imagery.”

For more on magic, mysticism, and the Platonic “source of all images,” see Scott McLaren on “Hermeticism and the Metaphysics of Goodness in the Novels of Charles Williams.” McLaren quotes Evelyn Underhill on magic vs. mysticism:

The fundamental difference between the two is this: magic wants to get, mysticism wants to give […] In mysticism the will is united with the emotions in an impassioned desire to transcend the sense-world in order that the self may be joined by love to the one eternal and ultimate Object of love […] In magic, the will unites with the intellect in an impassioned desire for supersensible knowledge. This is the intellectual, aggressive, and scientific temperament trying to extend its field of consciousness […] (Underhill 84; see also 178ff.)

— Underhill, Evelyn. Mysticism: A Study in the Nature and Development of Man’s Spiritual Consciousness. New York: Dutton, 1911.

For more on what Bloom calls the “Will-to-Power over nature,” see Faust in Copenhagen and the recent (20th- and 21st-century) history of Harvard University. These matters are also discussed in “Log24 – Juneteenth through Midsummer Night.”

For more on what Underhill calls “the intellectual, aggressive, and scientific temperament trying to extend its field of consciousness,” see the review, in the August 2007 Notices of the American Mathematical Society, of a book by Douglas Hofstadter– a writer on the nature of consciousness— by magician Martin Gardner.

Monday, July 23, 2007

Monday July 23, 2007

Daniel Radcliffe
is 18 today.
Daniel Radcliffe as Harry Potter

Greetings.

“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”

Jorge Luis Borges, “Avatars of the Tortoise”

El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”

Jorge Luis Borges, “Los Avatares de la Tortuga

Autonomous Apparition

At Midsummer Noon:

“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.
Related material:
It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure 

Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit,

And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.

– Wallace Stevens, “The Rock”

See also
as well as
Hofstadter on
his magnum opus:
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
Goedel Escher Bach coverHofstadter’s cover.

Here are three patterns,
“shadows” of a sort,
derived from a different
“central object”:
Faces of Solomon's Cube, related to Escher's 'Verbum'

Click on image for details.

Saturday, July 21, 2007

Saturday July 21, 2007

Filed under: General — Tags: — m759 @ 9:45 am

Death of a Nominalist

“All our words from loose using have lost their edge.” –Ernest Hemingway

(The Hemingway quotation is from the AP’s “Today in History” on July 21, 2007; for the context, see Death in the Afternoon.)

Today seems as good a day as any for noting the death of an author previously discussed in Log24 on January 29, 2007, and January 31, 2007.

Joseph Goguen
died on July 3, 2006. (I learned of his death only after the entries of January 2007 were written. They still hold.)

Goguen’s death may be viewed in the context of the ongoing war between the realism of Plato and the nominalism of the sophists. (See, for instance, Log24 on August 10-15, 2004, and on July 3-5, 2007.)

Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf):

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.’ Similarly, the ‘situations’ in the situation semantics of Barwise and Perry, which resemble conceptual spaces (but are more sophisticated– perhaps too sophisticated), are considered to be actually existing, real entities [23], even though they may include what are normally considered judgements.5 The classical semiotics of Charles Sanders Peirce [24] also tends towards a Platonist view of signs. The viewpoint of this paper is that all formalisms are constructed in the course of some task, such as scientific study or engineering design, for the heuristic purpose of facilitating consideration of certain issues in that task. Under this view, all theories are situated social entities, mathematical theories no less than others; of course, this does not mean that they are not useful.”

5 The “types” of situation theory are even further removed from concrete reality.

[23] Jon Barwise and John Perry. Situations and Attitudes. MIT (Bradford), 1983.
[24] Charles Sanders Peirce. Collected Papers. Harvard, 1965. In 6 volumes; see especially Volume 2: Elements of Logic.

From Log24 on the date of Goguen’s death:

Requiem for a clown:

“At times, bullshit can only be
countered with superior bullshit.”

Norman Mailer

This same Mailer aphorism was quoted, along with an excerpt from the Goguen passage above, in Log24 this year on the date of Norman Mailer’s birth.  Also quoted on that date:

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God….

Whether the above excerpt– from Hans Christian Oersted‘s The Soul in Nature (1852)– is superior to the similar remark of Goguen, the reader may decide.

Tuesday, July 3, 2007

Tuesday July 3, 2007

Filed under: General — m759 @ 9:29 pm
The Ignorance
of Stanley Fish

(continued from
June 18, 2002)

The “ignorance” referred to
is Fish’s ignorance of the
philosophical background
of the words
“particular” and “universal.”

Postmodern Warfare:
The Ignorance of Our
Warrior Intellectuals,”
by Stanley Fish,
Harper’s Magazine,
July 2002, contains
the following passages:

“The deepest strain in a religion is the particular and particularistic doctrine it asserts at its heart, in the company of such pronouncements as ‘Thou shalt have no other Gods before me.’ Take the deepest strain of religion away… and what remains are the surface pieties– abstractions without substantive bite– to which everyone will assent because they are empty, insipid, and safe. It is this same preference for the vacuously general over the disturbingly particular that informs the attacks on college and university professors who spoke out in ways that led them to be branded as outcasts by those who were patrolling and monitoring the narrow boundaries of acceptable speech. Here one must be careful, for there are fools and knaves on all sides.”

“Although it may not at first be obvious, the substitution for real religions of a religion drained of particulars is of a piece with the desire to exorcise postmodernism.”

“What must be protected, then, is the general, the possibility of making pronouncements from a perspective at once detached from and superior to the sectarian perspectives of particular national interests, ethnic concerns, and religious obligations; and the threat to the general is posed by postmodernism and strong religiosity alike, postmodernism because its critique of master narratives deprives us of a mechanism for determining which of two or more fiercely held beliefs is true (which is not to deny the category of true belief, just the possibility of identifying it uncontroversially), strong religiosity because it insists on its own norms and refuses correction from the outside. The antidote to both is the separation of the private from the public, the establishing of a public sphere to which all could have recourse and to the judgments of which all, who are not criminal or insane, would assent. The point of the public sphere is obvious: it is supposed to be the location of those standards and measures that belong to no one but apply to everyone. It is to be the location of the universal. The problem is not that there is no universal–the universal, the absolutely true, exists, and I know what it is. The problem is that you know, too, and that we know different things, which puts us right back where we were a few sentences ago, armed with universal judgments that are irreconcilable, all dressed up and nowhere to go for an authoritative adjudication.

What to do? Well, you do the only thing you can do, the only honest thing: you assert that your universal is the true one, even though your adversaries clearly do not accept it, and you do not attribute their recalcitrance to insanity or mere criminality–the desired public categories of condemnation–but to the fact, regrettable as it may be, that they are in the grip of a set of beliefs that is false. And there you have to leave it, because the next step, the step of proving the falseness of their beliefs to everyone, including those in their grip, is not a step available to us as finite situated human beings. We have to live with the knowledge of two things: that we are absolutely right and that there is no generally accepted measure by which our rightness can be independently validated. That’s just the way it is, and we should just get on with it, acting in accordance with our true beliefs (what else could we do?) without expecting that some God will descend, like the duck in the old Groucho Marx TV show, and tell us that we have uttered the true and secret word.”

From the public spheres
of the Pennsylvania Lottery:

PA Lottery logo

PA Lottery July 3, 2007: Mid-day 105, Evening 268

105 —

Log24 on 1/05:

“‘From your lips
to God’s ears,’
 goes the old
Yiddish wish.

 The writer, by contrast,
tries to read God’s lips
and pass along
the words….”

— Richard Powers   

268 —

This is a page number
that appears, notably,
in my June 2002
journal entry on Fish
,
and again in an entry,
The Transcendent Signified,”
dated July 26, 2003,
that argues against
Fish’s school, postmodernism,
 and in favor of what the pomos
call “logocentrism.”

Page 268
 
of Simon Blackburn’s Think
(Oxford Univ. Press, 1999):

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Fish may, if he wishes,
regard the particular
page number 268 as
delivered– five years late,
but such is philosophy–
by Groucho’s
winged messenger
in response to
Fish’s utterance of the
  “true and secret word”–
namely, “universal.”

When not arguing politics,
Fish, though from
a Jewish background, is
 said to be a Milton scholar.
Let us therefore hope he
is by now, or comes to be,
aware of the Christian
approach to universals–
an approach true to the
philosophical background
sketched in 1999 by
Blackburn and made
particular in a 1931 novel
 by Charles Williams,
The Place of the Lion.

Sunday, July 1, 2007

Sunday July 1, 2007

Filed under: General,Geometry — m759 @ 1:27 pm
Mozart
by the Numbers

PA Lottery June 30, 2007: Mid-day 221, Evening 127

2/21


A Superficial Beauty:

Structural Certainty:

murphy plant, murphy grow, a maryamyria- 10
meliamurphies, in the lazily eye of his lapis, 11

12
Geometry lesson 13

14
Uteralterance or Vieus Von DVbLIn, ’twas one of dozedeams 15
the Interplay of a darkies ding in dewood) the Turnpike under 16
Bones in the the Great Ulm (with Mearingstone in Fore 17
Womb. ground). 1 Given now ann linch you take enn 18
all. Allow me! And, heaving alljawbreakical 19
expressions out of old Sare Isaac’s 2 universal 20
The Vortex. of specious aristmystic unsaid, A is for Anna 21
Spring of Sprung like L is for liv. Aha hahah, Ante Ann you’re 22
Verse. The Ver- apt to ape aunty annalive! Dawn gives rise. 23
tex. Lo, lo, lives love! Eve takes fall. La, la, laugh 24
leaves alass! Aiaiaiai, Antiann, we’re last to 25
the lost, Loulou! Tis perfect. Now (lens 26

Finnegans Wake, Book II,
    Episode 2, page 293


1/27

“Mozart is a menace to musical progress, a relic of rituals that were losing relevance in his own time and are meaningless to ours. Beyond a superficial beauty and structural certainty, Mozart has nothing to give to mind or spirit in the 21st century. Let him rest.” —Norman Lebrecht

Sunday, June 24, 2007

Sunday June 24, 2007

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm
Raiders of
the Lost Stone

(Continued from June 23)

Scott McLaren on
Charles Williams:
 
"In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew
from a brief description in Waite's
The Holy Kabbalah (1929)
of a supernatural cubic stone
on which was inscribed
'the Divine Name.'"

The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.

Related material:

The image “http://www.log24.com/log/pix07/070624-Cube.gif” cannot be displayed, because it contains errors.

Solomon's Cube,

Geometry of the 4x4x4 Cube,

The Klein Correspondence,
Penrose Space-Time,
and a Finite Model

Wednesday, June 20, 2007

Wednesday June 20, 2007

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

Kernel

Mathematical Reviews citation:

MR2163497 (2006g:81002) 81-03 (81P05)
Gieser, Suzanne The innermost kernel. Depth psychology and quantum physics. Wolfgang Pauli's dialogue with C. G. Jung. Springer-Verlag, Berlin, 2005. xiv+378 pp. ISBN: 3-540-20856-9

A quote from MR at Amazon.com:

"This revised translation of a Swedish Ph. D. thesis in philosophy offers far more than a discussion of Wolfgang Pauli's encounters with the psychoanalyst Carl Gustav Jung…. Here the book explains very well how Pauli attempted to extend his understanding beyond superficial esotericism and spiritism…. To understand Pauli one needs books like this one, which… seems to open a path to a fuller understanding of Pauli, who was seeking to solve a quest even deeper than quantum physics." (Arne Schirrmacher, Mathematical Reviews, Issue 2006g)
 

An excerpt:

 

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

I do not yet know what Gieser means by "the innermost kernel." The following is my version of a "kernel" of sorts– a diagram well-known to students of anthropologist Claude Levi-Strauss and art theorist Rosalind Krauss:

The four-group is also known as the Vierergruppe or Klein group.  It appears, notably, as the translation subgroup of A, the group of 24 automorphisms of the affine plane over the 2-element field, and therefore as the kernel of the homomorphism taking A to the group of 6 automorphisms of the projective line over the 2-element field. (See Finite Geometry of the Square and Cube.)

Related material:

The "chessboard" of
   Nov. 7, 2006
(as revised Nov. 7, 2012)–

I Ching chessboard. Previous version replaced on Nov. 7, 2012, by original 1989 chessboard arrangement

I Ching chessboard

None of this material really has much to do with the history of physics, except for its relation to the life and thought of physicist Wolfgang Pauli— the "Mephistopheles" of the new book Faust in Copenhagen. (See previous entry.)

"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
 

Saturday, May 26, 2007

Saturday May 26, 2007

Filed under: General — m759 @ 1:09 pm

A Baffled Reader

A reader this morning commented on my first Xanga entry (July 20, 2002):

“To set one up (which I have not done because I don’t want anyone to know what I think),” … William Safire regarding “blogs”.

I still don’t know what you think.  Yet … I try, try, try.

Here’s one thing that I think– today– based on my “Hate Speech for Harvard,” on “Devil in the Details” (Log24, May 18 and 23), and, more recently, on

  1. last evening’s PA lottery number 005,
  2. the I Ching hexagram of the same number, and
  3. the New Yorker issue linked to at the end of the previous entry:
Revised New Yorker cover from 5/21/07
Revised version of the
New Yorker cover of 5/21/07
Commentary on the cover
by the PA lottery
on 5/25/07
in the form of the
evening number, 005.
In the I Ching, this
is the number of

HSU:
WAITING
(NOURISHMENT)

See also the previous entry
and Natalie Angier’s sneer
at a politician’s call for
prayer, which, she
said, involved the
“assumption that prayer is
some sort of miracle
Vicks VapoRub.”

Detail from the
5/21/07 New Yorker:

Detail, New Yorker cover, 5/21/07

THE IMAGE

Hexagram 5: Waiting (Nourishment)

Clouds rise up to heaven:
The image of WAITING.
Thus the superior man
eats and drinks,
Is joyous and
of good cheer.

AMEN.

Friday, May 25, 2007

Friday May 25, 2007

Filed under: General,Geometry — Tags: , , , , — m759 @ 7:11 am
Dance and the Soul

From Log24 on
this date last year:

"May there be an ennui
of the first idea?
What else,
prodigious scholar,
should there be?"

— Wallace Stevens,
"Notes Toward a
Supreme Fiction"

The Associated Press,
May 25, 2007–

Thought for Today:
"I hate quotations.
 Tell me what you know."
— Ralph Waldo Emerson

[Journals, on May 3, 1849]

The First Idea:

The Line, by S. H. Cullinane

Four Elements:
 

Four Elements (Diamond)

Square Dance:

Square Dance (Diamond Theorem)

This "telling of what
I know" will of course
mean little to those
who, like Emerson,
have refused to learn
through quotations.

For those less obdurate
than Emerson —Harold Bloom
on Wallace Stevens

and Paul Valery's
   "Dance and the Soul"–

"Stevens may be playful, yet seriously so, in describing desire, at winter's end, observing not only the emergence of the blue woman of early spring, but seeing also the myosotis, whose other name is 'forget-me-not.' Desire, hearing the calendar hymn, repudiates the negativity of the mind of winter, unable to bear what Valery's Eryximachus had called 'this cold, exact, reasonable, and moderate consideration of human life as it is.' The final form of this realization in Stevens comes in 1950, in The Course of a Particular, in the great monosyllabic line 'One feels the life of that which gives life as it is.' But even Stevens cannot bear that feeling for long. As Eryximachus goes on to say in Dance and the Soul:

A cold and perfect clarity is a poison impossible to combat. The real, in its pure state, stops the heart instantaneously….[…] To a handful of ashes is the past reduced, and the future to a tiny icicle. The soul appears to itself as an empty and measurable form. –Here, then, things as they are come together, limit one another, and are thus chained together in the most rigorous and mortal* fashion…. O Socrates, the universe cannot for one instant endure to be only what it is.

Valery's formula for reimagining the First Idea is, 'The idea introduces into what is, the leaven of what is not.' This 'murderous lucidity' can be cured only by what Valery's Socrates calls 'the intoxication due to act,' particularly Nietzschean or Dionysiac dance, for this will rescue us from the state of the Snow Man, 'the motionless and lucid observer.'" —Wallace Stevens: The Poems of Our Climate

* "la sorte… la plus mortelle":
    mortal in the sense
   "deadly, lethal"

Other quotations

(from March 28,
the birthday of
Reba McEntire):

Logical Songs

Reba McEntire, Saturday Evening Post, Mar/Apr 1995

Logical Song I
(Supertramp)

"When I was young, it seemed that
Life was so wonderful, a miracle,
Oh it was beautiful, magical
And all the birds in the trees,
Well they'd be singing so happily,
Joyfully, playfully watching me"

Logical Song II
(Sinatra)

"You make me feel so young,
You make me feel like
Spring has sprung
And every time I see you grin
I'm such a happy in-
dividual….

You and I are
Just like a couple of tots
Running across the meadow
Picking up lots
Of forget-me-nots"

Wednesday, March 28, 2007

Wednesday March 28, 2007

Filed under: General — m759 @ 1:00 pm
Logical Songs

Reba McEntire, Saturday Evening Post, Mar/Apr 1995

Logical Song I
(Supertramp)

“When I was young, it seemed that
Life was so wonderful, a miracle,
Oh it was beautiful, magical
And all the birds in the trees,
Well they’d be singing so happily,
Joyfully, playfully watching me”

Logical Song II
(Sinatra)

“You make me feel so young,
You make me feel like
Spring has sprung
And every time I see you grin
I’m such a happy in-
dividual….

You and I are
Just like a couple of tots
Running across the meadow
Picking up lots
Of forget-me-nots

Saturday, March 10, 2007

Saturday March 10, 2007

Filed under: General,Geometry — m759 @ 9:00 am

The Logic of Dreams

From A Beautiful Mind–

“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”

Ideas:

The image “http://www.log24.com/log/pix07/070309-NYlottery.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070309-PAlottery.jpg” cannot be displayed, because it contains errors.

These numbers may, in the mad way so well portrayed by Sylvia Nasar in the above book, be regarded as telling a story… a story that should, of course, not be taken too seriously.

Friday’s New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11.  Clicking on these dates will lead the reader to Log24 entries featuring, among others, T. S. Eliot and Stephen King– two authors not unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:

Chessboard (Detail)

This illustration refers to chess rather than to geometry, and to the mind of an addict rather than to that of a slave, but chess and geometry, like addiction and slavery, are not unrelated.


Friday’s Pennsylvania numbers, midday 429 and evening 038, suggest that the story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“–  “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)

Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).

More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.

Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:

The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Wednesday, January 31, 2007

Wednesday January 31, 2007

Filed under: General — Tags: — m759 @ 3:09 pm
Ontotheology

“At times, bullshit can only be
countered with superior bullshit.”
Norman Mailer

“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.'”

— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)

Goguen does not give a source for this alleged “thoughts of God” statement.

A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.

Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.

Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.

Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.

Gudder may have been misquoting some other author’s blather about Kepler.  Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature

“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?

Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of  Nature.

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”

Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.

The image “http://www.log24.com/log/pix07/070131-OerstedGudder.jpg” cannot be displayed, because it contains errors.

Friday, December 29, 2006

Friday December 29, 2006

Filed under: General — Tags: , — m759 @ 11:01 am
Tools
of Christ Church

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

Cover of Thomas, by Shelley Mydans: Sword and its shadow, a cross

Click on picture for details.

Today is the feast
of St. Thomas Becket.

In his honor, a meditation
on tools and causation:

"Lewis Wolpert, an eminent developmental biologist at University College London, has just published Six Impossible Things Before Breakfast, a pleasant, though rambling, look at the biological basis of belief. While the book focuses on our ability to form causal beliefs about everyday matters (the wind moved the trees, for example), it spends considerable time on the origins of religious and moral beliefs. Wolpert defends the unusual idea that causal thinking is an adaptation required for tool-making. Religious beliefs can thus be seen as an odd extension of causal thinking about technology to more mysterious matters. Only a species that can reason causally could assert that 'this storm was sent by God because we sinned.' While Wolpert's attitude toward religion is tolerant, he's an atheist who seems to find religion more puzzling than absorbing."

Review by H. Allen Orr in
The New York Review of Books,
Vol. 54, No. 1, January 11, 2007    


"An odd extension"–

Wolpert's title is, of course,
from Lewis Carroll.

Related material:

"It's a poor sort of memory
that only works backwards."
Through the Looking-Glass

An event at the Kennedy Center
broadcast on
December 26, 2006
(St. Steven's Day):

"Conductor John Williams, a 2004 Honoree, says, 'Steven, sharing our 34-year collaboration has been a great privilege for me. It's been an inspiration to watch you dream your dreams, nurture them and make them grow. And, in the process, entertain and edify billions of people around the world. Tonight we'd like to salute you, musically, with a piece that expresses that spirit beautifully … It was written by Leonard Bernstein, a 1980 Kennedy Center Honoree who was, incidentally, the first composer to be performed in this hall.' Backed by The United States Army Chorus and The Choral Arts Society, soprano Harolyn Blackwell and tenor Gregory Turay sing the closing number for Spielberg's tribute and the gala itself. It's the finale to the opera 'Candide,' 'Make Our Garden Grow,' and Williams conducts."

CBS press release

See also the following,
from the conclusion to

"Mathematics and Narrative"

(Log24, Aug. 22, 2005):

Diamond on cover of Narrative Form, by Suzanne Keen

"At times, bullshit can
only be countered
   with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to at least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

"Il faut cultiver notre jardin."
— Voltaire

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

Diamond in a square

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
 Regius Professor of Divinity,
  Christ Church College, Oxford
(the home of Lewis Carroll)

For further details,
click on the
Christ Church diamond.

Tuesday, November 28, 2006

Tuesday November 28, 2006

Filed under: General — m759 @ 9:00 am
Christkindl

“Christmas markets have been part of this festive time for centuries in Germany. They were usually held in front of churches and were looked at as part of a church visit. The oldest recorded market dates to 1310 in Munich, Germany. It was called Nikolausdult and was very different from the markets of today. It was an opportunity for farmers to come to town, do some shopping and at the same time, offer their wares.

The reformation of the church in the 16th century brought changes to the Christmas markets. Nikolaus was replaced by the Christkindl (Christchild) as the gift giver and the Nikolaus markets became Christkindl markets. This custom began in the Protestant areas of Bavaria with Nuremberg being the first city to call its market Christkindlesmarkt. Munich, a Catholic city, changed its Nikolausdult to Christkindlmarkt in 1805.”

Background for Christkindl Market in Kitchener, Ontario

This will also serve as background for today’s New York Times story on Chicago’s Christkindlmarkt:

“The Christkindl, the Christmas Fairy, is a cherished highlight during the Holiday Tree Lighting. The Christmas Fairy proclaims the opening of Christkindlmarket Chicago.”

Also from the official Chicago Christkindl website:

On the “Christkindl,” the Christmas Fairy & our sister-market visit

  • www.christkindlesmarkt.de

    The famous “Christkindl,” the Christmas Fairy, is the trademark of Christkindlmarket Chicago and its sister-market Christkindlesmarket Nürnberg, Germany

In its English version, the Nuremberg website calls the alleged “Christmas Fairy” an angel:

“The Nuremberg Christmas Angel with her white and golden dress, long blond curls and her golden crown, has been the symbol for the Christmas Market for many decades. During Advent time, the Christmas Angel is the most important representative of the city and of the traditional Christmas Market.

Every year, on the Friday before the first Advent Sunday, the Nuremberg Christmas Angel opens the Nuremberg Christmas Market by reciting a solemn prologue.”

The German version of the Nuremberg site calls the Christmas Angel the Christkind (Christ Child).  This confusion of the Christ Child with a supernatural bringer of gifts– hence, later, an angel, and, in Chicago, a fairy– is said to have originated with Martin Luther.

From a Radio Deutsche Welle website–

Nuremberg, City of Angels

The making of a myth

 

The Christkind was originally introduced in the 16th century by religious reformer Martin Luther.  Until then, it was always Saint Nicholas who brought gifts on Dec. 6.  But as Protestants can’t have saints, Luther needed a new Christmas tradition for his followers. “Luther wanted to move the gift-giving away from the Catholic holiday on Dec. 6,” said Nuremberg tourism manager Michael Weber. “So he reinvented the tradition for Protestants by moving it to Christmas Eve and making the Christkind— really, the baby Jesus– the person who brought the gifts.”

 

It was under the rule of the National Socialists that the image of today’s Christkind was ultimately anchored in the collective German mind.  They built on Nuremberg’s tradition of producing tinsel angels, and in 1933, had a young girl in an angel costume open the city’s Christmas Market for the first time.  After the second World War, Nuremberg’s tinsel angels became simply the Nuremberg Christkind, and the figures were sold nation-wide. 

Here is the banner for the Nuremberg site:

The image “http://www.log24.com/log/pix06B/061128-Nuremberg2.jpg” cannot be displayed, because it contains errors.

  The banner reads:
Nuremberg Christkindlesmarkt–
Where the Christ Child
is at home

Maybe.

Sunday, October 29, 2006

Sunday October 29, 2006

Filed under: General — Tags: — m759 @ 1:00 am
Decrease
 
(Readings for the
Halloween season)


In 1692 on July 31, at the time of the Salem witchcraft trials, Increase Mather reportedly "delivered a sermon… in Boston in which he posed the question… 'O what makes the difference between the devils in hell and the angels of heaven?'"

Increase, the father of Cotton Mather, was president of Harvard from June 27, 1692, to Sept. 6, 1701.  His name is memorialized by Harvard's Mather House.

From Log24 on Jan. 15, 2003:

Locating Hell

"Noi siam venuti al loco ov' i' t'ho detto
            che tu vedrai le genti dolorose
    c'hanno perduto il ben de l'intelletto
."

Dante, Inferno, Canto 3, 16-18

"We have come to where
              I warned you we would find
Those wretched souls
              who no longer have 
The intellectual benefits of the mind."

Dante, Hell, Canto 3, 16-18

From a Harvard student's weblog:

Heard in Mather  I hope you get gingivitis You want me to get oral cancer?! Goodnight fartface Turd. Turd. Turd. Turd. Turd. Make your own waffles!! Blah blah blah starcraft blah blah starcraft blah starcraft. It's da email da email. And some blue hair! Oohoohoo Izod! 10 gigs! Yeah it smells really bad. Only in the stairs though. Starcraft blah blah Starcraft fartface. Yeah it's hard. You have to get a bunch of battle cruisers. 40 kills! So good! Oh ho ho grunt grunt squeal.  I'm getting sick again. You have a final tomorrow? In What?! Um I don't even know. Next year we're draggin him there and sticking the needle in ourselves. 

" … one more line/ unravelling from the dark design/ spun by God and Cotton Mather"

— Robert Lowell

 

 

To honor Harvard's Oct. 28 founding,
here are yesterday's numbers from
the state of Grace (Kelly, of Philadelphia):

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Related material:

Log24 on 1/16,
and Hexagram 41,

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Decrease

The Image

At the foot of the mountain, the lake:
The image of Decrease.
Thus the superior man controls his anger
And restrains his instincts.

This suggests thoughts of
the novel Cold Mountain
 (see yesterday morning)
and the following from
Log24 on St. Luke's Day
this year:

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Lucero as portrayed by Megan Follows
Established in 1916,
Montreat College
is a private, Christian
college located in a
beautiful valley in the
Blue Ridge Mountains
of North Carolina.

From Nell:

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"The valley spirit never dies…"

See also St. Luke's Day, 2004,
as well as a journal entry
prompted by both
the ignorant religion
of Harvard's past
and the ignorant scientism
of Harvard's present–
 Hitler's Still Point:
A Hate Speech for Harvard
.

This last may, of course, not
quite fit the description of
the superior man
controlling his anger
so wisely provided by
yesterday's lottery and
Hexagram 41.
Nobody's perfect.

Tuesday, October 24, 2006

Tuesday October 24, 2006

Filed under: General — Tags: — m759 @ 2:56 pm

Critical Mass

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Thanks to University Diaries for
yesterday's entry on Harvard:

"I wonder if there's just been a critical mass of creepy stories about Harvard in the last couple of years… A kind of piling on of nastiness and creepiness…"

See also the previous Log24 entry, on yesterday's Pennsylvania lottery, and this description of an experiment I remember fondly from my youth:

"The floor in a large room was covered with mouse traps that were 'cocked' and on each was placed a ping pong ball. At the key moment an additional ping pong ball was tossed out and triggered a single mouse trap to go off. The net result after the balls started bouncing was a classic chain reaction."

"I thought Christmas
comes but once a year."
James Bond
 

Tuesday, September 26, 2006

Tuesday September 26, 2006

Filed under: General — m759 @ 8:48 am
Today’s Birthdays:
T. S. Eliot and Linda Hamilton

From Eliot’s
Ash Wednesday“–

“Prophesy to the wind,
    to the wind only for only
The wind will listen.
    And the bones sang chirping
With the burden of the grasshopper,
    saying….”         

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From The Man in the High Castle:

“Juliana said, ‘Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?’

‘You have a disconcertingly superstitious way of phrasing your question,’ Hawthorne said. But he had squatted down to witness the coin throwing. ‘Go ahead,’ he said; he handed her three Chinese brass coins with holes in the center. ‘I generally use these.’

She began throwing the coins; she felt calm and very much herself. Hawthorne wrote down her lines for her. When she had thrown the coins six times, he gazed down and said:

‘Sun at the top. Tui at the bottom. Empty in the center.’

‘Do you know what hexagram that is?’ she said. ‘Without using the chart?’

‘Yes,’ Hawthorne said.

‘It’s Chung Fu,’ Juliana said. ‘Inner Truth. I know without using the chart, too. And I know what it means.'”

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Our Lady of
Judgment Day

“One of the illusions is that the present hour is not the critical, decisive hour. Write it on your heart that every day is the best day in the year. No man has learned anything rightly until he knows that every day is Doomsday.”

Emerson, Ch. VII, “Works and Days,” in The Complete Works of Ralph Waldo Emerson, Vol. VII, Society and Solitude (1870)

Monday, September 18, 2006

Monday September 18, 2006

Filed under: General — Tags: — m759 @ 9:14 am
Apology

 

Excerpts from
Log 24, January 18, 2004:

 
A Living Church

"Plato has told you a truth; but Plato is dead. Shakespeare has startled you with an image; but Shakespeare will not startle you with any more. But imagine what it would be to live with such men still living. To know that Plato might break out with an original lecture to-morrow, or that at any moment Shakespeare might shatter everything with a single song. The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast. He is always expecting to see some truth that he has never seen before."

— G. K. Chesterton, Orthodoxy

C. P. Snow on G. H. Hardy in the foreword to A Mathematician's Apology:

"… he had another favourite entertainment…."

… If, as Chesterton might surmise, he… met Plato and Shakespeare in Heaven, the former might discuss with him the eternal Platonic form of the number 17*, while the latter might offer….

* Footnote of 9/18/06: For the Platonic form of 17, see Feast of the Triumph of the Cross (9/14/06) and Medal (9/15/06).

A Living Church,
continued…

Apology:
An Exercise in Rhetoric

Related material:


MOVIE RELEASED
ON 6-6-6 —


"Seamus Davey-Fitzpatrick stars in a scene from the R-rated movie 'The Omen.' An official of the Australian bishops conference took on the superstition surrounding the movie's release date of June 6, 2006, noting that 'I take evil far too seriously to think "The Omen" is telling me anything realistic or important.'" (CNS/20th Century Fox)

and

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Thursday, August 31, 2006

Thursday August 31, 2006

Filed under: General — Tags: , — m759 @ 11:09 pm
Wag the Dogma
(continued from 2001)
Ingrid Thulin and
Glenn Ford in
“The 4 Horsemen
of the Apocalypse”:

The 4 Horsemen, Ingrid Thulin, Glenn Ford

A sneering review from TIME Magazine, March 23, 1962:

“Hero Ford, a playboy from Argentina, falls pampassionately in love with Heroine Thulin, a Parisienne married to a patriotic editor. When the editor joins the Resistance, the hero realizes his duty and secretly does the same. Unaware of his decision, the heroine decides that he is merely a lightweight, and goes back to her husband. At the fade, while the violins soar among the bomb bursts, the poor misunderstood playboy dies heroically in an attempt to weaken the Wehrmacht’s defenses in Normandy.

The tale is trite, the script clumsy, and the camera work grossly faked. Though the lovers wander all over Paris, the Cathedral of Notre Dame turns up in the background practically everywhere they go, almost as if it were following them around like a little dog.”

TIME Magazine is still wearing the Ivy League sneer it displayed so impressively in 1962.

A less dismissive summary from Answers.com:

“The World War I setting of the original Blasco-Ibanez novel has been updated to World War II, but the basic plot remains the same. A well-to-do Argentinian family, rent asunder by the death of patriarch Lee J. Cobb, scatters to different European countries in the late 1930s. Before expiring, Cobb had warned his nephew Carl Boehm that the latter’s allegiance to the Nazis would bring down the wrath of the titular Four Horsemen: War, Conquest, Famine and Death. Ford, Cobb’s grandson, has promised to honor his grandfather’s memory by thwarting the plans of Boehm. At the cost of his own life, Ford leads allied bombers to Boehm’s Normandy headquarters.”

In memory of Glenn Ford, a talented character actor who died at 90 yesterday, the opening paragraphs of an obituary in The Scotsman:

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Screen icon Glenn Ford
dies at 90

RHIANNON EDWARD

GLENN Ford, one of the most enduring stars of the silver screen, has died at the age of 90.

Ford, who appeared in more than 200 films in a career spanning five decades, died at his home in Beverly Hills.

The actor’s health had been in decline for a number of years after he suffered a series of strokes.

Although he never achieved the superstardom he craved, Ford was widely acclaimed as one of the best character actors in the business.

The business of narrative:

From a narrative suggested by the name of The Scotsman‘s reporter and related, if only by association with Normandy, to Ford’s “Four Horsemen” film:

“The Vandaleurs are a family of Norman nobles with a heritable version of the mages’ Gift. They have been using magic covertly for what appears to have been a very long time…. Another branch of the family is known to hold a fief in Normandy, but it is not yet known if they are covert magicians as well.”

The Vandaleur narrative may be of interest to fans of The Da Vinci Code. (Ford is said to have been a Freemason, a charter member of Riviera Lodge No. 780, Pacific Palisades, California.)

For Catholics and others who prefer more traditional narratives:

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 Illuminated parchment,
1047 A.D.,
The Four Horsemen
of the Apocalypse

Related material:

Yesterday’s entries, and
an entry from April 7. 2003,
that they link to:

Mathematics and The Seventh Seal

Wednesday, August 30, 2006

Wednesday August 30, 2006

Filed under: General,Geometry — Tags: , — m759 @ 10:07 am
The Seventh Symbol:

A Multicultural Farewell

to a winner of the
Nobel Prize for Literature,
the Egyptian author of
The Seventh Heaven:
Supernatural Stories
 —

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"Jackson has identified
the seventh symbol."
Stargate

Other versions of
the seventh symbol —

Chinese version:

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pictorial version:

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algebraic version:

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"… Max Black, the Cornell philosopher, and others have pointed out how 'perhaps every science must start with metaphor and end with algebra, and perhaps without the metaphor there would never have been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962, page 242, as quoted in Dramas, Fields, and Metaphors, by Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25

Saturday, August 19, 2006

Saturday August 19, 2006

Filed under: General — Tags: — m759 @ 4:28 pm
Metaphysical
Wonderlands

"With no means to verify its truth, superstring theory, in the words of Burton Richter, director emeritus of the Stanford Linear Accelerator Center, may turn out to be 'a kind of metaphysical wonderland.' Yet it is being pursued as vigorously as ever, its critics complain, treated as the only game in town."

— "The Inelegant Universe," by George Johnson, in the Sept. 2006 Scientific American

Some may prefer metaphysics of a different sort:

"To enter Cervantes’s world, we cross a threshold that is Shakespearean and quixotic into a metaphysical wonderland where time expands to become space and vast vaulted distances bend back on themselves, where the threads of fiction and the strands of history shuttle back and forth in the great loom of the artist’s imagination."

As wonderlands go, I personally prefer Clive Barker's Weaveworld.
 

Friday, August 11, 2006

Friday August 11, 2006

Filed under: General — Tags: — m759 @ 11:07 pm

Under God

Adapted from August 7:

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“Saomai, the Vietnamese name
for the planet Venus, was the
eighth major storm to hit China
during an unusually violent
typhoon season.”

AP online tonight 

Memorable Quotes 

Lieutenant Daniel Taylor:
Where the Hell is
this God of yours?
 
Forrest Gump:
[narrating]
It’s funny Lieutenant Dan
said that, ’cause right then,
God showed up.

 Wind and thunder:
the image of Increase.
Thus the superior man:
If he sees good,
he imitates it;
If he has faults,
he rids himself of them.

Hexagram 42 

For further details,
see
recent entries
(August 7-11)
and also

Symmetry and Change
In the Dreamtime
.

Update of 1:06 AM ET
from KHYI:

Mercy Now 
Written by Mary Gauthier

My father could use a little mercy now
The fruits of his labor
Fall and rot slowly on the ground
His work is almost over
It won’t be long and he won’t be around
I love my father, and he could use some mercy now

My brother could use a little mercy now
He’s a stranger to freedom
He’s shackled to his fears and doubts
The pain that he lives in is
Almost more than living will allow
I love my brother, and he could use some mercy now

My church and my country could use a little mercy now
As they sink into a poisoned pit
That’s going to take forever to climb out
They carry the weight of the faithful
Who follow them down
I love my church and country, and they could use some mercy now

Every living thing could use a little mercy now
Only the hand of grace can end the race
Towards another mushroom cloud
People in power, well
They’ll do anything to keep their crown
I love life, and life itself could use some mercy now

Yeah, we all could use a little mercy now
I know we don’t deserve it
But we need it anyhow
We hang in the balance
Dangle ‘tween hell and hallowed ground
Every single one of us could use some mercy now
Every single one of us could use some mercy now
Every single one of us could use some mercy now

Wednesday, August 9, 2006

Wednesday August 9, 2006

Filed under: General — m759 @ 10:00 pm

Night Listener
 
(See previous entry.)

Thanks to Natalie at
KHYI, 95.3 FM, Plano, Texas
(hard country music),
for just now playing
A Fine Line, by Radney Foster:

There’s a curve in the highway, just south of town
where a man has pulled over to figure life out
with only his concience and the lonesome sound
of diesels winding up grade
he’s got a wife and two kids, and they love him so
he’s got a woman down in georgia,
   and she’s startin’ to show
he’s damned if he leaves her,
   and he’s sure damned if he don’t
and he wonders how life got this way
cuase it’s a fine line in between right and wrong
yea he’s been crossing over that border
   way too long
he should’ve seen it coming at him
   right from the start
now there aint’ no escape from a broken heart
now the call of the highway is a powerful thing
like the pull of a lover, or a child in a swing
gave his heart to two women
   only one wears his ring
they’re both gonna have his babies now
so how do you confess,
   what words don’t explain
he never intended to cause this much pain
now he feels like a farmer
   who went praying for the rain
got more than he bargained from the clouds
[chorus]
he’ll turn his car around tonight,
   go home and try to face the truth
everyone involved’s getting hurt,
   now there aint nothing he can do
[chorus]

Wind and thunder:
the image of Increase.
Thus the superior man:
If he sees good,
he imitates it;
If he has faults,
he rids himself of them.

Hexagram 42

  (10:00:42 PM ET)

Update of 11:08 PM ET…

and, Natalie, for playing
Late Night Grande Hotel
just now, thanks big time.

Monday, July 3, 2006

Monday July 3, 2006

Filed under: General — Tags: — m759 @ 10:13 am
Requiem for a Clown

For Jan Murray,
who died yesterday–


Into the Sunset, Part I:

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Into the Sunset, Part II:

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Requiem for a clown:

“At times, bullshit can only be
countered with superior bullshit.”

Norman Mailer

See also 10/13.

Saturday, April 15, 2006

Saturday April 15, 2006

Filed under: General — Tags: — m759 @ 2:02 pm
High Society


(See previous entry,
on Francis L. Kellogg)\

More bookmarks, in the spirit of
  Hemingway rather than Fitzgerald,
 from the date of Kellogg's death–

New York State lottery
on April 6, 2006:

Mid-day: 338
 Evening: 323

From A Flag for Sunrise, page 338:

"She seemed, superficially, to have
thrown every grain of her energy
into the driving…. She was stone
beautiful, he thought; to his eye
outrageously and provocatively
beautiful…."

Related material:
 
Compare with Grace Kelly driving
Cary Grant in "To Catch a Thief"
and Frank Sinatra in "High Society."

Those who prefer a different sort
of high may also prefer a different
page in A Flag for Sunrise: 323.

"He was very high, higher than he
had ever been.  His thoughts
twisted off into spools,
arabesques, snatches of
music."

 Related material:

"Harrowing," from
Holy Saturday, 2003.

Saturday, March 4, 2006

Saturday March 4, 2006

Filed under: General — m759 @ 10:34 am

Women’s History Month continues.

Contender

Miss O’Hara
on the Oscars:
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“Cinderella Man: To me, this is the best film of 2005 (qualifier: I have not yet seen Walk the Line). Cinderella Man is a terrific film – maybe even a great one. It isn’t flashy, it isn’t brimming with special effects, porn stars, or snappy one-liners. But it is a terrific story, one that you feel good after watching. It’s a slice of the true Golden Age of Hollywood – a solid story about good people that is well-acted by a superb cast. It’s a very family-friendly film – although some of the boxing scenes may be too intense for little ones. I can’t recommend this film highly enough, and am still furious that it was snubbed for the Oscars – then again, perhaps I shouldn’t be. It would be an insult to the movie, the actors, and the writers to nominate this fine film with the dreck they are glorifying this year. Watch this movie. I guarantee you’ll enjoy it.”

Tuesday, February 21, 2006

Tuesday February 21, 2006

Filed under: General — Tags: — m759 @ 1:00 pm
Conceptual Lens

"Contemporary literary theory did not emerge in an intellectual and cultural vacuum. The subordination of art to argument and ideas has been a long time in the works. In The Painted Word, a rumination on the state of American painting in the 1970s, Tom Wolfe described an epiphany he had one Sunday morning while reading an article in the New York Times on an exhibit at Yale University. To appreciate contemporary art– the paintings of Jackson Pollock and still more so his followers– which to the naked eye appeared indistinguishable from kindergarten splatterings and which provided little immediate pleasure or illumination, it was 'crucial,' Wolfe realized, to have a 'persuasive theory,' a prefabricated conceptual lens to make sense of the work and bring into focus the artist's point. From there it was just a short step to the belief that the critic who supplies the theories is the equal, if not the superior, of the artist who creates the painting."

Peter Berkowitz, "Literature in Theory"


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Cover art by Rea Irvin

On this date in 1925,
The New Yorker
first appeared.

Related material:

Aldous Huxley on
The Perennial Philosophy
(ART WARS, March 13, 2003)
and William James on religion:

"James points out that… a mystical experience displays the world through a different lens than is present in ordinary experience. The experience, in his words, is 'ineffable'…."

For an experience that is
perhaps more effable,
see the oeuvre of
 Jill St. John.

Related material:

A drama for Mardi Gras,
The Crimson Passion,
and (postscript of 2:56 PM)
today's Harvard Crimson
(pdf, 843k)

Wednesday, February 8, 2006

Wednesday February 8, 2006

Filed under: General — m759 @ 12:00 pm
Iconography
(continued)

“… iconography,
the concept and image
of the bride of Christ–
the sponsa Christi
assumed particular relevance in
the definition of women’s identity.”

Silvia Evangelisti in
Historiographical Reviews

The image “http://www.log24.com/log/pix06/060208-Sponsa.jpg” cannot be displayed, because it contains errors.

Related material:

 Arts & Letters Daily
(Feb. 8, 2006) annotated:

Dan Brown is not the first to have suggested that Jesus had a sex life– even Martin Luther said it. So what about the lady, Mary Magdalene?… more

“In ‘The Little Mermaid,’ Ariel’s true identity is the ‘Lost Bride,’ the Magdalene.”
Joan Acocella on pop religion in this week’s New Yorker

For literature profs of today, Theory is what the Dialectic was to Marxist intellectuals of the past: the key to almost everything… more

“Contemporary literary theory did not emerge in an intellectual and cultural vacuum. The subordination of art to argument and ideas has been a long time in the works. In The Painted Word, a rumination on the state of American painting in the 1970s, Tom Wolfe described an epiphany he had one Sunday morning while reading an article in the New York Times on an exhibit at Yale University. To appreciate contemporary art– the paintings of Jackson Pollack and still more so his followers– which to the naked eye appeared indistinguishable from kindergarten splatterings and which provided little immediate pleasure or illumination, it was ‘crucial,’ Wolfe realized, to have a ‘persuasive theory,’ a prefabricated conceptual lens to make sense of the work and bring into focus the artist’s point. From there it was just a short step to the belief that the critic who supplies the theories is the equal, if not the superior, of the artist who creates the painting.”
Peter Berkowitz, “Literature in Theory”

The idea that anyone, regardless of learning or class, could “come to Christ” went along with the idea of equal rights in America. William Jennings Bryan… more

“… evangelical Protestantism has always been an integral part of American political history.”
Michael Kazin, Dissent Magazine, Winter 2006

And from non-Protestantism, for the birthday of John “Star Wars” Williams, we have…

Sanctus from Missa “Veni Sponsa Christi” (pdf), by Manuel Cardoso (1566-1650).

Related material: Catholic Tastes and
                           A Mass for Lucero.

Friday, January 27, 2006

Friday January 27, 2006

Filed under: General — m759 @ 8:25 am

Mozart, 2006

Mozart, 1935

Poet, be seated at the piano.
Play the present, its hoo-hoo-hoo,
Its shoo-shoo-shoo, its ric-a-nic,
Its envious cachinnation.

If they throw stones upon the roof
While you practice arpeggios,
It is because they carry down the stairs
A body in rags.
Be seated at the piano.

That lucid souvenir of the past,
The divertimento;
That airy dream of the future,
The unclouded concerto . . .
The snow is falling.
Strike the piercing chord.

Be thou the voice,
Not you. Be thou, be thou
The voice of angry fear,
The voice of this besieging pain.

Be thou that wintry sound
As of the great wind howling,
By which sorrow is released,
Dismissed, absolved
In a starry placating.

We may return to Mozart.
He was young, and we, we are old.
The snow is falling
And the streets are full of cries.
Be seated, thou.

— Wallace Stevens, Ideas of Order (1936)

From the center:

“‘Mozart, 1935’ immediately discloses a will to counter complaints of pure poetry, to refute that charge heard regularly from Stevens’s critics, to find ‘his particular celebration out of tune today’ on his own if necessary; and, in short, to meet the communist [poet and critic Willard] Maas’s ‘respect for his magnificent rhetoric’ at least halfway across from right to left.”

— Alan Filreis, Modernism from Right to Left: Wallace Stevens, the Thirties, and Literary Radicalism (Cambridge: Cambridge University Press, 1994), p. 211

From the left:

Norman Lebrecht on this year’s celebration of the 250th anniversary of Mozart’s birth (January 27, 1756):

   “… Mozart, it is safe to say, failed to take music one step forward….
   … Mozart merely filled the space between staves with chords that he knew would gratify a pampered audience. He was a provider of easy listening, a progenitor of Muzak….
   …  He lacked the rage of justice that pushed Beethoven into isolation, or any urge to change the world. Mozart wrote a little night music for the ancien regime. He was not so much reactionary as regressive….
   … Little in such a mediocre life gives cause for celebration….
   … The bandwaggon of Mozart commemorations was invented by the Nazis in 1941….
   …  In this orgy of simple-mindedness, the concurrent centenary of Dmitri Shostakovich– a composer of true courage and historical significance– is being shunted to the sidelines, celebrated by the few.
    Mozart is a menace to musical progress, a relic of rituals that were losing relevance in his own time and are meaningless to ours. Beyond a superficial beauty and structural certainty, Mozart has nothing to give to mind or spirit in the 21st century. Let him rest. Ignore the commercial onslaught. Play the Leningrad Symphony. Listen to music that matters.”
     
The left seems little changed since 1935.

Monday, December 19, 2005

Monday December 19, 2005

Filed under: General,Geometry — Tags: , — m759 @ 2:45 am
 "There is an
underlying timelessness
in the basic conversation
that is mathematics
."
Barry Mazur (pdf)

It's Quarter to Three
(continued):

 
"I could tell you a lot
but you gotta be
 true to your code."
— Sinatra

Today is the birthday of Helmut Wielandt (Dec. 19, 1910 – Feb. 14, 2001).

From MacTutor:

"In his speech accepting membership of the Heidelberg Academy in 1960 he said:-

It is to one of Schur's seminars that I owe the stimulus to work with permutation groups, my first research area. At that time the theory had nearly died out. It had developed last century, but at about the turn of the century had been so completely superseded by the more generally applicable theory of abstract groups that by 1930 even important results were practically forgotten – to my mind unjustly."

Permutation groups are still not without interest.  See today's updates (Notes [01] and [02]) to Pattern Groups.

 

Tuesday, November 29, 2005

Tuesday November 29, 2005

Filed under: General — m759 @ 12:25 am
The Way of the Pilgrim,
Part III:
 
For the Birthday
of C. S. Lewis

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The Tao, Chapter I

“The Chinese… speak of a great thing (the greatest thing) called the Tao. It is the reality beyond all predicates, the abyss that was before the Creator Himself. It is Nature, it is the Way, the Road. It is the Way in which the universe goes on, the Way in which things everlastingly emerge, stilly and tranquilly, into space and time. It is also the Way which every man should tread in imitation of that cosmic and supercosmic progression, conforming all activities to that great exemplar.”

— C. S. Lewis in The Abolition of Man

“In his preface to That Hideous Strength, Lewis says the novel has a serious point that he has tried to make in this little book, The Abolition of Man.  The novel is a work of fantasy or science fiction, while Abolition is a short philosophical work about moral education, but as we shall see the two go together; we will understand either book better by having read and thought about the other.”

— Dale Nelson, Notes on The Abolition of Man

“In Epiphany Term, 1942, C.S. Lewis delivered the Riddell Memorial Lectures… in….  the University of Durham….  He delivered three lectures entitled ‘Men without Chests,’ ‘The Way,’ and ‘The Abolition of Man.’  In them he set out to attack and confute what he saw as the errors of his age. He started by quoting some fashionable lunacy from an educationalists’ textbook, from which he developed a general attack on moral subjectivism.  In his second lecture he argued against various contemporary isms, which purported to replace traditional objective morality.  His final lecture, ‘The Abolition of Man,’ which also provided the title of the book published the following year, was a sustained attack on hard-line scientific anti-humanism. The intervening fifty years have largely vindicated Lewis.”

— J. R. Lucas, The Restoration of Man

Tuesday, November 22, 2005

Tuesday November 22, 2005

Filed under: General — Tags: — m759 @ 4:23 am

Cartoon Graveyard
(continued)

From yesterday’s New York Post:

By LARRY CELONA, JOHN MAZOR and DAN MANGAN

November 21, 2005 — The former tour manager for superstars Paul Simon and Billy Joel was stabbed to death yesterday by his prostitute girlfriend on his 57th birthday less than a block from Gracie Mansion, cops said.

“It looked like a horror movie in there,” said an NYPD detective after seeing the blood-drenched bed in the couple’s sixth-floor studio at 530 East 89th St., where cops say music producer Danny Harrison was stabbed twice in the chest with a long butcher knife by his live-in lover just before 1 p.m.

I need a photo opportunity
I want a shot at redemption
Don’t want to end up a cartoon
In a cartoon graveyard

     — Paul Simon

Below: cartoonist Lou Myers,
who also died on Sunday, Nov. 20,
with a horse from yesterday’s entry.

The image “http://www.log24.com/log/pix05B/051121-Horse.jpg” cannot be displayed, because it contains errors.

“... and behold: a pale horse.
And his name, that sat on him,
was Death. And Hell
followed with him
.”

Johnny Cash

Related material:
Log24 entries of
Sept. 15, 2003.

 

Tuesday, November 15, 2005

Tuesday November 15, 2005

Filed under: General,Geometry — m759 @ 2:56 am
Spider Woman

    “Time traveling, which is not quite the good clean boyish fun it’s cracked up to be, started for me when this woman with the sigil on her forehead looked in on me from the open doorway of the hotel bedroom where I’d hidden myself and the bottles and asked me, ‘Look, Buster, do you want to live?’….
    Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question.

Fritz Leiber's 'Spider' symbol

Bordered version
of the sigil

The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar.  An X superimposed on a plus sign.  It looked permanent.”

— Fritz Leiber, “Damnation Morning

For Vine Deloria Jr., who died at 72 on Sunday, Nov. 13, 2005:

        Things forgotten are shadows.
        The shadows will be as real
        as wind and rain and song and light,
        there in the old place.
        Spider Woman atop your rock,
        I would greet you,
        but I am going the other way.
        Only a fool would pursue a Navajo
        into the Canyon of Death.

— Roger Zelazny, Eye of Cat

Related material:
from a Log24 entry
on the morning of
Deloria’s death–

Kaleidoscope turning…
Shifting pattern
within unalterable structure…

— Roger Zelazny, Eye of Cat

  

Monday, October 31, 2005

Monday October 31, 2005

Filed under: General — Tags: , , , , , — m759 @ 2:00 am

Balance

The image “http://log24.com/log/pix03/030109-gridsmall.gif” cannot be displayed, because it contains errors.

"An asymmetrical balance is sought since it possesses more movement. This is achieved by the imaginary plotting of the character upon a nine-fold square, invented by some ingenious writer of the Tang dynasty. If the square were divided in half or in four, the result would be symmetrical, but the nine-fold square permits balanced asymmetry."

— Chiang Yee, Chinese Calligraphy, quoted in Aspen no. 10, item 8

"'Burnt Norton' opens as a meditation on time. Many comparable and contrasting views are introduced. The lines are drenched with reminiscences of Heraclitus' fragments on flux and movement….  the chief contrast around which Eliot constructs this poem is that between the view of time as a mere continuum, and the difficult paradoxical Christian view of how man lives both 'in and out of time,' how he is immersed in the flux and yet can penetrate to the eternal by apprehending timeless existence within time and above it. But even for the Christian the moments of release from the pressures of the flux are rare, though they alone redeem the sad wastage of otherwise unillumined existence. Eliot recalls one such moment of peculiar poignance, a childhood moment in the rose-garden– a symbol he has previously used, in many variants, for the birth of desire. Its implications are intricate and even ambiguous, since they raise the whole problem of how to discriminate between supernatural vision and mere illusion. Other variations here on the theme of how time is conquered are more directly apprehensible. In dwelling on the extension of time into movement, Eliot takes up an image he had used in 'Triumphal March': 'at the still point of the turning world.' This notion of 'a mathematically pure point' (as Philip Wheelwright has called it) seems to be Eliot's poetic equivalent in our cosmology for Dante's 'unmoved Mover,' another way of symbolising a timeless release from the 'outer compulsions' of the world. Still another variation is the passage on the Chinese jar in the final section. Here Eliot, in a conception comparable to Wallace Stevens' 'Anecdote of the Jar,' has suggested how art conquers time:

       Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— F. O. Matthiessen, The Achievement of T.S. Eliot,
Oxford University Press, 1958, as quoted in On "Burnt Norton"

 

Monday, August 29, 2005

Monday August 29, 2005

Filed under: General — Tags: — m759 @ 4:00 pm
VALE

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George and Esther Szekeres

From the weblog of
David Michael Brown, Jr.:
 

Date:     Sun, 28 Aug 2005
             12:30:40 -0400
From:    Alf van der Poorten AM
           
Subject: Vale George Szekeres and
             Esther Klein Szekeres

Members of the Number Theory List will be sad to learn that George and Esther Szekeres both died this morning.  George, 94, had been quite ill for the last 2-3 days, barely conscious, and died first at 06:30.  Esther, 95, died a half hour later.

Both George Szekeres and Esther Klein will be recalled by number theorists as members of the group of young Hungarian mathematicians of the 1930s including Turan and Erdos.  George and Esther's coming to Australia in the late 40s played an important role in the invigoration of Australian Mathematics.  George was also an expert in group theory and relativity; he was my PhD supervisor.

Emeritus Professor
Alf van der Poorten AM
Centre for Number Theory Research
1 Bimbil Place, Killara NSW

 

Related material:

AVE

3:09 PM EDT Thursday, Aug. 25, 2005:
 

  "Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

 

  "A very short space of time through very short times of space….
   Am I walking into eternity along Sandymount strand?"

   — James Joyce, Ulysses, Proteus chapter

A very short space of time through very short times of space….

   "It is demonstrated that space-time should possess a discrete structure on Planck scales."

   — Peter Szekeres, abstract of Discrete Space-Time

Peter Szekeres is the son of George and Esther Szekeres.
 

ATQUE

"At present, such relationships can at best be heuristically described in terms that invoke some notion of an 'intelligent user standing outside the system.'"

Gian-Carlo Rota in Indiscrete Thoughts, p. 152
 

Related material:
High Concept and
Nothing Nothings (Again).

Monday, August 22, 2005

Monday August 22, 2005

Filed under: General — Tags: , , — m759 @ 4:07 pm
The Hole

Part I: Mathematics and Narrative

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Apostolos Doxiadis on last month's conference on "mathematics and narrative"–

Doxiadis is describing how talks by two noted mathematicians were related to

    "… a sense of a 'general theory bubbling up' at the meeting… a general theory of the deeper relationship of mathematics to narrative…. "

Doxiadis says both talks had "a big hole in the middle."  

    "Both began by saying something like: 'I believe there is an important connection between story and mathematical thinking. So, my talk has two parts.  [In one part] I’ll tell you a few things about proofs.  [And in the other part] I’ll tell you about stories.' …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other."
  "And the hole?"
  "This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’  But the similarity was not clearly explained: the hole, you see, the ‘miracle.’  Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one."
 

Part II: Possible Worlds

"At times, bullshit can only be countered with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

Background:

Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole
 

Part III: Modal Theology

 
  "'What is this Stone?' Chloe asked….
  '…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

  — Many Dimensions, by Charles Williams, 1931 (Eerdmans paperback, April 1979, pp. 43-44)


"The lapis was thought of as a unity and therefore often stands for the prima materia in general."

  — Aion, by C. G. Jung, 1951 (Princeton paperback, 1979, p. 236)

 

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."

  — The Stars My Destination, by Alfred Bester, 1956 (Vintage hardcover, July 1996, p. 216)
 
"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

 

 

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Friday, July 1, 2005

Friday July 1, 2005

Filed under: General — m759 @ 8:00 pm

Big Dreams

“For more than a century, Los Angeles has been synonymous with big dreams. The Australian writer and critic Clive James said it this way. ‘Call Los Angeles any dirty name you like… The fact remains that you are already living in it before you get there.'”

— Today’s inaugural address by Mayor Villaraigosa

See also the previous entry.

Update of 2:24 PM July 2:

Yesterday afternoon I picked up a copy of George Steiner’s Grammars of Creation I had ordered.  A check of Amazon.com to see what others had to say about this book yielded the following:

“Steiner’s account of Hope as something exclusively transcendental and relative to the future is poor and superficial: the person who hopes is not only walking ‘towards’ Eternal Life, but is already walking ‘in’ Eternal Life, walking the Kingdom.”

— Matías Cordero, Santiago, Chile

See also an entry of April 7, 2005, Nine is a Vine.

Friday, June 10, 2005

Friday June 10, 2005

Filed under: General — m759 @ 1:25 am

From Andrew Cusack’s weblog:

April 21, 2005

‘For Christ and Liberty’

Though [it is] a purely Protestant institution (literally), I am rather fond of Patrick Henry College. Indeed, it takes some courage in this day and age to only admit students willing to sign a ten-point profession of Protestant Reformed faith. They also happen to have an old-fashioned ball featuring ‘English country dancing, delicacies such as cream puffs and truffles and leisurely strolls about the scenic grounds of the historic Selma Plantation’.

Anyhow, the college, whose motto is ‘For Christ and Liberty’, was visited [by] Anthony Esolen, a contributing editor to Touchstone magazine, who makes these comments:

Today I received a request to write a short article on Pope Benedict XVI from a club called the De Tocqueville Society, in a small college in Northern Virginia.

That such a request came was no surprise. Its provenance is, and cheeringly so. For this De Tocqueville Society is made up of a group of students at the new Patrick Henry College, founded by Mike Farris, the President of the Home School Legal Defense Association. More than ninety percent of the college’s students were homeschooled. If there’s a Roman Catholic in the bunch, I’ve yet to hear about it, and I’ve been to that campus twice to give lectures. [Note: Esolen does not seem to be aware that PHC requires its students to be Protestant.]

More on that in a moment. I could spend all evening singing the praises of PHC (as the students fondly call it), but let me share one discovery I made that should gratify Touchstone readers. The first time I spoke there, two years ago, I was stunned to meet young men and women who—who were young men and women. I am not stretching the truth; go to Purcellville and see it for yourselves if you doubt it; I believe my wife took a couple of pictures, just to quiet the naysayers. The young men stand tall and look you in the eye—they don’t skulk, they don’t scowl and squirm uncomfortably in the back chairs as they listen to yet another analysis of Rebecca of Sunnybrook Farm, or one of the healthier poems of Sylvia Plath. They’re frank and generous and respectful, but they hold their own in an argument, and they are eager to engage you in those. They are comfortable in their skins; they wear their manhood easily. And the young ladies are beautiful. They don’t wither away in class, far from it; but they wear skirts, they are modest in their voices and their smiles, they clearly admire the young men and are esteemed in turn; they are like creatures from a faraway planet, one sweeter and saner than ours.

Two years ago I spoke to them about medieval Catholic drama. They are evangelicals, half of them majors in Government, the rest, majors in Liberal Arts. They kept me and my wife in that room for nearly three hours after the talk was over. “Doctor Esolen, what you say about the habits of everyday life—to what extent is it like what Jean Pierre de Coussade calls ‘the sacrament of the present moment’?” “Doctor Esolen, do you see any connections between the bodiliness of this drama and the theology of Aleksandr Schmemann?” “Doctor Esolen, you have spoken a great deal about our recovery of a sense of beauty, but don’t you think that artists can also use the grotesque as a means of bringing people to the truth?” “You’ve suggested to us that Christians need to reclaim the Renaissance as our heritage, yet we are told that that was an age of the worship of man for his own sake. To what extent is the art of that period ours to reclaim?” And on and on, until nearly midnight.

The questions were superior to any that I have ever heard from a gathering of professors—and alas, I’ve been to many of those. I mean not only superior in their enthusiasm and their insistence, but in their penetrating to the heart of the problem, their willingness to make connections apparently far afield but really quite apropos, and their sheer beauty—I can think of no better word for it.

A few weeks ago I was in town for another talk, on the resurrection of the body. The Holy Father had passed away. At supper, ten or fifteen of the students packed our table, to ask questions before the talk. They were reverent and extraordinarily well informed; most especially they were interested in the Theology of the Body. The questions on that topic continued after the lecture, and I had the same experience I’d had before, but now without the surprise.

And these are the young people who are devoting an entire issue of their journal to the thought of Cardinal Ratzinger, now the new head of the Roman Catholic Church. They are hungry to know about him; in the next week or two they will do what our slatternly tarts and knaves, I mean our journalists, have never done and will not trouble themselves to do, and that is to read what Benedict XVI has said, read it with due appreciation for their differences with him, and due deference to a holy and humble man called by Christ to be a light not only to Roman Catholics but to all the nations.

These students don’t know it, but in their devotion to their new school (they are themselves the guards, the groundskeepers, the janitors; they ‘own’ the school in a way that is hard to explain to outsiders), they live the community life extolled by Leo XIII in Rerum Novarum; in their steadfastness to the truth they are stalwart participators in the quest set out by John Paul II in Fides et Ratio; in their welcoming of me and, God bless them, of the good Benedict XVI, they live in the true spirit of Lumen Gentium, that greathearted document of the council so often invoked for the lame tolerance of every betrayal of the ancient faith. And for what it’s worth, they are readers of Touchstone Magazine.

Be silent, Greeleys and Dowds of the world. These young people have you whipped, if for no other reason than that they believe in the One who is Truth, and who sets us free. How can I praise these my young brothers and sisters any more highly? God bless them and Patrick Henry College. And the rest of us, let’s keep an eye on them. We’ll be seeing quite a harvest from that seedbed!

Many of the points Esolen commends are things I hope will be found in the colleges of my university when I get around to starting it. I particularly admire that Patrick Henry College’s young men and women are just that, according to Esolen. This is all too often hard to achieve in modern American higher education, where students are quite often just elderly adolescents. (Though I suspect this has more to do with parents and family than education).

The absurdist drinking age that the Federal government underhandedly coerced each state into passing hinders maturity as well. Indeed, when I start the first college or colleges of the university I’m planning, each will have a private college bar which will serve anyone over the age of 16 or so. (Probably at the barman or barmaid’s discretion). Civil disobedience is the only solution.

Though the graduates Patrick Henry College provides will be Protestant (at least at the time of their graduation), I have no doubt that they will act as leaven to raise up the social and political life of our United States. I’m not particularly fond that they proudly advertise their commendation as “One of America’s Top Ten Conservative Colleges”. I’m not of the view that colleges ought to be ‘conservative’ or ‘liberal’ per se. They ought to be seen more as communities of inquisitive, curious, intelligent people united in the quest for truth. Labels like ‘conservative’ and ‘liberal’ are far too narrow and allow the simple-minded to pidgeon-hole things which are too complex for such monikers.

But anyhow, cheers for Patrick Henry College.

Posted by Andrew Cusack at April 21, 2005 05:25 PM

Saturday, June 4, 2005

Saturday June 4, 2005

Filed under: General,Geometry — m759 @ 7:00 pm
  Drama of the Diagonal
  
   The 4×4 Square:
  French Perspectives

Earendil_Silmarils:
The image “http://www.log24.com/log/pix05A/050604-Fuite1.jpg” cannot be displayed, because it contains errors.
  
   Les Anamorphoses:
 
   The image “http://www.log24.com/log/pix05A/050604-DesertSquare.jpg” cannot be displayed, because it contains errors.
 
  “Pour construire un dessin en perspective,
   le peintre trace sur sa toile des repères:
   la ligne d’horizon (1),
   le point de fuite principal (2)
   où se rencontre les lignes de fuite (3)
   et le point de fuite des diagonales (4).”
   _______________________________
  
  Serge Mehl,
   Perspective &
  Géométrie Projective:
  
   “… la géométrie projective était souvent
   synonyme de géométrie supérieure.
   Elle s’opposait à la géométrie
   euclidienne: élémentaire
  
  La géométrie projective, certes supérieure
   car assez ardue, permet d’établir
   de façon élégante des résultats de
   la géométrie élémentaire.”
  
  Similarly…
  
  Finite projective geometry
  (in particular, Galois geometry)
   is certainly superior to
   the elementary geometry of
  quilt-pattern symmetry
  and allows us to establish
   de façon élégante
   some results of that
   elementary geometry.
  
  Other Related Material…
  
   from algebra rather than
   geometry, and from a German
   rather than from the French:  

This is the relativity problem:
to fix objectively a class of
equivalent coordinatizations
and to ascertain
the group of transformations S
mediating between them.”
— Hermann Weyl,
The Classical Groups,
Princeton U. Press, 1946

The image “http://www.log24.com/log/pix05/050124-galois12s.jpg” cannot be displayed, because it contains errors.

Evariste Galois

 Weyl also says that the profound branch
of mathematics known as Galois theory

   “… is nothing else but the
   relativity theory for the set Sigma,
   a set which, by its discrete and
    finite character, is conceptually
   so much simpler than the
   infinite set of points in space
   or space-time dealt with
   by ordinary relativity theory.”
  — Weyl, Symmetry,
   Princeton U. Press, 1952
  
   Metaphor and Algebra…  

“Perhaps every science must
start with metaphor
and end with algebra;
and perhaps without metaphor
there would never have been
any algebra.” 

   — attributed, in varying forms, to
   Max Black, Models and Metaphors, 1962

For metaphor and
algebra combined, see  

  “Symmetry invariance
  in a diamond ring,”

  A.M.S. abstract 79T-A37,
Notices of the
American Mathematical Society,
February 1979, pages A-193, 194 —
the original version of the 4×4 case
of the diamond theorem.

  
More on Max Black…

“When approaching unfamiliar territory, we often, as observed earlier, try to describe or frame the novel situation using metaphors based on relations perceived in a familiar domain, and by using our powers of association, and our ability to exploit the structural similarity, we go on to conjecture new features for consideration, often not noticed at the outset. The metaphor works, according to Max Black, by transferring the associated ideas and implications of the secondary to the primary system, and by selecting, emphasising and suppressing features of the primary in such a way that new slants on it are illuminated.”

— Paul Thompson, University College, Oxford,
    The Nature and Role of Intuition
     in Mathematical Epistemology

  A New Slant…  

That intuition, metaphor (i.e., analogy), and association may lead us astray is well known.  The examples of French perspective above show what might happen if someone ignorant of finite geometry were to associate the phrase “4×4 square” with the phrase “projective geometry.”  The results are ridiculously inappropriate, but at least the second example does, literally, illuminate “new slants”– i.e., diagonals– within the perspective drawing of the 4×4 square.

Similarly, analogy led the ancient Greeks to believe that the diagonal of a square is commensurate with the side… until someone gave them a new slant on the subject.

Sunday, May 1, 2005

Sunday May 1, 2005

Filed under: General — Tags: — m759 @ 1:11 pm
Logos

Harvard's Barry Mazur on
one mathematical style:

"It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else."

Samuel Beckett, Quad (1981):

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line logo:

"They are the same six lines
that exist in the I Ching….
Now observe the square more closely:
four of the lines are of equal length,
the other two are longer….
For this reason symmetry
cannot be statically produced
and a dance results."
 
— Marie-Louise von Franz,
Number and Time (1970),
Northwestern U. Press
paperback, 1979, p. 108

A related logo from
Columbia University's
Department of Art History
and Archaeology
:

The image “http://www.log24.com/log/pix05/050501-ArtHist2.gif” cannot be displayed, because it contains errors.
 
Also from that department:

Rosalind Krauss,

The image “http://www.log24.com/log/pix05/050501-Krauss.jpg” cannot be displayed, because it contains errors.

Meyer Schapiro Professor
of Modern Art and Theory:

"There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape
and the Pandora's box
of spiritual reference
that is opened
once one uses it."

"In the garden of Adding
live Even and Odd…"
— The Midrash Jazz Quartet in
City of God, by E. L. Doctorow

THE GREEK CROSS

A cross in which all the arms
are the same length.

Here, for reference, is a Greek cross
within a nine-square grid:

The image “http://www.log24.com/log/pix05/050501-GrCross.gif” cannot be displayed, because it contains errors.

 Related religious meditation for
    Doctorow's "Garden of Adding"…

 4 + 5 = 9.

Types of Greek cross
illustrated in Wikipedia
under "cross":

The image “http://www.log24.com/log/pix05/GrCross.gif” cannot be displayed, because it contains errors.

From designboom.com:

THE BAPTISMAL CROSS

The image “http://www.log24.com/log/pix05/050501-BaptismalCross.gif” cannot be displayed, because it contains errors.

 

is a cross with eight arms:
a Greek cross, which is superimposed
on a Greek 'chi,' the first letter
of the Greek word for 'Christ.'
Since the number eight is symbolic
of rebirth or regeneration,
this cross is often used
as a baptismal cross.

Related material:

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

Fritz Leiber's "spider"
or "double cross" logo.
See Why Me? and
A Shot at Redemption.

Happy Orthodox Easter.

Saturday, April 30, 2005

Saturday April 30, 2005

Filed under: General — m759 @ 9:00 pm
City of God

Kevin Baker in 2001 on
E. L. Doctorow’s City of God:

“…the nature of the cosmos
(Augustine’s City of God?)”

David Van Biema in Time Magazine
(May 2, 2005, p. 43)

The image “http://www.log24.com/log/pix05/050430-TIME.jpg” cannot be displayed, because it contains errors.

on Augustine’s City of God:

“A key concept in Augustine’s great
The City of God is that the Christian church
is superior and essentially alien

to its earthly surroundings.”


The image “http://www.log24.com/log/pix05/050430-Easter.jpg” cannot be displayed, because it contains errors.

 
  Click on the above for a rendition of
  Appalachian Spring.

This year’s April – Mathematics Awareness Month –
theme is “Mathematics and the Cosmos.”

For my own views on this theme as it applies
to education, see Wag the Dogma.

For some other views, see this year’s
Mathematics Awareness Month site.

One of the authors at that site,
which is mostly propaganda
for the religion of Scientism,
elsewhere quotes
an ignorant pedagogue:

“‘The discovery of non-Euclidean geometries
contradicted the “absolute truth” view
of the Platonists.'”

Sarah J. Greenwald,
   Associate Professor,
   Department of Mathematics
   Appalachian State University, Boone, NC

Damned nonsense.  See Math16.com.

Tuesday, April 26, 2005

Tuesday April 26, 2005

Filed under: General — Tags: — m759 @ 6:29 am
The Ring of Falsehood
 
In memory of Philip Morrison, bombmaker,

The image “http://www.log24.com/log/pix05/050426-Morrison.jpg” cannot be displayed, because it contains errors.
Morrison

Scientific American columnist,
  pioneer of the
Search for Extraterrestrial Intelligence (SETI)
and author of
The Ring of Truth.

Morrison died
in Cambridge, Massachusetts,
on Friday, April 22, 2005.

From The Measure of a Life:

Does religion play a role in attitudes toward ETIs? Philip Morrison gave his considered opinion… “Well, it might, but I think that it’s just one of the permissive routes; it isn’t an essential factor. My parents were Jewish. Their beliefs were conventional but not very deep. They belonged to the Jewish community; they went to services infrequently, on special occasions—funerals and high holidays”….

Although Sagan did not believe in God, he nevertheless said this about SETI’s importance… “It touches deeply into myth, folklore, religion, mythology; and every human culture in some way or another has wondered about that type of question. It’s one of the most basic questions there is.” In fact, in Sagan’s novel/film Contact, described by Keay Davidson as “one of the most religious science-fiction tales ever written”… Ellie discovers that pi—the ratio of the circumference of a circle to its diameter—is numerically encoded in the cosmos and this is proof that a super-intelligence designed the universe…

The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle—another circle, drawn kilometers downstream of the decimal point. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe.

Nell

See also yesterday's entry Mathematical Style.

Extra credit:
Discuss the difference betweeen physical constants and mathematical constants. Use the results of your discussion to show that the above discussion of pi is nonsense.

Tuesday, March 22, 2005

Tuesday March 22, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 4:01 pm

Make a Différance

From Frida Saal's
Lacan The image “http://www.log24.com/log/pix05/050322-Diamond.gif” cannot be displayed, because it contains errors. Derrida:

"Our proposal includes the lozenge (diamond) in between the names, because in the relationship / non-relationship that is established among them, a tension is created that implies simultaneously a union and a disjunction, in the perspective of a theoretical encounter that is at the same time necessary and impossible. That is the meaning of the lozenge that joins and separates the two proper names. For that reason their respective works become totally non-superposable and at the same time they were built with an awareness, or at least a partial awareness, of each other. What prevails between both of them is the différance, the Derridean signifier that will become one of the main issues in this presentation."

 


From a Contemporary Literary Theory website:

"Différance is that which all signs have, what constitutes them as signs, as signs are not that to which they refer: i) they differ, and hence open a space from that which they represent, and ii) they defer, and hence open up a temporal chain, or, participate in temporality. As well, following de Sassure's famous argument, signs 'mean' by differing from other signs. The coined word 'différance' refers to at once the differing and the deferring of signs. Taken to the ontological level†, the differing and deferring of signs from what they mean, means that every sign repeats the creation of space and time; and ultimately, that différance is the ultimate phenomenon in the universe, an operation that is not an operation, both active and passive, that which enables and results from Being itself."

From a text purchased on
Make a Difference Day, Oct. 23, 1999:

The image “http://www.log24.com/log/pix05/050322-Fig39.gif” cannot be displayed, because it contains errors.22. Without using the Pythagorean Theorem prove that the hypotenuse of  an isosceles right triangle will have the length The image “http://www.log24.com/log/pix05/050322-Sqtr2.gif” cannot be displayed, because it contains errors.  if the equal legs have the length 1.  Suggestion: Consider the similar triangles in Fig. 39.
23.  The ancient Greeks regarded the Pythagorean Theorem as involving areas, and they proved it by means of areas.  We cannot do so now because we have not yet considered the idea of area.  Assuming for the moment, however, the idea of the area of a square, use this idea instead of similar triangles and proportion in Ex. 22 above to show that x = The image “http://www.log24.com/log/pix05/050322-Sqtr2.gif” cannot be displayed, because it contains errors. .

 

— Page 98 of Basic Geometry, by George David Birkhoff, Professor of Mathematics at Harvard University, and Ralph Beatley, Associate Professor of Education at Harvard University (Scott, Foresman 1941)



Though it may be true, as the president of Harvard recently surmised, that women are inherently inferior to men at abstract thought — in particular, pure mathematics*  — they may in other respects be quite superior to men:

The image “http://www.log24.com/log/pix05/050322-Reba2.jpg” cannot be displayed, because it contains errors.

The above is from October 1999.
See also Naturalized Epistemology,
from Women's History Month, 2001.

* See the remarks of Frida Saal above and of Barbara Johnson on mathematics (The Shining of May 29, cited in Readings for St. Patrick's Day).


† For the diamond symbol at "the ontological level," see Modal Theology, Feb. 21, 2005.  See also Socrates on the immortality of the soul in Plato's Meno, source of the above Basic Geometry diamond.

Wednesday, March 2, 2005

Wednesday March 2, 2005

Filed under: General — Tags: — m759 @ 2:22 pm

White Stone

"I have stolen more quotes and thoughts and purely elegant little starbursts of writing from the Book of Revelation than anything else in the English language– and it is not because I am a biblical scholar, or because of any religious faith, but because I love the wild power of the language and the purity of the madness that governs it and makes it music."

— Hunter S. Thompson, Author's Note, Generation of Swine

In memory of Peter Foy,
who died in Las Vegas
on 2/17

The image “http://log24.com/log/pix05/050302-Peter2.jpg” cannot be displayed, because it contains errors.

Revelation 2:17:

"And I will give him a white stone…."

The image “http://log24.com/log/pix05/050302-Diamond1.jpg” cannot be displayed, because it contains errors.

Related material:

2003 2/17: "immortal diamond"
2004 2/17:  "hard core"           
2005 2/17:  "the diamond"       

For an "elegant starburst," see

"Starflight," from 10/10, 2004

The image “http://www.log24.com/log/pix05/050302-S.jpg” cannot be displayed, because it contains errors.

the date of
Christopher Reeve's death.

See also
Revelation 10:10

"And I took the little book
out of the angel's hand,
and ate it up; and it was in my mouth
sweet as honey: and as soon as I had
eaten it, my belly was bitter."

For the relationship of this verse to
the style of Hunter Thompson, see

The image “http://www.log24.com/log/pix05/050302-Apo.jpg” cannot be displayed, because it contains errors.

From the Department of Justice:
"LSD generally is taken by mouth.
The drug is colorless and odorless
but has a slightly bitter taste."
Among the street terms for LSD
is "Superman."

Wednesday, January 5, 2005

Wednesday January 5, 2005

Filed under: General — Tags: , — m759 @ 7:11 am

Death and the Spirit

A meditation for Twelfth Night
on "the whirligig of time"

Today's New York Times obituaries feature two notable graphic artists: 
  • Frank Kelly Freas, who created, among other works, 400 portraits of saints for the Franciscans and the covers of Mad Magazine from 1958 through 1962. "I found it difficult to shift my artistic gears from the sublime to the ridiculous and back again," he said of his departure from Mad.
  • Will Eisner, "an innovative comic-book artist who created the Spirit, a hero without superpowers, and the first modern graphic novel."

Yesterday's entry provided an approach to The Dark Lady, Kali, that was, in Freas's apt word, "ridiculous."  The illustration below, "Mate," is an attempt to balance yesterday's entry with an approach that is, if not sublime, at least more serious.  It is based on a similar illustration from Jan. 31, 2003, with actress Judy Davis playing The Dark Lady.  Today it seems appropriate to replace Davis with another actress (anonymous here, though some may recognize her).  I once knew her (unlike Davis) personally.  One of my fondest memories of high school is reading Mad Magazine with her in the school lunch room.  Our lives diverged after high school, but I could happily have spent my life in her company.

Mate

– S. H. Cullinane, Twelfth Night, 2005

The image “http://log24.com/log/pix05/050105-Mate.jpg” cannot be displayed, because it contains errors.

A diamond and its dual "whirl" figure—
or a "jewel-box and its mate"

For details, see the five Log24 entries
ending on Feb. 1, 2003, and the
perceptive remarks of Ryan Benedetti
on Sam Spade and Brigid O'Shaughnessy.

As for Eisner and "The Spirit,"
which has been called
"the quintessential noir detective series,"
those preferring non-graphic stories
may picture Spade or his creator,
Dashiell Hammett, in the title role.

Then, of course, there are Eisner's later
  story, "A Contract With God,"
  John 4:24, and 1916 4/24.

Sunday, December 5, 2004

Sunday December 5, 2004

Filed under: General — Tags: , , — m759 @ 3:00 pm

Chorus from
The Rock

Author Joan Didion is 70 today.

On Didion’s late husband, John Gregory Dunne:

“His 1989 memoir Harp includes Dunne’s early years in Hartford and his Irish-Catholic family’s resentment of WASP social superiority: ‘Don’t stand out so that the Yanks can see you,’ he wrote, ‘don’t let your pretensions become a focus of Yank merriment and mockery.'”

The Hartford Courant, August 4, 2002

From a Hartford Protestant:

The American Sublime

How does one stand
To behold the sublime,
To confront the mockers,
The mickey mockers
And plated pairs?

When General Jackson
Posed for his statue
He knew how one feels.
Shall a man go barefoot
Blinking and blank?

But how does one feel?
One grows used to the weather,
The landscape and that;
And the sublime comes down
To the spirit itself,

The spirit and space,
The empty spirit
In vacant space.
What wine does one drink?
What bread does one eat?

— Wallace Stevens

A search of the Internet for “Wallace Stevens”  + “The Rock” + “Seventy Years Later” yields only one quotation…

Log24 entries of Aug. 2, 2002:

From “Seventy Years Later,” Section I of “The Rock,” a poem by Wallace Stevens:

A theorem proposed
between the two —
Two figures in a nature
of the sun….

From page 63 of The New Yorker issue dated August 5, 2002:

“Birthday, death-day —
what day is not both?”
— John Updike

From Didion’s Play It As It Lays:

Everything goes.  I am working very hard at not thinking about how everything goes.  I watch a hummingbird, throw the I Ching but never read the coins, keep my mind in the now.
— Page 8

From Play It As It Lays:

I lie here in the sunlight, watch the hummingbird.  This morning I threw the coins in the swimming pool, and they gleamed and turned in the water in such a way that I was almost moved to read them.  I refrained.
— Page 214

And the sublime comes down
To the spirit itself,
The spirit and space,
The empty spirit
In vacant space.

One heart will wear a Valentine.
— Sinatra, 1954

Friday, November 19, 2004

Friday November 19, 2004

Filed under: General — Tags: — m759 @ 11:30 am

Goin' to Carolina
in My Mind

From today's New York Times:

"Bobby Frank Cherry, the former Klansman whose conviction two years ago for the church bombing that killed four black girls in Birmingham, Ala., in 1963 resolved one of the most shocking cases of the civil rights era, died yesterday at the Kilby Correctional Facility near Montgomery, Ala., a prison spokesman said. He was 74."

From

The Footprints of God

(Log24.net, July 31, 2004):

"If Trinity is everything you say it is," she said, "then why in God's name would it be based in North Carolina?"

This I hadn't expected.  "Aren't you the top Jungian analyst in the world?"

"Well… one of them."

"Why are you based in North Carolina?"


From

The Fiery Cross —
A Call to Arms
:

"The western portions of Virginia and the Carolinas, the northern portions of Georgia and Alabama, and most of Tennessee, were settled by the hardy race of Scotch-Irish, in whose veins the Scotch blood was warm."

From the LA Times story
cited in yesterday's entry:

"Born in Charlotte, N.C., Graham grew up in a family of Scottish Presbyterians…. Since 1950,  [he has] lived in an Appalachian log home… near Asheville, N.C."

The image “http://www.log24.com/log/pix04B/041119-Graham72.jpg” cannot be displayed, because it contains errors. The image “http://www.log24.com/log/pix04B/041119-MethFlag.gif” cannot be displayed, because it contains errors.
Graham
in 1972
Methodist
Flag

 

"The Cross and Flame is a registered trademark and the use is supervised by the General Council on Finance and Administration of The United Methodist Church. Permission to use the Cross and Flame must be obtained from the General Council on Finance and Administration of The United Methodist Church – Legal Department, 1200 Davis Street, Evanston, IL 60201."  — www.bobmay.info

Today's birthday:
Poet Allen Tate

"In the riven troughs the splayed leaves
Pile up, of nature the casual sacrament
To the seasonal eternity of death."

Ode to the Confederate Dead

Friday, November 5, 2004

Friday November 5, 2004

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

A Harvard Education
in a Sentence

Harvard alumnus Norman Mailer:

At times, bullshit can only be countered with superior bullshit.

For Harvard bullshit, see
The Crimson Passion.

For superior bullshit, see
Shrine of the Holy Whapping.

Thursday, October 14, 2004

Thursday October 14, 2004

Filed under: General — m759 @ 5:14 pm

Star Wars,
continued

The Eight

Lest the reader of the previous entry mistakenly take Katherine Neville’s book The Eight more seriously than Fritz Leiber’s greatly superior writings on eightness, here are two classic interpretations of Leiber’s “spider” or “double cross” symbol:

The image “http://www.log24.com/log/pix04A/Trigrams04.gif” cannot be displayed, because it contains errors.

Aristotle:
The 4 elements and
the 4 qualities
(On Generation and
Corruption, II, 3
)

 

The image “http://www.log24.com/log/pix04A/Trigrams02A.gif” cannot be displayed, because it contains errors.

Richard Wilhelm:
The 8 trigrams
(Understanding
the I Ching
,
154-175)

The Six

Less impressive, but not
completely without interest,
is the six-pointed star:

This symbol consists of
two triangles

representing
male and female,
fire and water,
up and down,
etc., etc., etc.

For some deeper properties
of the number eight, see a
Log24.net entry of 4/4/03.

Tuesday, August 17, 2004

Tuesday August 17, 2004

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

The Zen of Abraham

Today’s Zen Chautauqua, prompted by the fact that this is Abrahamic week at the real Chautauqua, consists of links to

The Matrix of Abraham,

Matrix of the Death God, and

Happy Birthday, Kate and Kevin.

The real Chautauqua’s program this week is, of course, Christian rather than Zen.  Its theme is “Building a Global Neighborhood: The Abrahamic Vision 2004.”  One of the featured performers is Loretta Lynn; in her honor (and, of course, that of Sissy Spacek), I will try to overcome the fear and loathing that the Semitic (i. e., “Abrahamic”) religions usually inspire in me.

To a mathematician, the phrase “global neighborhood” sounds like meaningless politico-religious bullshit —  a phrase I am sure accurately characterizes most of the discourse at Chautauqua this week.  But a Google search reveals an area of research — “particle swarm optimization” in which the phrase “global neighborhood” actually means something.  See

A Hybrid Particle Swarm
and Neural Network Approach
for Reactive Power Control,
by Paulo F. Ribeiro and
W. Kyle Schlansker
(pdf).

This article includes the following:

Given the sophistication of his writing, I am surprised at Schlansker’s Christian background:

A good omen for the future is the fact that Schlansker balances the looney Semitic (or “Abrahamic”) teachings of Christianity with good sound Aryan religion, in the form of the goddess Themis.

 Themis, often depicted as “Justice”

For those who must have an Abraham, Schlansker’s paper includes the following:

A Themis figure I prefer to the above:

For more on religious justice
at midnight in the garden of
good and evil, see the Log24
entries of Oct. 1-15, 2002.

For material on Aryan religion that is far superior to the damned nonsense at Chautauqua, New York, this week, see

Jane Ellen Harrison’s Themis: a Study of the Social Origins of Greek Religion, with an excursus on the ritual forms preserved in Greek tragedy by Gilbert Murray and a chapter on the origin of the Olympic games by F. M. Cornford.  Rev. 2nd ed., Cambridge, Cambridge U.P., 1927.

Those who prefer the modern religion of Scientism will of course believe that Themis is purely imaginary, and that truth is to be found in modern myths like that of Carl Sagan’s novel Contact, illustrated below.

Jodie Foster (an admirer of
Leni Riefenstahl) and the
opening of the 1936 Olympics

“Heraclitus…. says: ‘The ruler whose prophecy occurs at Delphi oute legei oute kryptei, neither gathers nor hides, alla semainei, but gives hints.'”
An Introduction to Metaphysics, by Martin Heidegger, Yale University Press paperback, 1959, p. 170

“The lord whose oracle is in Delphi neither indicates clearly nor conceals, but gives a sign.”
Adolf Holl, The Left Hand of God, Doubleday, 1998, p. 50

Monday, August 16, 2004

Monday August 16, 2004

Filed under: General — m759 @ 12:00 am

Classic to Romantic

“Ben Webster is probably best known for his eloquent ballad playing. On JAZZ ‘ROUND MIDNIGHT, we are treated to no less than 15 ballads, all of which are performed superbly. Webster is one of the great jazz romantics….”

Friday, August 6, 2004

Friday August 6, 2004

Filed under: General — m759 @ 5:01 pm

Sermon for Hiroshima Day

In a comment, a Xangan recently made a pun on the name “Gennifer” (as in Flowers)… “geno-pher.”  I am still not sure what he meant, but I appreciate his prompting me to look up the etymology of gen words, one of which is…

genesis – O.E., from L. genesis, adopted as title of first book of Old Testament in Vulgate, from Gk. genesis “origin, creation, generation,” from gignesthai “to be born,” related to genos “race, birth, descent” (see genus). As such, it translated Heb. bereshith, lit. “in the beginning,” which was the first word of the text, taken in error as its title. Extended sense of “origin, creation” first recorded in Eng. 1604.

This ties in with the end of the previous entry, which recommended that the reader consult Log24 entries of Aug. 6, 2002.  Taking my own advice, I did so, and found that the current pope on Aug. 6, 1993, cited Genesis 1:26 —

And God said, Let us
make man in our image,
after our likeness….

Taking the chapter and verse numbers as also having deep religious significance, let us  consult the Log24 entries for 1/26 2003 and 1/26 2004.

In Our Image  

We find that 1/26 2003, and the entries on earlier days that lead up to it, deals with Paul Newman, Our Town, The Hustler, Super Bowl Sunday, and God.

After Our Likeness

We find that 1/26 2004 deals with God’s self-definition on Mount Sinai.  Lucifer also appears.  Karol Wojtyla would do well to click on the following link for an expert characterization of Lucifer:

hypocrite lecteur!
mon semblable, mon frère
.

Saturday, July 31, 2004

Saturday July 31, 2004

Filed under: General — m759 @ 4:01 pm

It’s Alive!

“People once worried about the boundary between the living and the nonliving. Today, the boundary seems meaningless….”

— Attributed to Francis Crick
    (now among the nonliving) 

Opening of
the above novel:

“My name is David Tennant, M.D.
I’m professor of ethics at the
University of Virginia Medical School,
and if you’re watching
this tape, I’m dead.”

From a public-relations newsletter
of the University of Southern California’s
Health Sciences Campus
dated April 20, 2001:

Discussing the Ethics
of Frankenstein

W. French Anderson, the physician and scientist who carried out the first human gene therapy clinical trial, will discuss the ethical issues involved in human genetic engineering and how science fiction has shaped the public’s perception of this budding new technology, Thursday, May 3, at noon, in USC’s Mayer Auditorium.

The lecture, titled “Frankenstein, GATTACA and Gene Therapy,” is free and open to the public. Mayer Auditorium is located on USC’s Health Sciences campus.

In his talk, Anderson will analyze the book Frankenstein and its filmic progeny and discuss how the Frankenstein story has captured the public’s imagination. He will also examine the ethical and moral issues raised by the book and movies and address the charge that, like Dr. Frankenstein, today geneticists are attempting to play God.

Anderson will evaluate the 1997 movie GATTACA, a cautionary tale about injustice in a 21st century society run by genetically “superior” elites. Anderson, who was a scientific consultant for the movie and is now proposing to carry out the first in utero gene therapy trial, will discuss the impact of GATTACA on the public’s understanding of genetic engineering.

See also the previous entry,
on Anderson’s arrest Friday
on charges of child molestation.

For the origin of the title GATTACA,
see The Diamond Code

Thursday, July 15, 2004

Thursday July 15, 2004

Filed under: General — m759 @ 3:04 pm
Identity Crisis

From a summer movie guide:

“Ready for more international espionage and intrigue? On July 23, Matt Damon returns as amnesiac spy Jason Bourne in the sequel to 2002’s surprise hit, ‘The Bourne Identity.’ ….

At the end of ‘Identity,’ Bourne promised retaliation to Treadstone (the super-secret agency that created him) if it came after him.”

And now…

Bad Will Hunting

The image “http://www.log24.com/log/pix04A/040715-Damon2.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix04A/040715-Group.jpg” cannot be displayed, because it contains errors.

Super-secret?

You can’t make this stuff up.

Sunday, June 6, 2004

Sunday June 6, 2004

Filed under: General — m759 @ 4:30 pm
The X Factor

On OSS veteran Charles Hostler,
an unsung D-Day hero, now sung:

“He was trained by the British MI6
intelligence agency for an operation
known as X2 – or ‘double cross.’ “

Beth Gardiner, AP, June 6, 2004

 From Fritz Leiber’s
“Damnation Morning,” 1959:

Bordered version
of the sigil

The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar.  An X superimposed on a plus sign.  It looked permanent….

… “Here is how it stacks up:  You’ve bought your way with something other than money into an organization of which I am an agent….”

“It’s a very big organization,” she went on, as if warning me.  “Call it an empire or a power if you like.  So far as you are concerned, it has always existed and always will exist.  It has agents everywhere, literally.  Space and time are no barriers to it.  Its purpose, so far as you will ever be able to know it, is to change, for its own aggrandizement, not only the present and the future, but also the past.  It is a ruthlessly competitive organization and is merciless to its employees.”

“I. G. Farben?” I asked grabbing nervously and clumsily at humor.

She didn’t rebuke my flippancy, but said, “And it isn’t the Communist Party or the Ku Klux Klan, or the Avenging Angels or the Black Hand, either, though its enemies give it a nastier name.”

“Which is?” I asked.

“The Spiders,” she said.

That word gave me the shudders, coming so suddenly.  I expected the sigil to step off her forehead and scuttle down her face and leap at me — something like that.

She watched me.  “You might call it the Double Cross,” she suggested, “if that seems better.”

Sunday June 6, 2004

Filed under: General — Tags: — m759 @ 1:29 pm
From
The Man in
the High Castle

by Philip K. Dick

Juliana said, “Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?”

“You have a disconcertingly superstitious way of phrasing your question,” Hawthorne said. But he had squatted down to witness the coin throwing. “Go ahead,” he said; he handed her three Chinese brass coins with holes in the center. “I generally use these.”

She began throwing the coins; she felt calm and very much herself. Hawthorne wrote down her lines for her. When she had thrown the coins six times, he gazed down and said:

“Sun at the top. Tui at the bottom. Empty in the center.”

“Do you know what hexagram that is?” she said. “Without using the chart?”

“Yes,” Hawthorne said.

“It’s Chung Fu,” Juliana said. “Inner Truth. I know without using the chart, too. And I know what it means.”

From
The Book of
Ecclesiastes

12:5 … and the almond tree shall flourish, and the grasshopper shall be a burden, and desire shall fail: because man goeth to his long home, and the mourners go about the streets

 

Sunday June 6, 2004

Filed under: General,Geometry — Tags: — m759 @ 1:28 pm
Parallelisms

“I confess I do not believe in time.
I like to fold my magic carpet,
after use, in such a way
as to superimpose
one part of the pattern
upon another.”

(Nabokov, Speak, Memory)

From a review of On the Composition of Images, Signs & Ideas, by Giordano Bruno:

Proteus in the House of Mnemosyne (which is the fifth chapter of the Third Book) relies entirely on familiarity with Vergil’s Aeneid (even when the text shifts from verse to prose). The statement, “Proteus is, absolutely, that one and the same subject matter which is transformable into all images and resemblances, by means of which we can immediately and continually constitute order, resume and explain everything,” reads less clear than the immediate analogy, “Just as from one and the same wax we awaken all shapes and images of sensate things, which become thereafter the signs of all things that are intelligible.”

From an interview with Vladimir Nabokov published in Wisconsin Studies in Contemporary Literature, vol. VIII, no. 2, Spring 1967:

When I was your student, you never mentioned the  Homeric parallels in discussing Joyce’s Ulysses  But you did supply “special information” in introducing many of the masterpieces: a map of Dublin for Ulysses….  Would you be able to suggest some equivalent for your own readers?

Joyce himself very soon realized with dismay that the harping on those essentially easy and vulgar “Homeric parallelisms” would only distract one’s attention from the real beauty of his book. He soon dropped these pretentious chapter titles which already were “explaining” the book to non-readers.  In my lectures I tried to give factual data only. A map of three country estates with a winding river and a figure of the butterfly Parnassius mnemosyne for a cartographic cherub will be the endpaper in my revised edition of Speak, Memory.

For more on Joyce and Proteus,
see the May 27 entry
Ineluctable.

Saturday, May 22, 2004

Saturday May 22, 2004

Filed under: General — m759 @ 6:14 am

Star Wars

In memory of Melvin J. Lasky, editor, 1958-1990, of the CIA-funded journal Encounter:

“Once called as lively, and as bitchy, as a literary cocktail party, Encounter published articles of unrivalled authority on politics, history and literature.”

— Obituary in the Telegraph 

Lasky died on Wednesday, May 19, 2004.  From a journal entry of my own on that date:

This newly-digitized diagram is from a
paper journal note of October 21, 1999.

Note that the diagram’s overall form is that of an eight-point star.  Here is an excerpt from a Fritz Leiber story dealing with such a star, the symbol of a fictional organization:

Time traveling, which is not quite the good clean boyish fun it’s cracked up to be, started for me when this woman with the sigil on her forehead looked in on me from the open doorway of the hotel bedroom where I’d hidden myself and the bottles and asked me, “Look, Buster, do you want to live?”
….

Her right arm was raised and bent, the elbow touching the door frame, the hand brushing back the very dark bangs from her forehead to show me the sigil, as if that had a bearing on her question.

The sigil was an eight-limbed asterisk made of fine dark lines and about as big as a silver dollar.  An X superimposed on a plus sign.  It looked permanent.
….

… “Here is how it stacks up:  You’ve bought your way with something other than money into an organization of which I am an agent….”
….

“It’s a very big organization,” she went on, as if warning me.  “Call it an empire or a power if you like.  So far as you are concerned, it has always existed and always will exist.  It has agents everywhere, literally.  Space and time are no barriers to it.  Its purpose, so far as you will ever be able to know it, is to change, for its own aggrandizement, not only the present and the future, but also the past.  It is a ruthlessly competitive organization and is merciless to its employees.”

“I. G. Farben?” I asked grabbing nervously and clumsily at humor.

She didn’t rebuke my flippancy, but said, “And it isn’t the Communist Party or the Ku Klux Klan, or the Avenging Angels or the Black Hand, either, though its enemies give it a nastier name.”

“Which is?” I asked.

“The Spiders,” she said.

That word gave me the shudders, coming so suddenly.  I expected the sigil to step off her forehead and scuttle down her face and leap at me—something like that.

She watched me.  “You might call it the Double Cross,” she suggested, “if that seems better.”

— Fritz Leiber,
   “Damnation Morning,” 1959

From last year’s entry,
Indiana Jones and the Hidden Coffer,
of 6/14:

From Borges’s “The Aleph“:

“The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court…. The mosque dates from the seventh century; the pillars come from other temples of pre-Islamic religions…. Does this Aleph exist in the heart of a stone?”

(“Los fieles que concurren a la mezquita de Amr, en el Cairo, saben muy bien que el universo está en el interior de una de las columnas de piedra que rodean el patio central…. la mezquita data del siglo VII; las columnas proceden de otros templos de religiones anteislámicas…. ¿Existe ese Aleph en lo íntimo de una piedra?”)

From The Hunchback of Notre Dame:

Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar.

A coffer of great richness
In a pillar’s heart they found,
Within it lay new banners,
With figures to astound.

See also the figures obtained by coloring and permuting parts of the above religious symbol.

Lena Olin and Harrison Ford
in “Hollywood Homicide

Finally, from an excellent site
on the Knights Templar,
a quotation from Umberto Eco:

When all the archetypes burst out shamelessly, we plumb the depths of Homeric profundity. Two cliches make us laugh but a hundred cliches move us because we sense dimly that the cliches are talking among themselves, celebrating a reunion . . . Just as the extreme of pain meets sensual pleasure, and the extreme of perversion borders on mystical energy, so too the extreme of banality allows us to catch a glimpse of the Sublime.

— “Casablanca: Cult Movies and Intertextual Collage” (1984) from Travels in Hyperreality

Saturday, May 8, 2004

Saturday May 8, 2004

Filed under: General — Tags: — m759 @ 9:00 am

Slab!

Aphorism 2 from Wittgenstein's
Philosophical Investigations
with commentary on the right
by Lois Shawver

Let us imagine a language …The language is meant to serve for communication between a builder A and an assistant B.  A is building with building-stones; there are blocks, pillars, slabs and beams.  B has to pass the stones, and that in the order in which A needs them.  For this purpose they use a language consisting of the words 'block', 'pillar', 'slab', 'beam.'  A calls them out; — B brings the stone which he has learnt to bring at such-and-such a call. — Conceive this as a complete primitive language.

… this passage describes the prototypic primitive language-game….

There are piles of pillars, slabs, blocks and beams.  The supervisor calls out "Slab!" and the worker brings a slab and sets it at the supervisor's feet.  Pretty simple.

Wittgenstein puts forth [this] language-game in order to try to envision a language in which Augustine's picture of language works.

Click on pictures for details.

Friday, April 30, 2004

Friday April 30, 2004

Filed under: General,Geometry — m759 @ 5:24 pm

Notes

  

On “Notes Toward a Supreme Fiction,” by Wallace Stevens:

“This third section continues its play of opposing forces, introducing in the second canto a ‘blue woman,’ arguably a goddess- or muse-figure, who stands apart from images of fecundity and sexuality….”

Michael Bryson 

From a Beethoven’s Birthday entry:

Moulin Bleu

  

Kaleidoscope turning…
Shifting pattern
within unalterable structure…
— Roger Zelazny, Eye of Cat   

See, too, Blue Matrices, and
a link for Beethoven’s birthday:

Song for the
Unification of Europe
(Blue 1)

From today’s news:

PRAGUE, Czech Republic (AP) – Ushering in a bold new era, hundreds of thousands of people packed streets and city squares across Europe on Friday for festivals and fireworks marking the European Union’s historic enlargement to 25 countries from 15.

The expanded EU, which takes in a broad swath of the former Soviet bloc – a region separated for decades from the West by barbed wire and Cold War ideology – was widening to 450 million citizens at midnight (6 p.m.EDT) to create a collective superpower rivalling the United States.

“All these worlds are yours
except Europa.
Attempt no landing there.”

Tuesday, March 2, 2004

Tuesday March 2, 2004

Filed under: General — m759 @ 4:16 pm

Super Tuesday

O the days of the Kerry dancing….
When the boys began to gather,
    in the glen of a summer’s night.
And the Kerry piper’s tuning 
    made us long with wild delight.

For further details, see April 16, 2003.

Tuesday, February 10, 2004

Tuesday February 10, 2004

Filed under: General — m759 @ 12:07 pm

George W. Bush,
Liberal!

Part I:

 

2:09 PM PST, February 9, 2004

President’s Economic Report
Endorses Export of Jobs

By Warren Vieth and Edwin Chen,
Los Angeles Times Staff Writers

WASHINGTON — The movement of American factory jobs and white-collar work to other countries is part of a positive transformation that will enrich the U.S. economy over time, even if it causes short-term pain and dislocation, the Bush administration said today.

The embrace of foreign “outsourcing,” an accelerating trend that has contributed to U.S. job losses in recent years and has become an issue in the 2004 elections, is contained in the president’s annual report to Congress on the health of the U.S. economy….

Although trade expansion inevitably hurts some workers, it says, the benefits will eventually outweigh the costs as Americans are able to buy goods and services at lower costs and as jobs are created in growing sectors of the economy.

The report endorses the relatively new phenomenon of outsourcing high-end white-collar work to India and other countries, a trend that has created concern within affected professions such as computer programming and medical diagnostics.

Part II:

A search on liberal “free trade” leads to the following quote:

“One of the central concepts of classical liberal economic thought is the superiority of free trade over protectionism.”

Therefore George W. Bush, by courageously advocating free trade despite its political unpopularity, is a classic liberal.

Part III:

Context for the above quote:

The Liberal Agenda for the 21st Century

George W. Bush’s free-trade policy
fits right in.

Part IV:

The Conservative Alternative…

Patrick J. Buchanan,

author of “The Death of Manufacturing

and A Republic, Not an Empire.

“Let it be said: George Bush is beatable. He has no explanation and no cure for the hemorrhaging of manufacturing jobs at Depression rates, no plan to stop the outsourcing of white-collar jobs to Asia, no desire or will to stop the invasion from Mexico.

Yet, he remains a favorite against Kerry, because Kerry has no answers, either. Both are globalists. Both are free-traders. Both favor open borders. Again, it needs to be said:  There is no conservative party in America.”

Patrick J. Buchanan, Feb. 2, 2004

Not yet, there isn’t.

Tuesday, February 3, 2004

Tuesday February 3, 2004

Filed under: General — m759 @ 1:35 pm

Speaking Globally

On Janet Jackson at the Super Bowl:

“I don’t expect much but I am hoping that the whole episode rekindles a discussion in the country about the incredible double standard there is in the popular culture. Adults complain about the prevalence of teen sex, teen pregnancy, drug abuse, and lack of respect for appropriate authority but then place those very behaviors in front of children in the form of talented, attractive and highly paid role models. This is not a sensible approach. Speaking globally, this culture is asking for its own demise.”

Warren Throckmorton, 2/3/04

Sunday, January 11, 2004

Sunday January 11, 2004

Filed under: General — m759 @ 1:00 pm

Two-Dimensional Time

The following is from the Prime Quotes page at the website of Matthew R. Watkins…

“I have sometimes thought that the profound mystery which envelops our conceptions relative to prime numbers depends upon the limitations of our faculties in regard to time, which like space may be in essence poly-dimensional and that this and other such sort of truths would become self-evident to a being whose mode of perception is according to superficially as opposed to our own limitation to linearly extended time.”

J.J. Sylvester, from “On certain inequalities relating to prime numbers”, Nature 38 (1888) 259-262, and reproduced in Collected Mathematical Papers, Volume 4, page 600 (Chelsea, New York, 1973)
The link within the quote, supplied
by Watkins, is to a bibliography on time and causality.  On another page at his site, Watkins says:
Translated into contemporary English, Sylvester is saying more-or-less this:

“I have sometimes thought that if we were able to perceive time in some multi-dimensional way, more like a surface than like a line, then perhaps the distribution of prime numbers would be entirely self-evident, and would not seem at all mysterious to us.”

Many thanks to Heckler & Coch (5/19/03) for pointing out the Sylvester quotation.

For related thoughts on this topic, see Time Fold.

Saturday, November 15, 2003

Saturday November 15, 2003

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

Aes Triplex

The title, from a Robert Louis Stevenson essay, means “triple brass” (or triple bronze):

From the admirable site of J. Nathan Matias:

Aes Triplex means Triple Bronze, from a line in Horace’s Odes that reads ‘Oak and triple bronze encompassed the breast of him who first entrusted his frail craft to the wild sea.’ ”

From Philip K. Dick’s The Man in the High Castle:

Juliana said, “Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?”

“You have a disconcertingly superstitious way of phrasing your question,” Hawthorne said. But he had squatted down to witness the coin throwing. “Go ahead,” he said; he handed her three Chinese brass coins with holes in the center. “I generally use these.”

This passage, included in my earlier entry of Friday, combined with the opening of yet another major motion picture starring Russell Crowe, suggests three readings for that young man, who is perhaps the true successor to Marlon Brando.

Oracle, for Crowe as John Nash (A Beautiful Mind):

Understanding the I Ching

Mutiny, for Crowe as Jack Aubrey (Master and Commander):

Bartleby, the Scrivener

Storm, for Crowe as Maximus (Gladiator):

Pharsalia, Book V:
The Oracle, the Mutiny, the Storm

As background listening, one possibility is Sinatra’s classic “Three Coins”:

“Three hearts in the fountain,
Each heart longing for its home.
There they lie in the fountain
Somewhere in the heart of Rome.*” 

Personally, though, I prefer, as a tribute to author Joan Didion (who also wrote of coins and the Book of Transformations), the even more classic Sinatra ballad

Angel Eyes.”

 * Horace leads to “Acroceraunian shoals,” which leads to Palaeste, which leads to Pharsalia and to the heart of Rome.  (With a nod to my high school Latin teacher, the late great John Stachowiak.)

Friday, November 14, 2003

Friday November 14, 2003

Filed under: General — Tags: — m759 @ 2:56 am

Philip K. Dick Meets Joan Didion

From the ending of
The Man in the High Castle:

Juliana said, “I wonder why the oracle would write a novel. Did you ever think of asking it that?” ….

“You may say the question aloud,” Hawthorne said. “We have no secrets here.”

Juliana said, “Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?”

“You have a disconcertingly superstitious way of phrasing your question,” Hawthorne said. But he had squatted down to witness the coin throwing. “Go ahead,” he said; he handed her three Chinese brass coins with holes in the center. “I generally use these.”

She began throwing the coins; she felt calm and very much herself. Hawthorne wrote down her lines for her. When she had thrown the coins six times, he gazed down and said:

“Sun at the top. Tui at the bottom. Empty in the center.”

IMAGE- Hexagram 61

“Do you know what hexagram that is?” she said. “Without using the chart?”

“Yes,” Hawthorne said.

“It’s Chung Fu,” Juliana said. “Inner Truth. I know without using the chart, too. And I know what it means.”

From the ending of
Play It As It Lays:

I lie here in the sunlight, watch the hummingbird.  This morning I threw the coins in the swimming pool, and they gleamed and turned in the water in such a way that I was almost moved to read them.  I refrained.

One thing in my defense, not that it matters.  I know something Carter never knew, or Helene, or maybe you.  I know what “nothing” means, and keep on playing.

Why, BZ would say.

Why not, I say.

Friday, October 17, 2003

Friday October 17, 2003

Filed under: General,Geometry — m759 @ 4:15 pm

Happy Birthday, Arthur Miller

Miller, the author of “The Crucible,” is what Russell Baker has called a “tribal storyteller.”

From an essay by Baker in The New York Review of Books, issue dated November 6, 2003 (Fortieth Anniversary Issue):

“Among the privileges enjoyed by rich, fat, superpower America is the power to invent public reality.  Politicians and the mass media do much of the inventing for us by telling us stories which purport to unfold a relatively simple reality.  As our tribal storytellers, they shape our knowledge and ignorance of the world, not only producing ideas and emotions which influence the way we live our lives, but also leaving us dangerously unaware of the difference between stories and reality.”

— Russell Baker, “The Awful Truth,” NYRB 11/6/03, page 8 

Here is a rather similar view of the media:

“Who Rules America?”.

The attentive student of this second essay will have no difficulty finding a single four-letter word to replace both of Baker’s phrases “rich, fat, superpower America” and “politicians and the mass media.”

Baker’s concern for “the difference between stories and reality” is reflected in my own website The Diamond Theory of Truth.  In summary:

“Is it safe?” — Sir Laurence Olivier

Tuesday, September 2, 2003

Tuesday September 2, 2003

Filed under: General,Geometry — Tags: , — m759 @ 1:11 pm

One Ring to Rule Them All

In memory of J. R. R. Tolkien, who died on this date, and in honor of Israel Gelfand, who was born on this date.

Leonard Gillman on his collaboration with Meyer Jerison and Melvin Henriksen in studying rings of continuous functions:

“The triple papers that Mel and I wrote deserve comment. Jerry had conjectured a characterization of beta X (the Stone-Cech compactification of X) and the three of us had proved that it was true. Then he dug up a 1939 paper by Gelfand and Kolmogoroff that Hewitt, in his big paper, had referred to but apparently not appreciated, and there we found Jerry’s characterization. The three of us sat around to decide what to do; we called it the ‘wake.’  Since the authors had not furnished a proof, we decided to publish ours. When the referee expressed himself strongly that a title should be informative, we came up with On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. (This proved to be my second-longest title, and a nuisance to refer to.) Kolmogoroff died many years ago, but Gelfand is still living, a vigorous octogenarian now at Rutgers. A year or so ago, I met him at a dinner party in Austin and mentioned the 1939 paper. He remembered it very well and proceeded to complain that the only contribution Kolmogoroff had made was to point out that a certain result was valid for the complex case as well. I was intrigued to see how the giants grouse about each other just as we do.”

Leonard Gillman: An Interview

This clears up a question I asked earlier in this journal….

Wednesday, May 14, 2003

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.

See

The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

A response by Richard Cudney:

“In regard to your entry, it is largely correct.  The paper by Kolmogorov and Gelfand that you refer to is the one that I just read in his collected works.  So, I suppose my entry was unfair to Gelfand.  You’re right, the issue of credit is a bit touchy since Gelfand was his student.  In a somewhat recent essay, Arnol’d makes the claim that this whole thread of early work by Gelfand may have been properly due to Kolmogorov, however he has no concrete proof, having been but a child at the time, and makes this inference based only on his own later experience as Kolmogorov’s student.  At any rate, I had known about Gelfand’s representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them. 

And to clarify-where I speak of the credit for this theorem being obscured, I speak of my own experience as an algebraic geometer and not a functional analyst.  In the textbooks on algebraic geometry, one sees no explanation of why we use Spec A to denote the scheme corresponding to a ring A.  That question was answered when I took functional analysis and learned about Gelfand’s theorem, but even there, Kolmogorov’s name did not come up.

This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras.  In historical terms, this result precedes Gelfand’s theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique.  That is to say, this whole vein of Gelfand’s work started in this joint paper.

Of course, to be even more fair, I should say that Stone was the very first to prove a theorem like this, a debt which Kolmogorov and Gelfand acknowledge.  Stone’s paper is the true starting point of these ideas, but this paper of Kolmogorov and Gelfand is the second landmark on the path that led to Grothendieck’s concept of a scheme(with Gelfand’s representation theorem probably as the third).

As an aside, this paper was not Kolmogorov’s first foray into topological algebra-earlier he conjectured the possibility of a classification of locally compact fields, a problem which was solved by Pontryagin.  The point of all this is that I had been making use of ideas due to Kolmogorov for many years without having had any inkling of it.”

Posted 5/14/2003 at 8:44 PM by rcudney

Saturday, August 16, 2003

Saturday August 16, 2003

Filed under: General,Geometry — Tags: , , — m759 @ 2:16 am

My Personal Thorny Crown

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

" 'He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,' said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe's first big show at the Modern, 'High & Low.' 'Art was always material first — it was never, ever bound by a thorny crown of ideas.' "

For some background on the phrase "thorny crown of ideas," see the web page

Understanding.   

The phrase "thorny crown of ideas" is also of interest in the light of recent controversy over Mel Gibson's new film, "The Passion."

For details of the controversy, see Christopher Orlet's Aug. 14 essay at Salon.com,

Mel Gibson vs. "The Jews"

For a real "thorny crown of ideas," consider the following remarks by another art historian:

"Whether or not we can follow the theorist in his demonstrations, there is one misunderstanding we must avoid at all cost.  We must not confuse the analyses of geometrical symmetries with the mathematics of combination and permutation….

The earliest (and perhaps the rarest) treatise on the theory of design drives home this insight with marvellous precision."

— E. H. Gombrich, 1979, in
   The Sense of Order

This is perhaps the most stupid remark I have ever read.  The "treatise on the theory of design" that Gombrich refers to is

  • Dominique Douat, Methode pour faire une infinité de desseins differents avec des carreaux mipartis de deux couleurs par une ligne diagonale : ou observations du Pere Dominique Douat Religieux Carmes de la Province de Toulouse sur un memoire inséré dans l'Histoire de l'Académie Royale des Sciences de Paris l'année 1704, présenté par le Reverend Sebastien Truchet religieux du même ordre, Academicien honoraire, imprimé chez Jacques Quillau, Imprimeur Juré de l'Université, Paris 1722.

This is the title given at the web page

Truchet & Types:
Tiling Systems and Ornaments
,

which gives some background. 

Certain of the Truchet/Douat patterns have rather intriguing mathematical properties, sketched in my website Diamond Theory.  These properties become clear if and only we we do what Gombrich moronically declares that we must not do:  "confuse the analyses of geometrical symmetries with the mathematics of combination and permutation."  (The verb "confuse" should, of course, be replaced by the verb "combine.") 

What does all this have to do with

Mel Gibson vs. "The Jews" ?

As jesting Pilate seems to have realized, whenever Jews (or, for that matter, Christians) tell stories, issues of truth may arise.  Such issues, as shown by current events in that damned Semitic Hell-on-Earth that used to be referred to as "the Holy Land," can be of life-and-death importance.


Scene from
The Passion

The Roman soldiers may have fashioned a physical crown of thorns, but the Jews are quite capable of fashioning a very uncomfortable crown of, as Gopnik says, "ideas."

Here is an example.

"Ernst Hans Josef Gombrich, who as an author went by the name E. H. Gombrich, was born in Vienna in 1909….

The Gombrich family was Jewish, but his parents felt this had no particular relevance. In later years Mr. Gombrich said that whether someone was Jewish or not was a preoccupation for the Gestapo."

— Michael Kimmelman's obituary for Gombrich in the New York Times. Kimmelman is chief art critic for the New York Times and author of the Times's Aug. 15 Varnedoe obituary.

The web page Understanding cited above contains a link to

Pilate, Truth, and Friday the Thirteenth,

a page combining some religious remarks with a quotation of an extremely patronizing and superficial reference to my own work (and, in passing, to Truchet/Douat patterns).

This reference, and the above-quoted remark by Gombrich, constitute my own modest claim to what the Jew Gopnik jokingly calls a "thorny crown of ideas."

To me it is no joke.

This partly accounts for the rather strained quality of the attempt at humor in a web page I put together yesterday in response to Varnedoe's obituary:

Fahne Hoch, Macbeth!

Another reason for the strained quality is my being struck by the synchronicity of reading Varnedoe's obituary shortly after I had done a journal entry related to the death in July of an earlier Museum of Modern Art curator.  Like Robert A. Heinlein, I think the God of the Jews is a lousy deity and an even worse father figure.  I do, however, believe in synchronicity.
 

Sunday, May 25, 2003

Sunday May 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 9:26 pm

 STAR WARS  
opened on this date in 1977.

From the web page Amande:

Le Christ et la Vierge apparurent souvent entourés d’une auréole en forme d’amande: la mandorle.

Étymologiquement, le mot amande est une altération de amandala, qui dérive lui-même du latin classique amygdala….

L’amande a… une connotation symbolique, celle du sexe féminin. Elle figure souvent la vulve. Elle est alors en analogie avec la yoni du vocabulaire de l’hindouisme, la vulve ou la matrice, représentée par une amande ou une noix coupée en deux.

Screenshot of the online
New York Times, May 25, 2003:

Ariel the Hutt and Princess Amygdala

Introduction to Yantra

by Horia Cristescu and
Dan Bozaru 

The Triangle (TRIKONA)
The triangle (TRIKONA) is the symbol of
SHAKTI , the feminine energy or aspect of Creation. The triangle pointing down represents the YONI , the feminine sexual organ and the symbol of the supreme source of the Universe, and when the triangle is pointing upwards it signifies intense spiritual aspiration, the sublimation of one’s nature into the most subtle planes and the element of fire (AGNI TATTVA). The fire is always oriented upwards, thus the correlation with the upward triangle – SHIVA KONA. On the other hand, the downward pointing triangle signifies the element of water which always tends to flown and occupy the lowest possible position. This triangle is known as SHAKTI KONA.

The intersection of two geometric forms (lines, triangles, circles, etc.) represents forces that are even more intense than those generated by the simple forms. Such an interpenetration indicates a high level in the dynamic interaction of the correspondent energies. The empty spaces generated by such combinations are described as very efficient operational fields of the forces emanating from the central point of the YANTRA. That is why we can very often encounter representations of MANTRAS in such spaces. YANTRA and MANTRA are complementary aspects of SHIVA and their use together is much more efficient than the use of one alone.


The Six Points Star (SHATKONA)
A typical combination often found in the graphical structure of a YANTRA is the superposition of two triangles, one pointing upwards and the other downwards, forming a star with six points (SHATKONA), also known as David’s Star. This form symbolically represents the union of
PURUSHA and PRAKRITI or SHIVA-SHAKTI, without which there could be no Creation.

AMEN.

Thursday, May 15, 2003

Thursday May 15, 2003

Filed under: General,Geometry — Tags: — m759 @ 3:33 pm

The Only Pretty Ring Time

On May 14 five years ago, the night Sinatra died, the Pennsylvania (State of Grace) lottery evening number was 256:  see my note, Symmetries, of April 2, 2003.

On May 14 this year, the Pennsylvania lottery evening number was 147.  Having, through meditation, perhaps established some sort of minor covenant with whatever supernatural lottery powers may exist, this afternoon I sought the significance of this number in Q's 1939 edition of the Oxford Book of English Verse.  It is the number of "It was a Lover and his Lass," a song lyric by William Shakespeare.  The song includes the following lines:

In the spring time,
    the only pretty ring time,
When birds do sing,
    Hey ding a ding, ding;
Sweet lovers love the spring.

For the Sinatra connection, see
Metaphysics for Tina.

The selection of Q's book for consultation was suggested by the home page of Simon Nickerson at Jesus College, Cambridge University, and by the dedication page of Q's 1925 Oxford Book of English Prose, which names Nickerson's school.

Ian Lee on the communion of saints and the association of ideas:

"The association is the idea."

For translation of the Greek phrase in Q's 1925 dedication, see

Greek and Roman Grammarians
on Motion Verbs and Place Adverbials

Malcolm D. Hyman
Harvard University
January 4, 2003

Wednesday, May 14, 2003

Wednesday May 14, 2003

Filed under: General,Geometry — Tags: — m759 @ 2:00 pm

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.

See

The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

Friday, April 11, 2003

Friday April 11, 2003

Filed under: General — m759 @ 2:56 pm

Heaven’s Gate

“Rhetoric is concerned with the state of Babel after the Fall.”

— Kenneth Burke, A Rhetoric of Motives, quoted by Douglas Robinson at the site Linguistics and Language

Mesopotamian mathematics:

“Location: present-day Iraq, between the Tigris and Euphrates

Cities: Babylon, founded 2300 BC, 70 miles south of present Baghdad, on the Euphrates….

Babylon = Bab-ilu, “gate of God,” Hebrew: Babel or Bavel.”

Modern rendition
of “Bab-ilu

Kenneth
Burke

Perhaps the real heaven’s gate is at

Pottawatomie College.

Instant karma update:

 At 5:09 PM I read the following in the New York Review of Books, dated May 1, 2003, which arrived today.

From a review of Terror and Liberalism, by Paul Berman:

“As a general analysis of the various enemies of liberalism, and what ties them together, it is superb.  All — Nazis, Islamists, Bolsheviks, Fascists, and so on — are linked by Berman to the ‘ur-myth’ of the fall of Babylon.”

Speaking of Ur, Berman likes to quote a non-Biblical Abraham, named Lincoln.  The first, Biblical, Abraham was a damned homicidal lunatic, and the later American Abraham also delighted in blood sacrifice.  But that’s just my opinion.  For a different view, see the Chautauqua Abrahamic Program.

 

Sunday, March 2, 2003

Sunday March 2, 2003

Filed under: General — Tags: — m759 @ 10:20 pm

7:20 PM CALI Time

The Bus and the Bead Game:
 
The Communion of Saints as
 the Association of Ideas

On this date in 1955, “Bus Stop,” a play by William Inge, opened at the Music Box Theatre in New York City.

“I seemed to be standing in a bus queue by the side of a long, mean street.”

— C. S. Lewis, The Great Divorce, opening sentence

Today’s birthdays:

Sam Houston
Dr. Seuss
Kurt Weill
Mikhail Gorbachev
Tom Wolfe
Desi Arnaz
Jennifer Jones
Karen Carpenter

and many others.

Today is the feast day of  

St. Randolph Scott
St. Sandy Dennis
St. D. H. Lawrence, and
St. Charlie Christian.

“Your guitar, it sounds so sweet and clear…”

— Karen Carpenter singing “Superstar

“And if I find me a good man,
 I won’t be back at all.”

C. C. Rider lyrics

See (and hear) also “Seven Come Eleven,” played by St. Charlie Christian.

One might (disregarding separation in time and space — never major hindrances to the saints) imagine C. S. Lewis in Heaven listening to a conversation among the four saints listed above.  For more on the communion of saints, see my entry “State of the Communion” of Tuesday, Jan. 28, 2003.  This entry, quoting an old spiritual, concluded with “Now hear the word of the Lord”  — followed by this notation: 

 7:11 PM.

See also the N.Y. Times obituary of John P. Thompson of Dallas, former 7-Eleven chairman, who died, as it happened, on that very day (Jan. 28).  See also Karen Carpenter’s “first take luck.”

The sort of association of ideas described in the “Communion” entry is not unrelated to the Glasperlenspiel, or Glass Bead Game, of Hermann Hesse.  For a somewhat different approach to the Game, see

The Glass Bead Game,”

by John S. Wilson, group theorist and head of the Pure Mathematics Group at the University of Birmingham in England. Wilson is “not convinced that Hesse’s… game is only a metaphor.” Neither am I.

For the association-of-ideas approach, see the page cited in my “Communion” entry,

A Game Designer’s Holy Grail,”

and (if you can find a copy) one of the greatest forgotten books of the twentieth century,

The Third Word War,

by Ian Lee (A&W Publishers, Inc., New York, 1978).  As Lee remarks concerning the communion of saints and the association of ideas,

“The association is the idea.”
 

Thursday, January 30, 2003

Thursday January 30, 2003

Filed under: General — m759 @ 2:45 am

Poetic Justice:
The Peacock Throne

Yesterday was the death day of two proponents of Empire: George III (in 1820) and Robert Frost (in 1963).  Lord Byron argued that the King slipped through heaven's gate unobserved while a friend distracted St. Peter with bad poetry.  We may imagine, on this dark night of the soul, Frost performing a similar service.

Though poets of the traditional sort may still perform such services in Heaven, here on earth they have been superseded by writers of song lyrics.  An example, Roddy Frame (formerly of the group "Aztec Camera"), was born on yesterday's date in 1964.  A Frame lyric:

Transformed by some strange alchemy,*
You stand apart and point to me
And point to something I can't see….

Back Door to Heaven         

Namely:

    The Back Door to Heaven    

For poetic purposes, we may think of surreptitious entry into Heaven as being conveniently accomplished through a portal like the above back door, which is that of a small hotel in Cuernavaca, Mexico.

This is not your average Motel 6 back door.  As a former New York Times correspondent has written,

"Over the years, the guest list has drawn the likes of Prince Philip and the Shah of Iran, Richard Burton and Elizabeth Taylor. But informality still reigns."

This small hotel (or its heavenly equivalent), whose gardens are inhabited by various exotic birds, including peacocks, may still be haunted by the late Shah, who apparently styled himself "King of Kings and Emperor of the Peacock Throne."  Of course, the ghost of the King of Kings, after entering the garden of Paradise, may not be able to resume his former human shape.  He might still, however, be among those greeted by his fellow Emperor, George III, with the famous words

"My Lords and Peacocks…"

*For more on alchemy and Cuernavaca, see
  my journal note "The Black Queen."

Sunday, January 26, 2003

Sunday January 26, 2003

Filed under: General — m759 @ 5:55 pm

Our Town:
No There There?

Paul Newman, scheduled for his last performance in “Our Town” today, said in 1961:

“With that fifteen hundred, I could have beat him. That’s all I needed Charlie…You’d love to keep me hustlin’ for ya, huh, wouldn’t ya? I mean, a couple more years with me scufflin’ around, in them little towns and those back alleys, you might make yourself enough to get a little pool room back in Oakland – six tables and a handbook on the side…Lay down and die by yourself.”

— Fast Eddie Felson in “The Hustler

For another view of Oakland, see

Super Bowl XXXVII Live!


The Raiders take on the Buccaneers in Super Bowl XXXVII this afternoon.

Gertrude Stein on Oakland, California:

“There is no there there.”

Well, maybe a little pool room….

Monday, January 20, 2003

Monday January 20, 2003

Filed under: General — Tags: — m759 @ 5:00 pm

Shine On, Robinson Jeffers

"…be in nothing so moderate as in love of man, 
      a clever servant, insufferable master.
There is the trap that catches noblest spirits,
     that caught — they say — God, when he walked on earth."
Shine, Perishing Republic, by Robinson Jeffers

Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.

"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence.   His verse also flashes with a diamond's hardness when he portrays human pain and folly."
Gary Suttle  

"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov, 
   Grace To Be Said at the Supermarket 

"Across my foundering deck shone 
A beacon, an eternal beam. | Flesh fade, and mortal trash 
Fáll to the resíduary worm; | world's wildfire, leave but ash: 
In a flash, at a trumpet crash, 
I am all at once what Christ is |, since he was what I am, and 
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
    immortal diamond, 
Is immortal diamond."
— Gerard Manley Hopkins,
    That Nature is a Heraclitean Fire and of the Comfort of the Resurrection

"In the last two weeks, I've been returning to Hopkins.  Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
    in Vanity Fair, May 2002, page 162

"There's none but truth can stead you.  Christ is truth."
— Gerard Manley Hopkins

"The rock cannot be broken.  It is the truth."
— Wallace Stevens 

"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House

On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.

"…today, the Rock cries out to us, clearly, forcefully…."
Maya Angelou, January 20, 1993

"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX

Top view of
ordinary
diamond

Top view of
Hearts On Fire
diamond

Advertising Copy:

What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond.

 

"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
Symbols.com

"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame."
Song of Solomon

"The last words from the people in the towers and on the planes, over and over again, were 'I love you.'  Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock:  we are learning just how powerful love really is, even in the face of death."
The Rev. Kenneth E. Kovacs

"Then I'll get on my knees and pray
We don't get fooled again."
The Who 

See also my note, "Bright Star," of October 23, 2002.

 

Thursday, January 16, 2003

Thursday January 16, 2003

Filed under: General — m759 @ 5:05 pm

ART WARS
At the Still Point

“At the still point, there the dance is.”

— T. S. Eliot in Four Quartets

Humphrey Carpenter in The Inklings, his book on the Christian writers J. R. R. Tolkien, C. S. Lewis, and Charles Williams, says that

“Eliot by his own admission took the ‘still point of the turning world’ in Burnt Norton from the Fool in Williams’s The Greater Trumps.”

The Inklings, Ballantine Books, 1981, p. 106

Carpenter says Williams maintained that

It is the Christian’s duty to perceive “the declared pattern of the universe” — the “eternal dance” of Williams’s story The Greater Trumps — and to act according to it.

— Paraphrase of Carpenter, pp. 111-112

“The sun is not yet risen, and if the Fool moves there he comes invisibly, or perhaps in widespread union with the light of the moon which is the reflection of the sun.  But if the Tarots hold, as has been dreamed, the message which all things in all places and times have also been dreamed to hold, then perhaps there was meaning in the order as in the paintings; the tale of the cards being completed when the mystery of the sun has opened in the place of the moon, and after that the trumpets cry in the design which is called the Judgement, and the tombs are broken, and then in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps, by Charles Williams, Ch. 14

If we must have Christians telling stories, let them write like Charles Williams.

Note that although Williams says the Fool Tarot card has no number, it is in fact often numbered 0. See

The Fool as Zero.”

See also Sequel — about the work, life, and afterlife of Stan Rice, husband of Anne Rice (author of The Vampire Chronicles) — and the following story from today’s N.Y. Times:

The New York Times, Jan. 16, 2003:

‘Dance of the Vampires,’
a Broadway Failure, Is Closing

By JESSE McKINLEY

In one of the costliest failures in Broadway history, the producers of “Dance of the Vampires,” a $12 million camp musical at the Minskoff Theater, will close the show on Jan. 25, having lost their entire investment.

Its gross for the week ending on Sunday [Jan. 12], $459,784, was its lowest, and that, finally, was the kiss of death for the show.

The death and arrival at heaven’s gate
of The Producers‘ producer, Sidney Glazier,
on Dec. 14, 2002, is described in the web page
Eight is a Gate.
 

Friday, January 10, 2003

Friday January 10, 2003

Filed under: General,Geometry — Tags: — m759 @ 8:15 pm

Story

"How much story do you want?" 
— George Balanchine

While researching yesterday's entry on Balanchine, Apollo, and the nine Muses, I came across this architect's remarks, partially quoted yesterday and continued here:

"The icon that I use for this element is the nine-fold square…. This is the garden of Apollo, the field of Reason….  This is the Temple of Solomon, as inscribed, for example, by a nine-fold compartmentation to provide the ground plan of Yale, as described to me by Professor Hersey."

Duncanology Part 3

Checking this out yesterday, I came across the following at a Yale University Art Gallery site:

"This exhibition of nine boldly colored, asymmetrically designed quilts selected from a private collection will be displayed in the Matrix Gallery….

With the guidance of Professor Maude Southwell Wahlman, author of 'Signs and Symbols: African Images in African American Quilts,' the collector has explored and gathered examples…."

Exploring and gathering examples myself today, I received a book in the mail — W. M. Spackman's On the Decay of Humanism (Rutgers University Press, 1967) — and picked up a second-hand book at a sale — Barbara Michaels's Stitches in Time (Harper Collins Publishers, 1995).

The Spackman book includes the following poem at the end:

In sandarac etui for sepulchre
  lies the cered body of a poisoned queen;
     and in her mouth and hair, and at her feet,
     and in the grey folds of her winding-sheet,
  there sifts a dreamy powder, smooth and green,
the magic of an idle sorcerer,
  an ancient spell, cast when the shroud was spun.
     In death her hands clasp amourously a bowl
     that still contains the fragments of her soul,
  a tale of Beauty sought, and Beauty won,
his false lips kissed, and Beauty dead for her.

— Alexander B. Griswold, Princeton '28, in the
    Nassau Literary Magazine of December 1925

From a synopsis of Michaels's Stitches in Time:

"Michaels follows Rachel, a graduate student studying women's crafts–weaving, spinning, quilting, embroidery–and the superstitions connected with them. Linking all important rites of passage to the garments created as markers of these occasions leads Rachel to her theory: in societies in which magic was practiced, the garment was meant to protect its wearer. She gains evidence that her theory is valid when an evil antique bridal quilt enters her life."

Although Stitches in Time is about a quilt — stitched, not spun — Griswold's line

"an ancient spell, cast when the shroud was spun" 

is very closely related to the evil spell in Michaels's book. 

The above events display a certain synchronicity that Wallace Stevens might appreciate, especially in light of the following remark in a review of Stitches in Time:

"…the premise is too outlandish for even the suspension of disbelief…." (Publishers Weekly, 4/24/95)

Stevens might reply,

The very man despising honest quilts
Lies quilted to his poll in his despite.

— "The Comedian as the Letter C," Part V

Finally, those who prefer stories to the more formal qualities of pure dance (ballet) pure mathematics (see previous entry), pure (instrumental) music, and pure (abstract, as in quilt designs) art, can consult the oeuvre of Jodie Foster — as in my 

Pearl Harbor Day entry on Buddhism.

An art historian named Griswold — perhaps that very same Griswold quoted above — might have a thing or two to say to Jodie on her recent film "Anna and the King."  In the April, 1957, issue of The Journal of the Siam Society, Alexander B. Griswold takes issue with Broadway's and Hollywood's "grotesque caricature" of Siamese society, and ultimately with Anna herself:

"The real fault lies in the two books they ultimately spring from — The English Governess at the Court of Siam and The Romance of the Harem — both written by Mrs. Anna Leonowens.''

Is a puzzlement.

See also The Diamond 16 Puzzle for some quilt designs.

Thursday, January 9, 2003

Thursday January 9, 2003

Filed under: General — Tags: , , , , — m759 @ 4:48 pm

Balanchine's Birthday

Today seems an appropriate day to celebrate Apollo and the nine Muses.

From a website on Balanchine's and Stravinsky's ballet, "Apollon Musagete":

In his Poetics of Music (1942) Stravinsky says: "Summing up: What is important for the lucid ordering of the work– for its crystallization– is that all the Dionysian elements which set the imagination of the artist in motion and make the life-sap rise must be properly subjugated before they intoxicate us, and must finally be made to submit to the law: Apollo demands it."  Stravinsky conceived Apollo as a ballet blanc– a "white ballet" with classical choreography and monochromatic attire. Envisioning the work in his mind's eye, he found that "the absence of many-colored hues and of all superfluities produced a wonderful freshness." Upon first hearing Apollo, Diaghilev found it "music somehow not of this world, but from somewhere else above." The ballet closes with an Apotheosis in which Apollo leads the Muses towards Parnassus. Here, the gravely beautiful music with which the work began is truly recapitulated "on high"– ceaselessly recycled, frozen in time.

— Joseph Horowitz

 

Another website invoking Apollo:

The icon that I use… is the nine-fold square…. The nine-fold square has centre, periphery, axes and diagonals.  But all are present only in their bare essentials.  It is also a sequence of eight triads.  Four pass through the centre and four do not.  This is the garden of Apollo, the field of Reason…. 

In accordance with these remarks, here is the underlying structure for a ballet blanc:

A version of 'grid3x3.gif.'

This structure may seem too simple to support movements of interest, but consider the following (click to enlarge):

As Sir Arthur Quiller-Couch, paraphrasing Horace, remarks in his Whitsun, 1939, preface to the new edition of the Oxford Book of English Verse, "tamen usque recurret Apollo."

The alert reader will note that in the above diagrams, only eight of the positions move.

Which muse remains at the center?

Consider the remark of T. S. Eliot, "At the still point, there the dance is," and the fact that on the day Eliot turned 60, Olivia Newton-John was born.  How, indeed, in the words of another "sixty-year-old smiling public man," can we know the dancer from the dance?

Wednesday, November 6, 2002

Wednesday November 6, 2002

Filed under: General — m759 @ 2:22 pm

Today's birthdays: Mike Nichols and Sally Field.

Who is Sylvia?
What is she? 

 

From A Beautiful Mind, by Sylvia Nasar:

Prologue

Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of Thought, alone.
— WILLIAM WORDSWORTH

John Forbes Nash, Jr. — mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine — had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll's, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. "How could you," began Mackey, "how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?"

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. "Because," Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, "the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."

What I  take seriously:

Introduction to Topology and Modern Analysis, by George F. Simmons, McGraw-Hill, New York, 1963 

An Introduction to Abstract Harmonic Analysis, by Lynn H. Loomis, Van Nostrand, Princeton, 1953

"Harmonic Analysis as the Exploitation of Symmetry — A Historical Survey," by George W. Mackey, pp. 543-698, Bulletin of the American Mathematical Society, July 1980

Walsh Functions and Their Applications, by K. G. Beauchamp, Academic Press, New York, 1975

Walsh Series: An Introduction to Dyadic Harmonic Analysis, by F. Schipp, P. Simon, W. R. Wade, and J. Pal, Adam Hilger Ltd., 1990

The review, by W. R. Wade, of Walsh Series and Transforms (Golubov, Efimov, and Skvortsov, publ. by Kluwer, Netherlands, 1991) in the Bulletin of the American Mathematical Society, April 1992, pp. 348-359

Music courtesy of Franz Schubert.

Friday, August 30, 2002

Friday August 30, 2002

Filed under: General,Geometry — 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)

Thursday, August 29, 2002

Thursday August 29, 2002

Filed under: General — m759 @ 4:40 pm

For the feast day of

St. Ingrid Bergman:

Like Shakespeare, Ingrid Bergman was born and died on the same date… In her case, August 29.

To honor her performance in “Spellbound,” here is a copy of the first crossword puzzle ever published.

The Reversible Diamond Puzzle

“This puzzle appeared in the November 1874 number of ‘St. Nicholas.’

ACROSS, from top to bottom:

1. A consonant. 2. A number. 3. Measures of distance. 4. An abyss. 5. A consonant.

DOWN, from right to left:

1. A consonant. 2. A snare. 3. A name. 4. The point of anything small. 5. A consonant.

S
T E N
M I L E S
P I T
M

The across words are different from the down words, but there is a direct relation between them: one is the reversible form of the other.”

One might also compare an eerie sound clip from the  Oscar-winning score of “Spellbound” with a weird clip from “Selim,” by the World Saxophone Quartet.  The latter is from the album “Selim Sivad” (Miles Davis backwards). One reviewer claims that this album displays “astonishing, telepathic group interplay.” This may or may not be true; if the services of a psychiatrist are required to help decide the issue, let us hope she is as attractive as Saint Ingrid.

The above remarks are, of course, intended as a partial antidote to the music inevitably associated with Bergman… “As Time Goes By.”  (Please do not play it again, Sam.)  Of course, the World Saxophone Quartet may be too powerful an antidote… It reminds one, as does the greatly superior weird music from the “Forbidden Planet” soundtrack, of Monsters from the Id.  From such monsters, let us pray to Saint Ingrid for deliverance.

Wednesday, July 31, 2002

Bach’s Minuet in G

Filed under: General — m759 @ 11:29 pm
toys.jpg (17640 bytes)

The Toys

Left to right: June Montiero, Barbara Parritt, and Barbara Harris

From the website http://www.history-of-rock.com/toys.htm

In 1964 they were signed by the Publishing firm Genius, Inc., which teamed them with the songwriting duo Sandy Linzer and Denny Randell…. The writers took a classical finger exercise from Bach and put a Motown bassline to it and “A Lover’s Concerto” was born.

September 1965: “A Lover’s Concerto” on the Dynavoice label went #4 R&B, crossed over to pop charts #2, and also became a #5 hit in England. In 1965 the song sold over a million copies. The Toys began appearing on television shows such as “Shindig!,” “Hullabullo,” and “American Bandstand,”  toured with Gene Pitney, and appeared in the film It’s a Bikini World.

Other sites giving further details on Bach’s Minuet in G:

Search for the sheet music and a rendition of the work at codamusic.com’s Finale Showcase Search Page.

Seeing and hearing the music on this site requires that you download  Coda’s SmartMusic Viewer, and possibly requires that you adjust your browser settings, depending on the operating system you use.

For another look at Bach’s music, along with a midi rendition, you can download Music MasterWorks composing software from the Aspire Software site…

http://www.musicmasterworks.com/.

Then download the midi file of the Minuet in G itself,  “Minuet in G,  BWV841” (M.Lombardi), from the website

http://www.classicalarchives.com/bach.html.

(To do this, right-click on the minuet link and use the “Save Target As” option, if you, like me, are using Internet Explorer with Windows.)

After you have downloaded the midi file of the minuet, use the “File” and “Open” options in Music MasterWorks to display and play the music.

A comparison of these two versions of Bach is instructive for anyone planning to purchase music composition software.   The MasterWorks creates sheet music from its midi file that is quite sophisticated and rather hard to follow, but this music accurately reflects the superior musical performance in the downloaded midi file versus the rendition in the online Finale Showcase file.   The Showcase file is much simpler and easier to read, as the rendition it describes is also quite simple.

The Gentle Rain

For an even simpler version, those of us who were in our salad days in 1965 can consult our memories of The Toys:

How gentle is the rain
That falls softly on the meadow.
Birds high up in the trees
Serenade the clouds with their melodies.

Oh, see there beyond the hill,
The bright colors of the rainbow.
Some magic from above
Made this day for us just to fall in love.

Those of the younger generation with neither the patience nor the taste to seek out the original by Bach may be content with the following site —

A Lover’s Concerto in Venice

To a more mature audience, the picture of a Venetian sunset at the above site (similar to the photo below, from Shunya’s Italy)

will, together with the lyrics of The Toys, suggest that

The quality of mercy is not strained.
It droppeth as the gentle rain from heaven….

This line, addressed to Shylock in “The Merchant of Venice,” contradicts, to some extent, the statement by Igor Stravinsky in The Poetics of Music (1942, English version 1947) that music does not express anything at all. Stravinsky is buried in Venice.

From  Famous Graves:


Igor Stravinsky,

Venice

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