Wednesday, September 15, 2010
http://www.wittgen-cam.ac.uk/biogre9.html —
1935
With the expiry of his five-year Research Fellowship at Trinity College Wittgenstein was faced once more with the problem of loss of career. Accordingly he planned a journey to the Soviet Union, to find out whether he could find a suitable post there.
Wittgenstein’s constant quest for the right career was not, as it is often misunderstood, a flight from himself. Rather, it was a search for the right place, a being at one with himself: Return him [Man] to his rightful element and everything will unfold and appear as healthy.
(MS 125)
Since 1933/34 he had been taking lessons in Russian from the philosopher Fanja Pascal, initially with Francis Skinner. In June he asked Keynes for an introduction to the Soviet ambassador in London, Ivan M. Maiski. He sought contacts in two places above all, at the Northern Institute in Leningrad and the Institute for National Minorities in Moscow, writing to Keynes on 6 July: These Institutes, as I am told, deal with people who want to go to the ‘colonies’ the newly colonized parts at the periphery of the U. S. S. R.
(Letters to Russell, Keynes and Moore)
On 12 September Wittgenstein arrived in Leningrad. There he met the author and educator Guryevich at the Northern Institute, then an autonomous faculty of Leningrad University. On the evening of the following day he travelled on to Moscow, arriving there on the morning of the 14th. Here he had contacts with various western Europeans and Americans, including the correspondent of the Daily Worker, Pat Sloane. Most of his discussions, however, were with scientists, for example the young mathematician Yanovskaya and the philosopher Yushevich from Moscow University, who were both close to so-called Mach Marxism and the Vienna Circle. He was invited by the philosopher Tatiana Nikolayeva Gornstein, a member of the Soviet Academy of Sciences, to teach philosophy at Leningrad University. He traveled to Kazakhstan, where he was offered a chair at the famous university where Tolstoy once studied. On 1 October he was back in Cambridge. The trip was shorter than planned, and it appears that he had given up the idea of settling in Russia.
His friend Gilbert Pattison, who picked him up from the ship on his return, recalled that Wittgenstein’s view was that he could not live there himself: One could live there, but only if one kept in mind the whole time that one could never speak one’s mind. … It is as though one were to spend the rest of one’s life in an army, any army, and that is a rather difficult thing for people who are educated.
(Interview with Pattison)
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Thursday, September 2, 2010
Enigma Variations
The intercept control room in Hut 6 at Bletchley Park, 1943—
Photo: GETTY
The above photo is from today's London Telegraph obituary of Keith Batey, a Bletchley Park codebreaker who died at 91 on St. Augustine's Day, 2010. Also from that obituary—
Batey himself was responsible for some important breakthroughs in decrypting the Abwehr Enigma system, helping MI5 to control the entire German espionage network in Britain. The intelligence was crucial to the Double Cross system – under which MI5 turned German agents sent to Britain and used them to feed the Abwehr false information – as it showed that the information was being accepted as genuine; it further revealed what the Germans did and did not know about the D-Day invasion plans.
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Saturday, August 7, 2010
From the current index to obituaries at Telegraph.co.uk—
Teufel is also featured in today's New York Times—
"Mr. Teufel became a semicelebrity, helped in no small part by his last name, which means 'devil' in German."
From Group Analysis , June 1993, vol. 26 no. 2, 203-212—
The Problem of Good and Evil
by Ronald Sandison, Ledbury, Herefordshire HR8 2EY, UK
In my contribution to the Group Analysis Special Section: "Aspects of Religion in Group Analysis" (Sandison, 1993) I hinted that any consideration of a spiritual dimension to the group involves us in a discussion on whether we are dealing with good or evil spirits. But if we say that God is in the group, why is not the Devil there also? Can good and evil coexist in the same group matrix? Is the recognition of evil "nothing but" the ability to distinguish between good and bad? If not, then what is evil? Is it no more than the absence of good?
These and other questions were worked on at a joint Institute of Group Analysis and Group-Analytic Society (London) Workshop entitled "The Problem of Good and Evil." We considered the likelihood that good and evil coexist in all of us, as well as in the whole of the natural world, not only on earth, but in the cosmos and in God himself What we actually do with good and evil is to split them apart, thereby shelving the problem but at the same time creating irreconcilable opposites. This article examines this splitting and how we can work with it psychoanalytically.
This suggests a biblical remark—
"Now there was a day… when the sons of God
came to present themselves before the Lord,
and Satan came also among them."
— Job 1:6, quoted by Chesterton in The Man Who Was Thursday
Sandison died on June 18. See the Thursday, August 5, Log24 post "The Matrix."
Teufel died on July 6. See the Log24 posts for that day.
The title of this post, "rift designs," refers to a recurring theme in the July 6 posts. It is taken from Heidegger.
From a recent New Yorker review of Absence of Mind by Marilynne Robinson—
"Robinson is eloquent in her defense of the mind’s prerogatives, but her call for a renewed metaphysics might be better served by rereading Heidegger than by dusting off the Psalms."
Following this advice, we find—
"Propriation gathers the rift-design of the saying and unfolds it in such a way that it becomes the well-joined structure of a manifold showing."
— p. 415 of Heidegger's Basic Writings , edited by David Farrell Krell, HarperCollins paperback, 1993
"Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des vielfältigen Zeigens."
— Heidegger, Weg zur Sprache
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Thursday, June 17, 2010
Continued from yesterday evening's "Long Day's Journey into Nighttown"—
A detail from that post—
Related material from Nighttown—
The Sebastian Horsley Guide to Whoring—
Horsley, the author of Dandy in the Underworld, was
found dead this morning of a suspected heroin overdose.
"By groping toward the light we are made to realize
how deep the darkness is around us."
— Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118
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Friday, June 4, 2010
Continued from May 8
(Feast of Saint Robert Heinlein)
“Wells and trees were dedicated to saints. But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden. Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.”
— Charles Williams, Witchcraft, Faber and Faber, London, 1941
Why "Saint" Robert? See his accurate depiction of evil– the Eater of Souls in Glory Road.
For more on Williams's "other capacities," see Heinlein's story "Lost Legacy."
A related story– Fritz Leiber's "The Mind Spider." An excerpt:
The conference—it was much more a hyper-intimate
gabfest—proceeded.
"My static box bugged out for a few ticks this morning,"
Evelyn remarked in the course of talking over the
trivia of the past twenty-four hours.
The static boxes were an invention of Grandfather
Horn. They generated a tiny cloud of meaningless brain
waves. Without such individual thought-screens, there was
too much danger of complete loss of individual personality
—once Grandfather Horn had "become" his infant daughter
as well as himself for several hours and the unfledged
mind had come close to being permanently lost in its own
subconscious. The static boxes provided a mental wall be-
– hind which a mind could safely grow and function, similar
to the wall by which ordinary minds are apparently
always enclosed.
In spite of the boxes, the Horns shared thoughts and
emotions to an amazing degree. Their mental togetherness
was as real and as mysterious—and as incredible—as
thought itself . . . and thought is the original angel-cloud
dancing on the head of a pin. Their present conference
was as warm and intimate and tart as any actual family
gathering in one actual room around one actual table.
Five minds, joined together in the vast mental darkness
that shrouds all minds. Five minds hugged together for
comfort and safety in the infinite mental loneliness that
pervades the cosmos.
Evelyn continued, "Your boxes were all working, of
course, so I couldn't get your thoughts—just the blurs of
your boxes like little old dark grey stars. But this time
if gave me a funny uncomfortable feeling, like a spider
Crawling down my—Grayl! Don't feel so wildly! What
Is it?”
Then… just as Grayl started to think her answer…
something crept from the vast mental darkness and infinite
cosmic loneliness surrounding the five minds of the
Horns.
Grayl was the first to notice. Her panicky thought had
ttie curling too-keen edge of hysteria. "There are six of
us now! There should only be five, but there are six.
Count! Count, I tell you! Six!"
To Mort it seemed that a gigantic spider was racing
across the web of their thoughts….
See also this journal on May 30– "720 in the Book"– and on May 31– "Memorial for Galois."
("Obnoxious nerds"— a phrase Martin Gardner recently applied to Galois— will note that 720 (= 6!) is one possible result of obeying Leiber's command "Count! Count, I tell you! Six!")
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Friday, May 28, 2010
Happy Birthday,
Carey Mulligan
Star of "An Education"
In "An Education," Mulligan's character
applies for admission to Oxford.
Today's New York Times:
Related material:
Such words arrive on the page like suitcases at the baggage claim: You know there is something in them and they have travelled far, but you cannot tell what the writer means. The words are filled with unstated meaning. They are (the term is Ricoeur's) "packed" and need unpacking.
This method of using language, however, is not always a defect; radiantly evocative words have long been the language of myth, mysticism, and love. Also, in earlier centuries, educated readers expected to interpret writing on several different levels at once (e.g., literal, allegorical, moral, and anagogical or spiritual), so that multiple meanings were the norm. This was before the era of clear, expository, fully-explicit prose.
Visual thinkers are accustomed to their own kind of interpreting; the very act of visual perception, as Gregory (1966, 1970) and Gombrich (1959) have shown, is interpretive. When oral thinkers leave you to guess at something they have written, it is usually something that would have been obvious had the writing been a conversation. Such is not the case with visual thinkers, even whose spoken words can be mysterious references to visual thoughts invisible to anyone but the thinker.
Writing done in this "packed" manner makes more sense when read as poetry than when read as prose.
References:
Gombrich, E. H. (1959). Art and Illusion: A Study in the Psychology of Pictorial Representation. London: Phaidon.
Gregory, R. L. (1966). Eye and Brain: The Psychology of Seeing. New York: McGraw-Hill.
Gregory, R. L. (1970). The Intelligent Eye. New York: McGraw-Hill.
— "Stacking, Packing, and Enfolding Words," by Gerald Grow in "The Writing Problems of Visual Thinkers"
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Those wishing to emulate Mulligan's
character in "An Education" might,
having read the Times article above,
consult this journal's post of May 17,
"Rolling the Stone."
That post contains the following
image from the Times—
May 17 was, by the way, the day
that R. L. Gregory, author of
The Intelligent Eye, died.
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Friday, March 12, 2010
Steve Pond on “Crazy Heart” —
“… this gentle little movie… is, after all, a character study– and in an alcoholic country singer named Bad Blake, we’ve got one hell of a character.”
And then there’s Baaad Blake–
Related material:
This journal on the president of
London’s Blake Society and
Wikipedia on the founder of
Pergamon Press
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Saturday, February 13, 2010
“Logic is all about the entertaining of possibilities.”
– Colin McGinn, Mindsight: Image, Dream, Meaning,
Harvard University Press, 2004
Geometry of Language,
continued from St. George's Day, 2009—
Related material:
Prima Materia,
The Galois Quaternion,
and The Wake of Imagination.
See also the following from a physicist
(not of the most orthodox sort, but his remarks
here on Heisenberg seem quite respectable)–
Ian J. Thompson, 7 Dec. 2009—
Quantum mechanics describes the probabilities of actual outcomes in terms of a wave function, or at least of a quantum state of amplitudes that varies with time. The public always asks what the wave function is, or what the amplitudes are amplitudes of. Usually, we reply that the amplitudes are ‘probability amplitudes’, or that the wave function is a ‘probability wave function’, but neither answer is ontologically satisfying since probabilities are numbers, not stuff. We have already rehearsed the objections to the natural world being made out of numbers, as these are pure forms. In fact, ‘waves’, ‘amplitudes’ and ‘probabilities’ are all forms, and none of them can be substances. So, what are quantum objects made of: what stuff?
According to Heisenberg , the quantum probability waves are “a quantitative formulation of the concept of ‘dynamis’, possibility, or in the later Latin version, ‘potentia’, in Aristotle’s philosophy. The concept of events not determined in a peremptory manner, but that the possibility or ‘tendency’ for an event to take place has a kind of reality—a certain intermediate layer of reality, halfway between the massive reality of matter and the intellectual reality of the idea or the image—this concept plays a decisive role in Aristotle’s philosophy. In modern quantum theory this concept takes on a new form; it is formulated quantitatively as probability and subjected to mathematically expressible laws of nature.” Unfortunately Heisenberg does not develop this interpretation much beyond the sort of generality of the above statements, and the concept of ‘potentiality’ remains awkwardly isolated from much of his other thought on this subject . It is unclear even what he means by ‘potentia’.
Reference
Heisenberg, W. 1961 On Modern Physics, London: Orion Press.
Notes
[6] W. Heisenberg, ‘Planck’s discovery and the philosophical problems of atomic physics’, pp. 3-20 in Heisenberg (1961).
[7] Heisenberg, for example, brings into his thought on quantum physics the Kantian phenomena/noumena distinction, as well as some of Bohr’s ideas on ‘complementarity’ in experimental arrangements.
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Tuesday, January 26, 2010
From this journal:
Transition to the
Garden of Forking Paths–
(See For Baron Samedi)–
The Found Symbol
and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–
Pages 354-355
On the mirror-play of the fourfold
Pages 356-357
Shaking up a whole culture
Pages 358-359
Cornerstone and crossroads
Pages 360-361
A deep impression embedded in stone
Pages 362-363
A certain Y, a certain V
Pages 364-365
The world is Zeus's play
Page 366
It was necessary to begin again
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Sunday, January 10, 2010
A sermon for the father of Kal-El.
See also related material in this journal
on Vegas and on Maniacs.
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Friday, October 2, 2009
Edge on Heptads
Part I: Dye on Edge
“Summary: ….we obtain various orbits of partitions of quadrics over GF(2a) by their maximal totally singular subspaces; the corresponding stabilizers in the relevant orthogonal groups are investigated. It is explained how some of these partitions naturally generalize Conwell’s heptagons for the Klein quadric in PG(5,2).”
“Introduction: In 1910 Conwell… produced his heptagons in PG(5,2) associated with the Klein quadric K whose points represent the lines of PG(3,2)…. Edge… constructed the 8 heptads of complexes in PG(3,2) directly. Both he and Conwell used their 8 objects to establish geometrically the isomorphisms SL(4,2)=A8 and O6(2)=S8 where O6(2) is the group of K….”
— “Partitions and Their Stabilizers for Line Complexes and Quadrics,” by R.H. Dye, Annali di Matematica Pura ed Applicata, Volume 114, Number 1, December 1977, pp. 173-194
Part II: Edge on Heptads
“The Geometry of the Linear Fractional Group LF(4,2),” by W.L. Edge, Proc. London Math Soc., Volume s3-4, No. 1, 1954, pp. 317-342. See the historical remarks on the first page.
Note added by Edge in proof: “Since this paper was finished I have found one by G. M. Conwell: Annals of Mathematics (2) 11 (1910), 60-76….” |
Some context:
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Monday, September 28, 2009
Symmetry
for Germany
See Annals of Aesthetics,
January 13, 2009,
which features the following
example of modernism:
… and for readers of
the Sunday New York Times …
The funereal heart illustrates
a review of a book titled
Her Fearful Symmetry. The book is set, partly, in London's Highgate Cemetery.
The book's author, Audrey Niffenegger, has stated that her title refers to "the doubling and twinning and opposites" that are "essential to the theme and structure of the book." For examples of doubling, twinning, and opposites that I prefer to Niffenegger's, see this journal's Saturday and Sunday entries.
Fans of the New York Times's cultural coverage may prefer Niffenegger's own art work. They may also enjoy images from the weekend's London Art Book Fair that suggested the rather different sort of book in Saturday's entry.
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Saturday, September 26, 2009
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Thursday, September 24, 2009
Who Knows
What Evil Lurks…
The brain-in-a-jar on the cover of the new Pearl Jam album "Backspacer" (previous two entries) is apparently there because of a song on the album, "Unthought Known"–
"All the thoughts you never see
You are always thinking
Brain is wide, the brain is deep
Oh, are you sinking?"
The song title is from a book, The Shadow of the Object (Columbia U. Press, 1987), by psychoanalyst Christopher Bollas.
The "unthought known" phrase has been quoted widely by second-rate psychologizers and by some not so second-rate. Their lucubrations suggest that sinking brain-worshippers should seek a…
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Saturday, September 19, 2009
Slouching
Towards Kristen
Jerusalem Post Interview with Charles Krauthammer
by Hilary Leilea Krieger, JPost Correspondent, Washington
Krauthammer, a columnist for The Washington Post, is a winner of the Irving Kristol award.
Jerusalem Post, June 10, 2009:
Can you talk a little bit about your own Jewish upbringing and sense of Jewishness, and how that influences you? I assume it’s a factor in this particular project.
I grew up in a Modern Orthodox home [in Montreal]. I went to Jewish day school right through high school, so half of my day was spent speaking Hebrew from age six to 16. I studied thousands of hours of Talmud. My father thought I didn’t get enough Talmud at school, so I took the extra Talmud class at school and he had a rabbi come to the house three nights a week. One of those nights was Saturday night, so in synagogue Saturday morning my brother and I would pray very hard for snow so he wouldn’t be able to come on Saturday night and we could watch hockey night in Canada. That’s where I learned about prayer.
That didn’t seem to you to be a prayer that was likely to go unanswered?
Yeah, I was giving it a shot to see what side God was on.
And what did you determine?
It rarely snowed.
************************************
More on Krauthammer’s Canadian childhood:
“His parents were Orthodox and sent him to Hebrew day school. He also took private Gomorrah lessons twice a week.”
— “Charles Krauthammer: Prize Writer,” by Mitchell Bard
************************************
Also in the Jerusalem Post interview:
…. What, then, did you mean by a Jewish sensibility?
“…. In literature it’s an interesting question, what’s a Jewish novel?”
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My Prayer:
Private Gomorrah lessons
with Kristen.
Background:
“Heaven Can Wait”
at Haaretz.com
Happy Rosh Hashanah
(and Gemara).
Update, 5:01 AM Sept. 19
Before becoming a writer,
Krauthammer was, his
Washington Post biography says,
a resident and then chief resident
in psychiatry at
Massachusetts General Hospital.
Related Metaphors
This morning’s New York Times:
MicheleBachmann.com this morning:
See also:
James Hillman’s “acorn theory“
of personality development
(yesterday’s entry).
Comments Off on Saturday September 19, 2009
Monday, August 17, 2009
“… Kirkman has established an incontestable claim to be regarded as the founding father of the theory of designs.”
— “T.P. Kirkman, Mathematician,” by N.L. Biggs, Bulletin of the London Mathematical Society, Volume 13, Number 2 (March 1981), 97-120.
This paper is now available online for $12.
For more about this subject, see Design Theory, by Beth, Jungnickel, and Lenz, Cambridge U. Press, Volume I (2nd ed., 1999, 1120 pages) and Volume II (2nd ed., 2000, 513 pages).
For an apparently unrelated subject with the same name, see Graphic Design Theory: Readings from the Field, by Helen Armstrong (Princeton Architectural Press, 2009).
For what the two subjects have in common, see Block Designs in Art and Mathematics.
Comments Off on Monday August 17, 2009
Thursday, July 23, 2009
A Tangled Tale
Proposed task for a quantum computer:
"Using Twistor Theory to determine the plotline of Bob Dylan's 'Tangled up in Blue'"
One approach to a solution:
"In this scheme the structure of spacetime is intrinsically quantum mechanical…. We shall demonstrate that the breaking of symmetry in a QST [quantum space-time] is intimately linked to the notion of quantum entanglement."
— "Theory of Quantum Space-Time," by Dorje C. Brody and Lane P. Hughston, Royal Society of London Proceedings Series A, Vol. 461, Issue 2061, August 2005, pp. 2679-2699
(See also The Klein Correspondence, Penrose Space-Time, and a Finite Model.)
For some less technical examples of broken symmetries, see yesterday's entry, "Alphabet vs. Goddess."
That entry displays a painting in 16 parts by Kimberly Brooks (daughter of Leonard Shlain– author of The Alphabet Versus the Goddess— and wife of comedian Albert Brooks (real name: Albert Einstein)). Kimberly Brooks is shown below with another of her paintings, titled "Blue."
Click image to enlarge.
"She was workin' in a topless place
And I stopped in for a beer,
I just kept lookin' at the side of her face
In the spotlight so clear.
And later on as the crowd thinned out
I's just about to do the same,
She was standing there in back of my chair
Said to me, 'Don't I know your name?'
I muttered somethin' underneath my breath,
She studied the lines on my face.
I must admit I felt a little uneasy
When she bent down to tie the laces of my shoe,
Tangled up in blue."
-- Bob Dylan
Further entanglement with blue:
The website of the Los Angeles Police Department, designed by Kimberly Brooks's firm, Lightray Productions.
Further entanglement with shoelaces:
"Entanglement can be transmitted through chains of cause and effect– and if you speak, and another hears, that too is cause and effect. When you say 'My shoelaces are untied' over a cellphone, you're sharing your entanglement with your shoelaces with a friend."
— "What is Evidence?," by Eliezer Yudkowsky
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Friday, July 3, 2009
Damnation Morning
continued
“The tigers of wrath are wiser
than the horses of instruction.”
— Blake
“… the moment is not
properly an atom of time
but an atom of eternity.
It is the first reflection
of eternity in time, its first
attempt, as it were, at
stopping time….”
— Kierkegaard
Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.
— Rubén Darío
Related material:
The deaths of
Ernest Hemingway
on the morning of
Sunday, July 2, 1961,
and of Alexis Arguello
on the morning of
Wednesday, July 1, 2009.
See also philosophy professor
Clancy Martin in the
London Review of Books
(issue dated July 9, 2009)
on AA members as losers—
“the ‘last men,’ the nihilists,
the hopeless ones.”
Comments Off on Friday July 3, 2009
Wednesday, June 3, 2009
Epigraphs
to Four Quartets:
The Dissertations of Maximus Tyrius, translated from the Greek by Thomas Taylor, printed by C. Whittingham, London, for the translator, 1804, Vol. II, p. 55:
"You see the mutation of bodies, and the transition of generation, a path upwards and downwards according to Heraclitus; and again, as he says, one thing living the death, but dying the life of another. Thus fire lives the death of earth, and air lives the death of fire; water lives the death of air, and earth lives the death of water. You see a succession of life, and a mutation of bodies, both of which are the renovation of the whole."
For an interpretation
of the above figure
in terms of the classical
four elements discussed
in Four Quartets,
in Dissertations, and
in Angels & Demons,
see
Notes on Mathematics
and Narrative.
For a more entertaining
interpretation, see Fritz Leiber's
classic story "Damnation Morning."
Comments Off on Wednesday June 3, 2009
Friday, May 22, 2009
Steiner System
New York Times
banner this morning:
Click to enlarge.
Related material from
July 11, 2008:
The HSBC Logo Designer —
Henry Steiner
He is an internationally recognized corporate identity consultant. Based in Hong Kong, his work for clients such as HongkongBank, IBM and Unilever is a major influence in Pacific Rim design.
Born in Austria and raised in New York, Steiner was educated at Yale under Paul Rand and attended the Sorbonne as a Fulbright Fellow. He is a past President of Alliance Graphique Internationale. Other professional affiliations include the American Institute of Graphic Arts, Chartered Society of Designers, Design Austria, and the New York Art Directors' Club.
His Cross-Cultural Design: Communicating in the Global Marketplace was published by Thames and Hudson (1995).
— Yaneff.com
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Charles Taylor,
"Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477):
"… the object sets up
a kind of frame or space or field
within which there can be epiphany."
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Related material suggested by
an ad last night on
ABC's Ugly Betty season finale:
Diamond from last night's
Log24 entry, with
four colored pencils from
Diane Robertson Design:
See also
A Four-Color Theorem.
Comments Off on Friday May 22, 2009
Sunday, May 17, 2009
Design Theory
"My work is motivated by a hope that there may be a way to recapture the ancient and medieval vision of both Beauty and purpose in a way which is relevant to our own century. I even dare to hope that the two ideas may be related, that Beauty is actually part of the meaning and purpose of life."
Hans Ludwig de Vries, "
On Orthogonal Resolutions of the Classical Steiner Quadruple System SQS(16),"
Designs, Codes and Cryptography Vol. 48, No. 3 (Sept. 2008) 287-292 (DOI 10.1007/s10623-008-9207-5)–
"The Reverend T. P. Kirkman knew in 1862 that there exists a group of degree 16 and order 322560 with a normal, elementary abelian, subgroup of order 16 [1, p. 108]. Frobenius identified this group in 1904 as a subgroup of the Mathieu group M24 [4, p. 570]…."
1. Biggs N.L., "T. P. Kirkman, Mathematician," Bulletin of the London Mathematical Society 13, 97–120 (1981).
4. Frobenius G., "Über die Charaktere der mehrfach transitiven Gruppen," Sitzungsber. Königl. Preuss. Akad. Wiss. zu Berlin, 558–571 (1904). Reprinted in Frobenius, Gesammelte Abhandlungen III (J.-P. Serre, editor), pp. 335–348. Springer, Berlin (1968).
Olli Pottonen, "Classification of Steiner Quadruple Systems" (Master's thesis, Helsinki, 2005)–
"The concept of group actions is very useful in the study of isomorphisms of combinatorial structures."
"Simplify, simplify."
— Thoreau
"Beauty is bound up
with symmetry."
— Weyl
Pottonen's thesis is
dated Nov. 16, 2005.
For some remarks on
images and theology,
see Log24 on that date.
Click on the above image
for some further details.
Comments Off on Sunday May 17, 2009
Sunday, April 19, 2009
The Crimson Passion
continues…
(Background:
Truth and Style)
“We are here in the
Church of St. Frank,
where moral judgments
permit the true believer
to avoid any semblance
of thought.”
— Marjorie Garber on
Frank Kermode
Today’s sermon is a
link to a London publication
where one can purchase
Kermode’s excellent review
of the following:
Those who prefer
Garber’s Harvard sneer
may consult
The Crimson Passion
and the following
resurrection figure:
The Harvard Jesus
Crimson/Nancy K. Dutton
Comments Off on Sunday April 19, 2009
Friday, April 17, 2009
Begettings of
the Broken Bold
Thanks for the following
quotation (“Non deve…
nella testa“) go to the
weblog writer who signs
himself “Conrad H. Roth.”
… Yesterday I took leave of my Captain, with a promise of visiting him at Bologna on my return. He is a true
A PAPAL SOLDIER’S IDEAS OF PROTESTANTS 339
representative of the majority of his countrymen. Here, however, I would record a peculiarity which personally distinguished him. As I often sat quiet and lost in thought he once exclaimed “Che pensa? non deve mai pensar l’uomo, pensando s’invecchia;” which being interpreted is as much as to say, “What are you thinking about: a man ought never to think; thinking makes one old.” And now for another apophthegm of his; “Non deve fermarsi l’uomo in una sola cosa, perche allora divien matto; bisogna aver mille cose, una confusione nella testa;” in plain English, “A man ought not to rivet his thoughts exclusively on any one thing, otherwise he is sure to go mad; he ought to have in his head a thousand things, a regular medley.”
Certainly the good man could not know that the very thing that made me so thoughtful was my having my head mazed by a regular confusion of things, old and new. The following anecdote will serve to elucidate still more clearly the mental character of an Italian of this class. Having soon discovered that I was a Protestant, he observed after some circumlocution, that he hoped I would allow him to ask me a few questions, for he had heard such strange things about us Protestants that he wished to know for a certainty what to think of us.
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Notes for Roth:
The title of this entry,
“Begettings of the Broken Bold,”
is from Wallace Stevens’s
“The Owl in the Sarcophagus”–
This was peace after death, the brother of sleep,
The inhuman brother so much like, so near,
Yet vested in a foreign absolute,
Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,
Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,
And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.
Peace stood with our last blood adorned, last mind,
Damasked in the originals of green,
A thousand begettings of the broken bold.
This is that figure stationed at our end,
Always, in brilliance, fatal, final, formed
Out of our lives to keep us in our death....
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Related material:
Some further context:
Roth’s entry of Nov. 3, 2006–
“Why blog, sinners?“–
and Log24 on that date:
“First to Illuminate.”
Comments Off on Friday April 17, 2009
Wednesday, April 8, 2009
Good’s Singularity
Irving John “I.J.” Good died Sunday, April 5, 2009.
The date of his death was also Palm Sunday and the day of the Academy of Country Music Awards.
Information from Wikipedia:
Good, 92, was a cryptanalyst at Bletchley Park during World War II.
“He was born as Isidore Jacob Gudak to a Jewish family in London. In his publications he was called I. J. Good. He studied mathematics at Jesus College, Cambridge, graduating in 1938. He did research work under G.H. Hardy and Besicovitch before moving to Bletchley Park in 1941 on completing his doctorate.
At Bletchley Park, he was initially in Hut 8 under the supervision of Alan Turing…”
[Related material: the death of Turing (a major fan of the Evil Queen in Snow White) and yesterday’s entry]
Wikipedia states that “I. J. Good’s vanity car license plate, hinting at his spylike wartime work, was ‘007 IJG’…. He played chess to county standard, and helped to popularise Go, an Asian boardgame, through a 1965 article in New Scientist (he had learned the rules from Turing). In 1965, he described a concept similar to today’s meaning of technological singularity, in that it included in it the advent of superhuman intelligence:
- Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion,’ and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make….
- — Good, I. J. (1965). ‘Speculations Concerning the First Ultraintelligent Machine‘, Advances in Computers, Vol. 6.”
Comments Off on Wednesday April 8, 2009
Saturday, April 4, 2009
Annual Tribute to
The Eight
Other knight figures:
Click on the SpringerLink
knight for a free copy
(pdf, 1.2 mb) of
the following paper
dealing with the geometry
underlying the R.T. Curtis
knight figures above:
Context:
Literature and Chess and
Sporadic Group References
Details:
Adapted (for HTML) from the opening paragraphs of the above paper, W. Jonsson's 1970 "On the Mathieu Groups M22, M23, M24…"–
"[A]… uniqueness proof is offered here based upon a detailed knowledge of the geometric aspects of the elementary abelian group of order 16 together with a knowledge of the geometries associated with certain subgroups of its automorphism group. This construction was motivated by a question posed by D.R. Hughes and by the discussion Edge [5] (see also Conwell [4]) gives of certain isomorphisms between classical groups, namely
PGL(4,2)~PSL(4,2)~SL(4,2)~A8,
PSp(4,2)~Sp(4,2)~S6,
where A8 is the alternating group on eight symbols, S6 the symmetric group on six symbols, Sp(4,2) and PSp(4,2) the symplectic and projective symplectic groups in four variables over the field GF(2) of two elements, [and] PGL, PSL and SL are the projective linear, projective special linear and special linear groups (see for example [7], Kapitel II).
The symplectic group PSp(4,2) is the group of collineations of the three dimensional projective space PG(3,2) over GF(2) which commute with a fixed null polarity tau…."
References
4. Conwell, George M.: The three space PG(3,2) and its group. Ann. of Math. (2) 11, 60-76 (1910).
5. Edge, W.L.: The geometry of the linear fractional group LF(4,2). Proc. London Math. Soc. (3) 4, 317-342 (1954).
7. Huppert, B.: Endliche Gruppen I. Berlin-Heidelberg-New York: Springer 1967. |
Comments Off on Saturday April 4, 2009
Tuesday, March 17, 2009
"The diagram above is from a ninth century manuscript of Apuleius' commentary on Aristotle's Perihermaneias, probably one of the oldest surviving pictures of the square."
— Edward Buckner at The Logic Museum
From the webpage "Semiotics for Beginners: Paradigmatic Analysis," by Daniel Chandler:
The Semiotic Square
"The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully (Greimas 1987,* xiv, 49). The semiotic square is intended to map the logical conjunctions and disjunctions relating key semantic features in a text. Fredric Jameson notes that 'the entire mechanism… is capable of generating at least ten conceivable positions out of a rudimentary binary opposition' (in Greimas 1987,* xiv). Whilst this suggests that the possibilities for signification in a semiotic system are richer than the either/or of binary logic, but that [sic] they are nevertheless subject to 'semiotic constraints' – 'deep structures' providing basic axes of signification."
* Greimas, Algirdas (1987): On Meaning: Selected Writings in Semiotic Theory (trans. Paul J Perron & Frank H Collins). London: Frances Pinter
Another version of the semiotic square:
Krauss says that her figure "is, of course, a Klein Group."
Here is a more explicit figure representing the Klein group:
There is also the logical
diamond of opposition —
A semiotic (as opposed to logical)
diamond has been used to illustrate
remarks by Fredric Jameson,
a Marxist literary theorist:
"Introduction to Algirdas Greimas, Module on the Semiotic Square," by Dino Felluga at Purdue University–
The semiotic square has proven to be an influential concept not only in narrative theory but in the ideological criticism of Fredric Jameson, who uses the square as "a virtual map of conceptual closure, or better still, of the closure of ideology itself" ("Foreword"* xv). (For more on Jameson, see the [Purdue University] Jameson module on ideology.)
Greimas' schema is useful since it illustrates the full complexity of any given semantic term (seme). Greimas points out that any given seme entails its opposite or "contrary." "Life" (s1) for example is understood in relation to its contrary, "death" (s2). Rather than rest at this simple binary opposition (S), however, Greimas points out that the opposition, "life" and "death," suggests what Greimas terms a contradictory pair (-S), i.e., "not-life" (-s1) and "not-death" (-s2). We would therefore be left with the following semiotic square (Fig. 1):
As Jameson explains in the Foreword to Greimas' On Meaning, "-s 1 and -s 2"—which in this example are taken up by "not-death" and "not-life"—"are the simple negatives of the two dominant terms, but include far more than either: thus 'nonwhite' includes more than 'black,' 'nonmale' more than 'female'" (xiv); in our example, not-life would include more than merely death and not-death more than life.
* Jameson, Fredric. "Foreword." On Meaning: Selected Writings in Semiotic Theory. By Algirdas Greimas. Trans. Paul J. Perron and Frank H. Collins. Minneapolis: U of Minnesota P, 1976.
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"The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God."
— The Gameplayers of Zan, by M.A. Foster
"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon,
Gravity's Rainbow
Crosses used by semioticians
to baffle their opponents
are illustrated above.
Some other kinds of crosses,
and another kind of opponent:
Monday, July 11, 2005
Logos
for St. Benedict's Day
Click on either of the logos below for religious meditations– on the left, a Jewish meditation from the Conference of Catholic Bishops; on the right, an Aryan meditation from Stormfront.org.
Both logos represent different embodiments of the "story theory" of truth, as opposed to the "diamond theory" of truth. Both logos claim, in their own ways, to represent the eternal Logos of the Christian religion. I personally prefer the "diamond theory" of truth, represented by the logo below.
See also the previous entry
(below) and the entries
of 7/11, 2003.
Sunday, July 10, 2005
From Artemiadis's website:
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1986:
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Elected Regular Member
of the Academy of Athens
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1999:
|
Vice President
of the Academy of Athens
|
2000:
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President
of the Academy of Athens
|
"First of all, I'd like to
thank the Academy…"
— Remark attributed to Plato
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Comments Off on Tuesday March 17, 2009
Thursday, February 26, 2009
Truth and
Consequences:
From Roger Cohen
to Alain Badiou
to Wallace Stevens
“The Event of Truth,”
European Graduate School video:
Quoted by Badiou at
European Graduate School,
August 2002:
We live in a constellation Of patches and of pitches, Not in a single world, In things said well in music, On the piano and in speech, As in a page of poetry— Thinkers without final thoughts In an always incipient cosmos. The way, when we climb a mountain, Vermont throws itself together.
— Wallace Stevens, from “July Mountain”
Or Pennsylvania:
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Comments Off on Thursday February 26, 2009
Wednesday, February 18, 2009
Raiders of
the Lost Well
“The challenge is to
keep high standards of
scholarship while maintaining
showmanship as well.” |
— Olga Raggio, a graduate of the Vatican library school and the University of Rome who, at one point in her almost 60 years with the Metropolitan Museum of Art, organized “The Vatican Collections,” a blockbuster show. Dr. Raggio died on January 24.
The next day, “The Last Templar,” starring Mira Sorvino, debuted on NBC.
“The story, involving the Knights Templar, the Vatican, sunken treasure, the fate of Christianity and a decoding device that looks as if it came out of a really big box of medieval Cracker Jack, is the latest attempt to combine Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”
— The New York Times
Sorvino in “The Last Templar”
at the Church of the Lost Well:
“One highlight of Secretary of State Hillary Clinton’s first overseas trip will be a stop in China. Her main mission in Beijing will be to ensure that US-China relations under the new Obama administration get off to a positive start.”
— Stephanie Ho, Voice of America Beijing bureau chief, today
Symbol of The Positive,
from this journal
on Valentine’s Day:
“Stephanie started at the Voice of America as an intern in 1991. She left briefly to attend film school in London in 2000. Although she didn’t finish, she has always wanted to be a film school dropout, so now she’s living one of her dreams.
Stephanie was born in Ohio and grew up in California. She has a bachelor’s degree in Asian studies with an emphasis on Chinese history and economics, from the University of California at Berkeley.”
“She is fluent in
Mandrin Chinese.”
—VOA
As is Mira Sorvino.
Those who, like Clinton, Raggio, and
Sorvino’s fictional archaeologist in
“The Last Templar,” prefer Judeo-
Christian myths to Asian myths,
may convert the above Chinese
“well” symbol to a cross
(or a thick “+” sign)
by filling in five of
the nine spaces outlined
by the well symbol.
In so doing, they of course
run the risk, so dramatically
portrayed by Angelina Jolie
as Lara Croft, of opening
Pandora’s Box.
(See Rosalind Krauss, Professor
of Art and Theory at Columbia,
for scholarly details.)
Krauss
The Krauss Cross
Comments Off on Wednesday February 18, 2009
Saturday, February 7, 2009
DENNIS OVERBYE
"From the grave, Albert Einstein poured gasoline on the culture wars between science and religion this week.
A letter the physicist wrote in 1954 to the philosopher Eric Gutkind, in which he described the Bible as 'pretty childish' and scoffed at the notion that the Jews could be a 'chosen people,' sold for $404,000 at an auction in London. That was 25 times the presale estimate."
Einstein did not, at least in the place alleged, call the Bible "childish." Proof:
The image of the letter is
from the Sept./Oct. 2008
Search Magazine.
By the way, today is
the birthday of G. H. Hardy.
Here is an excerpt from his
thoughts on childish things:
"What 'purely aesthetic' qualities can we distinguish in such theorems as Euclid's or Pythagoras's?…. In both theorems (and in the theorems, of course, I include the proofs) there is a very high degree of unexpectedness, combined with inevitability and economy. The arguments take so odd and surprising a form; the weapons used seem so childishly simple when compared with the far-reaching results; but there is no escape from the conclusions."
"Space: what you
damn well have to see."
— James Joyce, Ulysses
Comments Off on Saturday February 7, 2009
Friday, December 5, 2008
Continued from
Monday:
A Version of
Heaven’s Gate
in memory of
Alexy II, the Russian Orthodox
patriarch who died today in Moscow:
The Pearly Gates of Cyberspace:
From Geoffrey Broadbent,
“Why a Black Square?” in Malevich
(London, Art and Design/
Academy Group, 1989, p. 49):
“Malevich’s Black Square seems to be
nothing more, nor less, than his
‘Non-Objective’ representation
of Bragdon’s (human-being-as) Cube
passing through the ‘Plane of Reality.’!”
Comments Off on Friday December 5, 2008
Sunday, November 23, 2008
At the Still Point
This morning’s entry quoted Ezra Pound:
“The first credential we should demand of a critic is his ideograph of the good.”
Dance critic Clive Barnes died Wednesday. Pound may have whispered his advice in St. Peter’s ear when Barnes stood before the Janitor Coeli at heaven’s gate. If so, another angel may have whispered in the other ear,
“Vide Forever Fonteyn.”
Comments Off on Sunday November 23, 2008
Sunday, August 3, 2008
Kindergarten
Geometry
Preview of a Tom Stoppard play presented at Town Hall in Manhattan on March 14, 2008 (Pi Day and Einstein’s birthday):
The play’s title, “Every Good Boy Deserves Favour,” is a mnemonic for the notes of the treble clef EGBDF.
The place, Town Hall, West 43rd Street. The time, 8 p.m., Friday, March 14. One single performance only, to the tinkle– or the clang?– of a triangle. Echoing perhaps the clang-clack of Warsaw Pact tanks muscling into Prague in August 1968.
The “u” in favour is the British way, the Stoppard way, “EGBDF” being “a Play for Actors and Orchestra” by Tom Stoppard (words) and André Previn (music).
And what a play!– as luminescent as always where Stoppard is concerned. The music component of the one-nighter at Town Hall– a showcase for the Boston University College of Fine Arts– is by a 47-piece live orchestra, the significant instrument being, well, a triangle.
When, in 1974, André Previn, then principal conductor of the London Symphony, invited Stoppard “to write something which had the need of a live full-time orchestra onstage,” the 36-year-old playwright jumped at the chance.
One hitch: Stoppard at the time knew “very little about ‘serious’ music… My qualifications for writing about an orchestra,” he says in his introduction to the 1978 Grove Press edition of “EGBDF,” “amounted to a spell as a triangle player in a kindergarten percussion band.”
— Jerry Tallmer in The Villager, March 12-18, 2008
Review of the same play as presented at Chautauqua Institution on July 24, 2008:
“Stoppard’s modus operandi– to teasingly introduce numerous clever tidbits designed to challenge the audience.”
— Jane Vranish, Pittsburgh Post-Gazette, Saturday, August 2, 2008
“The leader of the band is tired
And his eyes are growing old
But his blood runs through
My instrument
And his song is in my soul.”
— Dan Fogelberg
“He’s watching us all the time.”
— Lucia Joyce
Finnegans Wake,
Book II, Episode 2, pp. 296-297:
I’ll make you to see figuratleavely the whome of your eternal geomater. And if you flung her headdress on her from under her highlows you’d wheeze whyse Salmonson set his seel on a hexengown.1 Hissss!, Arrah, go on! Fin for fun!
1 The chape of Doña Speranza of the Nacion. |
ReciprocityFrom my entry of Sept. 1, 2003:
“…the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity….
… E. M. Forster famously advised his readers, ‘Only connect.’ ‘Reciprocity’ would be Michael Kruger’s succinct philosophy, with all that the word implies.”
— William Boyd, review of Himmelfarb, a novel by Michael Kruger, in The New York Times Book Review, October 30, 1994
Last year’s entry on this date:
The picture above is of the complete graph K6 … Six points with an edge connecting every pair of points… Fifteen edges in all.
Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4×4 array, and how such an array relates to group-theoretic concepts, including Sylvester’s synthematic totals as they relate to constructions of the Mathieu group M24.
If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites…. “Reciprocity” in the sense of Lao Tzu. See
Reciprocity and Reversal in Lao Tzu.
For a sense of “reciprocity” more closely related to Michael Kruger’s alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in
Shu: Reciprocity.
Kruger’s novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the K6 graph above, expresses the reciprocity of male and female, as my May 2003 archives illustrate. The star of David also appears as part of a graphic design for cubes that illustrate the concepts of diamond theory:
Click on the design for details.
Those who prefer a Jewish approach to physics can find the star of David, in the form of K6, applied to the sixteen 4×4 Dirac matrices, in
A Graphical Representation
of the Dirac Algebra.
The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.
Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss. See
The Jewel of Arithmetic and
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FinnegansWiki:
Salmonson set his seel:
“Finn MacCool ate the Salmon of Knowledge.”
Wikipedia:
“George Salmon spent his boyhood in Cork City, Ireland. His father was a linen merchant. He graduated from Trinity College Dublin at the age of 19 with exceptionally high honours in mathematics. In 1841 at age 21 he was appointed to a position in the mathematics department at Trinity College Dublin. In 1845 he was appointed concurrently to a position in the theology department at Trinity College Dublin, having been confirmed in that year as an Anglican priest.”
Comments Off on Sunday August 3, 2008
Saturday, August 2, 2008
Prattle
“Simon studies one of the most complicated groups of all: the Monster. He is, still, the world expert on it ….
Simon tells me he has a quasi-religious faith in the Monster. One day, he says, … the Monster will expose the structure of the universe.
… although Simon says he is keen for me to write a book about him and his work on the Monster and his obsession with buses, he doesn’t like talking, has no sense of anecdotes or extended conversation, and can’t remember (or never paid any attention to) 90 per cent of the things I want him to tell me about in his past. It is not modesty. Simon is not modest or immodest: he just has no self-curiosity. To Simon, Simon is a collection of disparate facts and no interpretative glue. He is a man without adjectives. His speech is made up almost entirely of short bursts of grunts and nouns.
This is the main reason why we spent three weeks together …. I needed to find a way to make him prattle.”
Those in search of prattle and interpretive glue should consult Anthony Judge’s essay ““Potential Psychosocial Significance of Monstrous Moonshine: An Exceptional Form of Symmetry as a Rosetta Stone for Cognitive Frameworks.” This was cited here in Thursday’s entry “Symmetry in Review.” (That entry is just a list of items related in part by synchronicity, in part by mathematical content. The list, while meaningful to me and perhaps a few others, is also lacking in prattle and interpretive glue.)
Those in search of knowledge, rather than glue and prattle, should consult Symmetry and the Monster, by Mark Ronan. If they have a good undergraduate education in mathematics, Terry Gannon‘s survey paper “Monstrous Moonshine: The First Twenty-Five Years” (pdf) and book– Moonshine Beyond the Monster— may also be of interest.
Comments Off on Saturday August 2, 2008
Saturday, July 26, 2008
From Josephine Klein, Jacob’s Ladder: Essays on Experiences of the Ineffable in the Context of Contemporary Psychotherapy, London, Karnac Books, 2003–
Page 14 —
Gerard Manley Hopkins
“Quiddity and haeccity were contentious topics in medieval discussions about the nature of reality, and the poet Gerard Manley Hopkins would have encountered these concepts during his Jesuit training. W. H. Gardner, who edited much of Hopkins’s work, writes that
in 1872, while studying medieval philosophy… Hopkins came across the writing of Duns Scotus, and in that subtle thinker’s Principles of Individuation and Theory of Knowledge he discovered what seemed to be a philosophical corroboration of his own private theory of inscape and instress. [Gardner, Gerard Manley Hopkins: Poems and Prose, Penguin, 1953, p. xxiii]
In this useful introduction to his selection of Hopkins’s work, Gardner writes that Hopkins was always looking for the law or principle that gave an object ‘its delicate and surprising uniqueness.’ This was for Hopkins ‘a fundamental beauty which is the active principle of all true being, the source of all true knowledge and delight.’ Clive Bell called it ‘significant form’; Hopkins called it ‘inscape’– ‘the rich and revealing oneness of the natural object’ (pp. xx-xxiv). In this chapter, I call it quiddity.”
Comments Off on Saturday July 26, 2008
Wednesday, July 2, 2008
Let Noon Be Fair
“The serpent’s eyes shine
As he wraps around the vine”
A Good Year
— Last summer’s journal
Related material:
Cover illustration:
Spies returning from the land of
Canaan with a cluster of grapes.
Colored woodcut from
Biblia Sacra Germanica,
Nuremberg, Anton Koberger, 1483.
Victoria and Albert Museum, London.
Comments Off on Wednesday July 2, 2008
Saturday, June 28, 2008
The Cocktail
G. H. Hardy on chess problems–
"… the key-move should be followed by a good many variations, each requiring its own individual answer."
(A Mathematician's Apology, Cambridge at the University Press, first edition, 1940)
Brian Harley on chess problems–
"It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver's banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be."
(Mate in Two Moves, London, Bell & Sons, first edition, 1931)
Comments Off on Saturday June 28, 2008
Sunday, June 1, 2008
The conclusion of yesterday’s commentary on the May 30-31 Pennsylvania Lottery numbers:
Thomas Pynchon, Gravity’s Rainbow:
“The fear balloons again inside his brain. It will not be kept down with a simple Fuck You…. A smell, a forbidden room, at the bottom edge of his memory. He can’t see it, can’t make it out. Doesn’t want to. It is allied with the Worst Thing.
He knows what the smell has to be: though according to these papers it would have been too early for it, though he has never come across any of the stuff among the daytime coordinates of his life, still, down here, back here in the warm dark, among early shapes where the clocks and calendars don’t mean too much, he knows that’s what haunting him now will prove to be the smell of Imipolex G.
Then there’s this recent dream he is afraid of having again. He was in his old room, back home. A summer afternoon of lilacs and bees and
286”
What are we to make of this enigmatic 286? (No fair peeking at page 287.)
One possible meaning, given The Archivist‘s claim that “existence is infinitely cross-referenced”–
Page 286 of Ernest G. Schachtel, Metamorphosis: On the Conflict of Human Development and the Psychology of Creativity (first published in 1959), Hillsdale NJ and London, The Analytic Press, 2001 (chapter– “On Memory and Childhood Amnesia”):
“Both Freud and Proust speak of the autobiographical [my italics] memory, and it is only with regard to this memory that the striking phenomenon of childhood amnesia and the less obvious difficulty of recovering any past experience may be observed.”
The concluding “summer afternoon of lilacs and bees” suggests that 286 may also be a chance allusion to the golden afternoon of Disney’s Alice in Wonderland. (Cf. St. Sarah’s Day, 2008)
Some may find the Disney afternoon charming; others may see it as yet another of Paul Simon’s dreaded cartoon graveyards.
More tastefully, there is poem 286 in the 1919 Oxford Book of English Verse– “Love.”
For a midrash on this poem, see Simone Weil, who became acquainted with the poem by chance:
“I always prefer saying chance rather than Providence.”
— Simone Weil, letter of about May 15, 1942
Weil’s brother André might prefer Providence (source of the Bulletin of the American Mathematical Society.)
Related material:
Log24, December 20, 2003–
White, Geometric, and Eternal—
A description in
Gravity’s Rainbow of prewar Berlin as “white and geometric” suggested, in combination with a reference elsewhere to “the eternal,” a citation of the following
illustration of the concept “white, geometric, and eternal”–
For more on the mathematical significance of this figure, see (for instance) Happy Birthday, Hassler Whitney, and Combinatorics of Coxeter Groups, by Anders Björner and Francesco Brenti, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005.
This book is reviewed in the current issue (July 2008) of the above-mentioned Providence Bulletin.
The review in the Bulletin discusses reflection groups in continuous spaces.
Comments Off on Sunday June 1, 2008
Friday, May 16, 2008
“From the grave, Albert Einstein poured gasoline on the culture wars between science and religion this week.
A letter the physicist wrote in 1954 to the philosopher Eric Gutkind, in which he described the Bible as ‘pretty childish’ and scoffed at the notion that the Jews could be a ‘chosen people,’ sold for $404,000 at an auction in London. That was 25 times the presale estimate.”
A less controversial Einstein-related remark:
“The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time.”
— Hermann Weyl, “Relativity Theory as a Stimulus in Mathematical Research,” Proceedings of the American Philosophical Society, Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949 (Dec. 30, 1949), pp. 535-541
Comments Off on Friday May 16, 2008
Friday, May 9, 2008
Comments Off on Friday May 9, 2008
Thursday, March 27, 2008
A Saint for
Richard Widmark
From this morning’s
New York Times:
Click image to enlarge.
The “Boy’s Life” illustration is of an Arthur C. Clarke story, “Against the Fall of Night.” This, according to the review quoted below, was Clarke’s first story, begun in 1936 and first published in 1948. The title is from a poem by A. E. Housman, “Smooth Between Sea and Land.” See Log24 on the Feast of St. Mark, 2003.
From a book review by Christopher B. Jones:
“Against the Fall of Night describes well how it often takes youth to bring forth change. The older mind becomes locked in a routine, or blocks out things because it has been told that it shouldn’t think or talk about them. But the young mind is ever the explorer, seeking out knowledge without the taboos placed on it by a rigid society. Alvin is a breath of fresh air in the don’t-look-over-the-wall society of Diaspar.
Myths play a big role, and an interesting religious overtone pervades the story with a long since departed being whose origins are unknown and who played an important part in Earth’s past. Parallels to Jesus can easily be drawn, and the forecast shown for the longevity of religions in general seems to me to be rather accurate….
Finally, when Alvin uncovers part of the truth he has been looking for, he learns of the dangers and stagnation that can befall a xenophobic society. There are still a few such societies in the world today, and this characteristic almost always comes with negative effects– even if it has been cultivated with the intention to protect.”
An example of such a xenophobic society is furnished by the Hadassah ad currently running in the New York Times obituaries section: “Who will say Kaddish in Israel?”
Another example:
Tom Stoppard, in the London Times of Sunday, March 16, 2008, on the social unrest of forty years ago in 1968–
“Altering the psyche was supposed to change the social structure but, as a Marxist, Max knows it really works the other way: changing the social structure is the only way to change the psyche. The idea that ‘make love, not war’ is a more practical slogan than ‘workers of the world unite’ is as airy-fairy as the I Ching.”
Airy-fairy, Jewey-phooey.
Clarke’s 1948 story was the basis of his 1956 novel, The City and the Stars. In memory of the star Richard Widmark, here are two illustrations from St. Mark’s Day, 2003:
Housman asks the reader
to tell him of runes to grave
or bastions to design
“against the fall of night.”
Here, as examples, are
one rune and one bastion.
Neither part of this memorial suits the xenophobic outlook of Israel. Both parts, together, along with his classic film “The Long Ships,” seem somehow suited to the non-xenophobic outlook of Richard Widmark. As for the I Ching… perhaps Widmark has further voyages to make.
Comments Off on Thursday March 27, 2008
Monday, January 21, 2008
Serious Numbers
"When times are mysterious
Serious numbers will always be heard."
— Paul Simon
Recent events in world financial markets suggest a return to this topic, considered here on October 13, 2007.
That day's entry, on mathematics and theology, may be of use to those who are considering, as their next financial move, prayer.
Some related material:
- The review in the Jan. 22 New York Times of a book by mathematics vulgarizer John Allen Paulos refuting arguments for the existence of God.
- Arguments in a less controversial area– for and against the consistency of elementary number theory:
FOR: Kurt
Gödel, Steven H. Cullinane, and John Dawson (See Log24– Nov. 30 and Dec. 2, 2005– and "Gödel, Inconsistency, Provability, and Truth: An Exchange of Letters" (pdf), in the American Mathematical Society Notices of April 2006.)
AGAINST: E. B. Davies, King's College London (See above.)
- André Weil: "God exists since mathematics is consistent, and the Devil exists since we cannot prove it."
- God: "605." (NY Lottery, mid-day Jan. 20, 2008) This can, of course, be interpreted as "6/05"– which is perhaps a reference to "God, the Devil, and a Bridge." Or perhaps not.
Comments Off on Monday January 21, 2008
Sunday, December 16, 2007
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
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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.
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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.
Comments Off on Sunday December 16, 2007
Friday, December 14, 2007
Nicole Kidman at
a press conference
for the London premiere of
“The Golden Compass” on November 27:
Deep Beauty
See also Zen and the Art of
Motorcycle Maintenance —
“Plato hadn’t tried to destroy areté. He had encapsulated it; made a permanent, fixed Idea out of it; had converted it to a rigid, immobile Immortal Truth. He made areté the Good, the highest form, the highest Idea of all. It was subordinate only to Truth itself, in a synthesis of all that had gone before.That was why the Quality that Phaedrus had arrived at in the classroom had seemed so close to Plato’s Good. Plato’s Good was taken from the rhetoricians. Phaedrus searched, but could find no previous cosmologists who had talked about the Good. That was from the Sophists. The difference was that 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.”
— as well as Cold Mountain —
Page 48: “It’s claimed that if
you take a mirror and look
backwards into a well, you’ll
see your future down in the water.”
“So in short order Ada found herself bent backward over the mossy well lip, canted in a pose with little to recommend it in the way of dignity or comfort, back arched, hips forward, legs spraddled for balance. She held a hand mirror above her face, angled to catch the surface of the water below.
Ada had agreed to the well-viewing as a variety of experiment in local custom and as a tonic for her gloom. Her thoughts had been broody and morbid and excessively retrospective for so long that she welcomed the chance to run counter to that flow, to cast forward and think about the future, even though she expected to see nothing but water at the bottom of the well.
She shifted her feet to find better grip on the packed dirt of the yard and then tried to look into the mirror. The white sky above was skimmed over with backlit haze, bright as a pearl or as a silver mirror itself. The dark foliage of oaks all around the edges framed the sky, duplicating the wooden frame of the mirror into which Ada peered, examining its picture of the well depths behind her to see what might lie ahead in her life. The bright round of well water at the end of the black shaft was another mirror. It cast back the shine of sky and was furred around the edges here and there with sprigs of fern growing between stones.
Ada tried to focus her attention on the hand mirror, but the bright sky beyond kept drawing her eye away. 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, as if she could at any moment pitch backward and plunge head first down the well shaft and drown there, the sky far above her, her last vision but a bright circle set in the dark, no bigger than a full moon.
Her head spun and she reached with her free hand and held to the stonework of the well. And then just for a moment things steadied, and there indeed seemed to be a picture in the mirror.”
— and Log24 on December 3 —
For further details, click on the well.
Comments Off on Friday December 14, 2007
Wednesday, July 25, 2007
The Comedy of
George Tabori
From AP “Obituaries in the News”–
Filed with The New York Times
at 11:16 p.m. ET July 24, 2007–
George Tabori
“BERLIN (AP) — Hungarian-born playwright and director George Tabori, a legend in Germany’s postwar theater world whose avant-garde works confronted anti-Semitism, died Monday [July 23, 2007]. He was 93.
Tabori, who as recently as three years ago dreamed of returning to stage to play the title role in Shakespeare’s ‘King Lear,’ died in his apartment near the theater, the Berliner Ensemble said Tuesday, noting that friends and family had accompanied him through his final days. No cause of death was given.
Born into a Jewish family in Budapest on May 24, 1914, Tabori fled in 1936 to London, where he started working for the British Broadcasting Corp., and became a British citizen. His father, and other members of his family, were killed at Auschwitz.
Tabori moved to Hollywood in the 1950s, where he worked as a scriptwriter, most notably co-writing the script for Alfred Hitchcock’s 1953 film, ‘I Confess.’
He moved to Germany in the 1970s and launched a theater career that spanned from acting to directing to writing. He used sharp wit and humor in his plays to examine the relationship between Germany and the Jews, as well as attack anti-Semitism.
Among his best-known works are ‘Mein Kampf,’ set in the Viennese hostel where Adolf Hitler lived from 1910-1913, and the ‘Goldberg Variations,’ both dark farces that poke fun at the Nazis.”
From Year of Jewish Culture:
“The year 2006 marks the 100th anniversary of the establishment of the Jewish Museum in Prague.”
From the related page Programme (October-December):
“Divadlo v Dlouhé
George Tabori: GOLDBERGOVSKÉ VARIACE / THE GOLDBERG VARIATIONS, 19 October, 7 p.m. A comedy on creation and martyrdom.”
Variations on
Birth and Death
From Log24 on the date of the Prague production of the Tabori “Goldberg Variations,” an illustration in honor of Sir Thomas Browne, who was born, and died, on that date:
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Theme
(Plato, Meno)
and Variations:
Click on “variations” above for some material on the “Goldberg Variations” of Johann Sebastian Bach.
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Comments Off on Wednesday July 25, 2007
Friday, July 6, 2007
Comments Off on Friday July 6, 2007
Thursday, July 5, 2007
Their Name is Legion
“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.”
— Stanley Fish, July 2002
The previous entry linked to an entry of June 2002 that attacked the nominalism of Stanley Fish. Here is another such attack:
From “Stanley Fish: The Critic as Sophist,” by R.V. Young, in Modern Age, June 22, 2003:
In one of the definitive works of conservatism in the twentieth century, Richard Weaver designates the rise of nominalism as a critical turn in the emergence of the intellectual and cultural disintegration associated with liberalism, which it is the business of a reviving conservatism to contest: “The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence.” It is nominalism that provides the intellectual foundation– if a paradox may be hazarded– for the attack by Fish and numerous others (their name is Legion) on the very idea of intellectual foundations:
It was William of Occam who propounded the fateful doctrine of nominalism, which denies that universals have real existence. His triumph tended to leave universal terms mere names serving our convenience. The issue ultimately involved is whether there is a source of truth higher than, and independent of, man; and the answer to the question is decisive for one’s view of the nature and destiny of humankind. The practical result of nominalist philosophy is to banish the reality which is perceived by the intellect and to posit as reality that which is perceived by the senses. (4)
(4). Ideas Have Consequences (Chicago and London, 1948), 3.
R.V. YOUNG is Professor of English at North Carolina State University and author of At War With the Word and Doctrine and Devotion in Seventeenth-Century Poetry (2000). |
Comments Off on Thursday July 5, 2007
Friday, April 27, 2007
It’s still the
same old story…
From today’s online
New York Times:
Photo by Carol T. Powers
for The New York Times
Also in today’s online Times:
“Mstislav Rostropovich, a cellist and conductor who was renowned not only as one of the great instrumentalists of the 20th century, but also as an outspoken champion of artistic freedom in Russia during the final decades of the Cold War, died in Moscow today. He was 80 and lived in Paris, with homes in Moscow, St. Petersburg, London and Lausanne, Switzerland….
Mr. Rostropovich… was widely known by his diminutive, Slava (which means glory in Russian)….”
Related material:
I. “Established on 8 November 1943, the Order of Glory (Orden Slavy – Орден Славы) was an Order (decoration) of the Soviet Union…. The Order of Glory… was modelled closely upon the Tsarist Cross of St. George….” —Wikipedia
II. Also on the 8th of November, in 2006 and 2002: Grave Matters and Religious Symbolism at Princeton.
III. “Mr. Rostropovich will be buried in Moscow at the Novodevichy Cemetery, where on Wednesday his friend, Boris Yeltsin, post-Soviet Russia’s first president, was laid to rest.” —New York Times
IV. “A graveyard smash.” –Bobby (Boris) Pickett, who died Wednesday.
Comments Off on Friday April 27, 2007
Sunday, April 22, 2007
Built
continued from
March 25, 2006
In honor of Scarlett Johansson's recent London films "Match Point" and "Scoop," here is a link to an entry of Women's History Month, 2006, with a discussion of an exhibition of the works of artist Liza Lou at London's White Cube Gallery. That entry includes the following illustrations:
Comments Off on Sunday April 22, 2007
Friday, February 16, 2007
“The much-borrowed Brown formula involves some very specific things. The name of a great artist, artifact or historical figure must be in the book’s story, not to mention on its cover. The narrative must start in the present day with a bizarre killing, then use that killing as a reason to investigate the past. And the past must yield a secret so big, so stunning, so saber-rattling that all of civilization may be changed by it. Probably not for the better.
This formula is neatly summarized….”
Cover illustration
for
The Judas Seat:
The Narrative:
The Secret:
Part I
“Little ‘Jack’ Horner was actually Thomas Horner, steward to the Abbot of Glastonbury during the reign of King Henry VIII…. Always keen to raise fresh funds, Henry had shown a interest in Glastonbury (and other abbeys). Hoping to appease the royal appetite, the nervous Abbot, Richard Whiting, allegedly sent Thomas Horner to the King with a special gift. This was a pie containing the title deeds to twelve manor houses in the hope that these would deflect the King from acquiring Glastonbury Abbey. On his way to London, the not so loyal courier Horner apparently stuck his thumb into the pie and extracted the deeds for Mells Manor, a plum piece of real estate. The attempted bribe failed and the dissolution of the monasteries (including Glastonbury) went ahead from 1536 to 1540. Richard Whiting was subsequently executed, but the Horner family kept the house, so the moral of this one is: treachery and greed pay off, but bribery is a bad idea.” –Chris Roberts, Heavy Words Lightly Thrown: The Reason Behind the Rhyme
“In medieval romance, the grail was said to have been brought to
Glastonbury in Britain by Joseph of Arimathea and his followers. In the time of Arthur, the quest for the Grail was the highest spiritual pursuit.” —
The Camelot Project
Part III
The Log24 entry for the date–
February 13, 2007–
of the above Bible scholar’s death,
and the three entries preceding it:
“And what the dead had no speech for, when living,
they can tell you, being dead:
the communication of the dead is tongued with fire
beyond the language of the living.”
— T. S. Eliot, Four Quartets
Comments Off on Friday February 16, 2007
Tuesday, February 13, 2007
Modern Times
vs. City Lights
Bob Dylan Wins a Folk Grammy
"Modern Times, his first album since Love and Theft, debuted at No. 1
on the US pop charts last September. At 65, Dylan became the oldest
living person to achieve this feat." –New Zealand Herald, Feb. 12
From an entry of
October 29, 2004:
"Each epoch has its singer."
— Jack London,
Oakland, California, 1901
"Anything but the void. And so we keep hoping to luck into a winning combination, to tap into a subtle harmony, trying like lock pickers to negotiate a compromise with the 'mystery tramp,' as Bob Dylan put it…."
— Dennis Overbye,
Quantum Baseball,
New York Times,
Oct. 26, 2004
"You said you'd never compromise
With the mystery tramp,
but now you realize
He's not selling any alibis
As you stare into
the vacuum of his eyes
And ask him do you want to
make a deal?"
— Bob Dylan,
Like a Rolling Stone
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"Climbing up on
Solsbury Hill…"
In today's meditation for
the Church of Peter Gabriel,
Dennis Overbye plays
the role of Jack Horner.
(See Overbye on Sagan in today's
New York Times, Sagan on Pi,
and Pi Day at Harvard.)
For more on Jack Horner, see
The Rise and Fall
of Popular Music,
by Donald Clarke,
Chapter One.
For two contrasting approaches
to popular music, see two artists
whose birthdays are today:
In other Grammy news–
At the end of Sunday's awards,
"Scarlett Johansson and Don Henley
put themselves in the pole position
to star in a remake of 'Adam's Rib'
with the following exchange:
Henley: So you're recording
your first album?
Johansson: Yeah. Do you
have any advice for me?
Henley: No."
— David Marchese, Salon.com
"Her wall is filled with pictures,
she gets 'em one by one…."
Comments Off on Tuesday February 13, 2007
Thursday, January 4, 2007
Readings for wise men
on the date of
T. S. Eliot's death:
"A cold coming we had of it…."
"… a Church is to be judged by its intellectual fruits, by its influence on the sensibility of the most sensitive and on the intellect of the most intelligent, and it must be made real to the eye by monuments of artistic merit."
— T. S. Eliot, For Lancelot Andrewes: Essays on Style and Order, published by Faber & Gwyer, London, in 1928.
The visual "monuments of artistic merit" I prefer are not those of a Church– except, perhaps, the Church of Modernism. Literary monuments are another matter. I recommend:
The Death of Adam,
The Novels of Charles Williams, and
Let Sleeping Beauties Lie.
Related material
on style and order:
Eliot's essay on Andrewes begins,
"The Right Reverend Father in God,
Lancelot Bishop of Winchester,
died on September 25, 1626."
For evidence of Andrewes's
saintliness (hence, that
of Eliot) we may examine
various events of the
25th of September.
("On September 25th most of
the Anglican Communion
commemorates the day on which
Lancelot Andrewes died.")
In Log24,
these events are…
Sept. 25, 2002 —
"Las Mañanitas"
Sept. 25, 2003 —
Aloha.
Sept. 25, 2004 —
Sept. 25, 2005 —
Sept. 25, 2006 —
(Yau and Perelman)
It seems that I am
somewhat out of step with
the Anglican Communion…
though perhaps, in a sense,
in step with Eliot.
Note his words in
"Journey of the Magi":
Birth or Death?
There was a Birth, certainly,
We had evidence and no doubt.
I had seen birth and death,
But had thought they were different;
this Birth was
Hard and bitter agony for us,
like Death, our death.
See also entries for
Dec. 27, 2006 (the day of
Itche Goldberg's death) —
— "Least Popular
Christmas Present
Revisited" —
and for the same date
three years earlier —
"If you don't play
some people's game, they say
that you have 'lost your marbles,'
not recognizing that,
while Chinese checkers
is indeed a fine pastime,
a person may also play dominoes,
chess, strip poker, tiddlywinks,
drop-the-soap or Russian roulette
with his brain.
One brain game that is widely,
if poorly, played is a gimmick
called 'rational thought.'"
— Tom Robbins
Comments Off on Thursday January 4, 2007
Friday, December 29, 2006
Tools
of Christ Church
"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon
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):
"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 ()
and logical possibility
with the diamond ()."
— Keith Allen Korcz
"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.
Comments Off on Friday December 29, 2006
Wednesday, September 20, 2006
Public Space
"… the Danish cartoons crisis last March showed 'two world views colliding in public space with no common point of reference.'"
— George Carey, Archbishop of Canterbury from 1991 to 2002, quoted in today's London Times.
Related material:
Geometry and Christianity
(Google search yielding
"about 1,540,000" results)
Geometry and Islam
(Google search yielding
"about 1,580,000" results)
MySpace.com/affine
A Public Space
— Motto of
Plato's Academy
Background from
Log24 on Feb. 15, 2006:
If we replace the Chinese word "I" (change, transformation) with the word "permutation," the relevance of Western mathematics (which some might call "the Logos") to the I Ching ("Changes Classic") beomes apparent.
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For the relevance of Plato to
Islam, see David Wade's
Pattern in Islamic Art
and a Google search on
Plato and Islam
("about 1,680,000" results).
"We should let ourselves be guided by what is common to all. Yet although the
Logos is common to all, most men live as if each had a private intelligence of his own."
— Heraclitus of Ephesus, about 500 B.C.
Comments Off on Wednesday September 20, 2006
Sunday, June 4, 2006
Images
and Words
for Baccalaureate
Day at Princeton
From Hermann Weyl’s
Symmetry,
Princeton University
Press, page 140
Adapted from the
cover of Alan Watts’s
The Spirit of Zen
Romani flag, courtesy of
myspace.com/RomArmando
Related material:
“The Scholar Gypsy”
in The Oxford Book
of English Prose, 1923,
edited by
Sir Arthur Quiller-Couch
This is available online:
From The Vanity of Dogmatizing,
by Joseph Glanvill
(London, printed by E.C. for
Henry Eversden at the Grey-Hound
in St.Pauls-Church-Yard, 1661)
Pages 195-201:
That one man should be able to bind the thoughts of another, and determine them to their particular objects; will be reckon’d in the first rank of Impossibles: Yet by the power of advanc’d Imagination it may very probably be effected; and story abounds with Instances. I’le trouble the Reader but with one; and the hands from which I had it, make me secure of the truth on’t. There was very lately a Lad in the University of Oxford, who being of very pregnant and ready parts, and yet wanting the encouragement of preferment; was by his poverty forc’d to leave his studies there, and to cast himself upon the wide world for a livelyhood. Now, his necessities growing dayly on him, and wanting the help of friends to relieve him; he was at last forced to joyn himself to a company of Vagabond Gypsies, whom occasionally he met with, and to follow their Trade for a maintenance. Among these extravagant people, and by the insinuating subtilty of his carriage, he quickly got so much of their love, and esteem; as that they discover’d to him their Mystery: in the practice of which, by the pregnancy of his wit and parts he soon grew so good a proficient, as to be able to out-do his Instructors. After he had been a pretty while exercis’d in the Trade; there chanc’d to ride by a couple of Scholars who had formerly bin of his acquaintance. The Scholars had quickly spyed out their old friend, among the Gypsies; and their amazement to see him among such society, had well-nigh discover’d him: but by a sign he prevented their owning him before that Crew: and taking one of them aside privately, desired him with his friend to go to an Inn, not far distant thence, promising there to come to them. They accordingly went thither, and he follows: after their first salutations, his friends enquire how he came to lead so odd a life as that was, and to joyn himself with such a cheating beggarly company. The Scholar-Gypsy having given them an account of the necessity, which drove him to that kind of life; told them, that the people he went with were not such Impostours as they were taken for, but that they had a traditional kind of learning among them, and could do wonders by the power of Imagination, and that himself had learnt much of their Art, and improved in further than themselves could. And to evince the truth of what he told them, he said, he’d remove into another room, leaving them to discourse together; and upon his return tell them the sum of what they had talked of: which accordingly he perform’d, giving them a full acount of what had pass’d between them in his absence. The Scholars being amaz’d at so unexpected a discovery, ernestly desir’d him to unriddle the mystery. In which he gave them satisfaction, by telling them, that what he did was by the power of Imagination, his Phancy binding theirs; and that himself had dictated to them the discourse, they held together, while he was from them: That there were warrantable wayes of heightening the Imagination to that pitch, as to bind anothers; and that when he had compass’d the whole secret, some parts of which he said he was yet ignorant of, he intended to give the world an account of what he had learned.
Now that this strange power of the Imagination is no Impossibility; the wonderful signatures in the Foetus caus’d by the Imagination of the Mother, is no contemptible Item. The sympathies of laughing & gaping together, are resolv’d into this Principle: and I see not why the phancy of one man may not determine the cogitation of another rightly qualified, as easily as his bodily motion. This influence seems to be no more unreasonable, then [sic] that of one string of a Lute upon another; when a stroak on it causeth a proportionable motion in the sympathizing confort, which is distant from it and not sensibly touched. Now if this notion be strictly verifiable; ’twill yeeld us a good account of how Angels inject thoughts into our minds, and know our cogitations: and here we may see the source of some kinds of fascination. If we are prejudic’d against the speculation, because we cannot conceive the manner of so strange an operation; we shall indeed receive no help from the common Philosophy: But yet the Hypothesis of a Mundane soul, lately reviv’d by that incomparable Platonist and Cartesian, Dr. H. More, will handsomely relieve us. Or if any would rather have a Mechanical account; I think it may probably be made out some such way as follow. Imagination is inward Sense. To Sense is required a motion of certain Filaments of the Brain; and consequently in Imagination there’s the like: they only differing in this, that the motion of the one proceeds immediately from external objects; but that of the other hath its immediate rise within us. Now then, when any part of the Brain is stringly agitated; that, which is next and most capable to receive the motive Impress, must in like manner be moved. Now we cannot conceive any thing more capable of motion, then the fluid matter, that’s interspers’d among all bodies, and contiguous to them. So then, the agitated parts of the Brain begetting a motion in the proxime Aether; it is propagated through the liquid medium, as we see the motion is which is caus’d by a stone thrown into the water. Now, when the thus moved matter meets with anything like that, from which it received its primary impress; it will proportionably move it, as it is in Musical strings tuned Unisons. And thus the motion being convey’d, from the Brain of one man to the Phancy of another; it is there receiv’d from the instrument of conveyance, the subtil matter; and the same kind of strings being moved, and much of whay after the same manner as in the first Imaginant; the Soul is awaken’d to the same apprehensions, as were they that caus’d them. I pretend not to any exactness or infallibility in this account, fore-seeing many scruples that must be removed to make it perfect: ‘Tis only a hint of the possibility of mechanically solving the Phaenomenon; though very likely it may require many other circumstances completely to make it out. But ’tis not my business here to follow it: I leave it therefore to receive accomplishment from maturer Inventions.
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Sunday, May 28, 2006
Related
Philosophy:
6.54 My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)
He must surmount these propositions; then he sees the world rightly.
7 Whereof one cannot speak, thereof one must be silent.
— Ludwig Wittgenstein, Tractatus Logico-Philosophicus, Routledge and Kegan Paul, London, 1922
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Related
Art in Our Schools:
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Former President of Dartmouth Dies
From today’s New York Times:
“In one widely publicized episode, in 1988, he condemned The Dartmouth Review, a conservative student newspaper, for ridiculing blacks, gay men and lesbians, women and Jews.”
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Comments Off on Sunday May 28, 2006
Friday, May 12, 2006
Tesseract
"Does the word 'tesseract'
mean anything to you?"
— Robert A. Heinlein in
The Number of the Beast
(1980)
My reply–
Part I:
A Wrinkle in Time, by
Madeleine L'Engle
(first published in 1962)
Part II:
Diamond Theory in 1937
and
Geometry of the 4×4 Square
Part III:
Catholic Schools Sermon
Conclusion:
"Wells and trees were dedicated to saints. But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden. Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy."
— Charles Williams, Witchcraft, Faber and Faber, London, 1941
Related material:
A New Yorker profile of Madeleine L'Engle from April 2004, which I found tonight online for the first time. For a related reflection on truth, stories, and values, see Saint's Day. For a wider context, see the Log24 entries of February 1-15, 2003 and February 1-15, 2006.
Comments Off on Friday May 12, 2006
Saturday, April 8, 2006
April 8 two years ago:
Art is magic delivered from
the lie of being truth.
— Theodor Adorno, Minima moralia,
London, New Left Books, 1974, p. 222
(First published in German in 1951.)
The director, Carol Reed, makes…
impeccable use of the beauty of black….
— V. B. Daniel on The Third Man
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Friday, April 7, 2006
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Friday, March 31, 2006
Reason and Rhyme
"Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday…."
— Bernard Holland in
The New York Times
Monday, May 20, 1996
Related material:
"flower"
Birds, Beasts & Flowers
As performed by
Princess Grace of Monaco
Presented at
St James's Palace, London,
on 22nd November 1978
in the presence of Her Majesty,
Queen Elizabeth
The Queen Mother
Comments Off on Friday March 31, 2006
Sunday, March 26, 2006
Clint Eastwood on the
“Midnight in the Garden
of Good and Evil”
soundtrack CD—
“Accentuate the positive”–
and an entry from last Christmas:
Compare and contrast:
(Click on pictures for details.)
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“Recollect what I have said to you,
that this world is a comedy
to those who think,
a tragedy to those who feel.
This is the quint-essence of all
I have learnt in fifty years!”
— Horace Walpole,
letter to Horace Mann,
5 March, 1772
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Saturday, March 25, 2006
Built
In memory of Rolf Myller,
who died on Thursday,
March 23, 2006, at
Mount Sinai Hospital
in Manhattan:
Myller was,
according to the
New York Times,
an architect
whose eclectic pursuits
included writing
children’s books,
The Bible Puzzle Book, and
Fantasex: A Book of Erotic Games.
He also wrote, the Times says,
“Symbols and Their Meaning
(1978), a graphic overview of
children’s nonverbal communication.”
This is of interest in view of the
Log24 reference to “symbol-mongers”
on the date of Myller’s death.
In honor of Women’s History Month
and of Myller’s interests in the erotic
and in architecture, we present
the following work from a British gallery.
This work might aptly be
retitled “Brick Shithouse.”
Related material:
(1) the artist’s self-portrait
and, in view of the cover
illustration for Myller’s
The Bible Puzzle Book,
(2) the monumental treatise
by Leonard Shlain
The Alphabet Versus
the Goddess: The Conflict
Between Word and Image.
For devotees of women’s history
and of the Goddess,
here are further details from
the
White Cube gallery:
Liza Lou
03.03.06 – 08.04.06
White Cube is pleased to present the first UK solo exhibition by Los Angeles-based artist Liza Lou.
Combining visionary, conceptual and craft approaches, Lou makes mixed-media sculptures and room-size installations that are suggestive of a transcendental reality. Lou’s work often employs familiar, domestic forms, crafted from a variety of materials such as steel, wood, papier-mâché and fibreglass, which is then covered with tiny glass beads that are painstakingly applied, one at a time, with tweezers. Dazzling and opulent and constantly glistening with refracted light, her sculptures bristle with what Peter Schjeldahl has aptly described as ‘surreal excrescence’.
This exhibition, a meditation on the vulnerability of the human body and the architecture of confinement, will include several new figurative sculptures as well as two major sculptural installations. Security Fence (2005) is a large scale cage made up of four steel, chain link walls, topped by rings of barbed wire and Cell (2004-2006), as its name suggests, is a room based on the approximate dimensions of a death row prison cell, a kind of externalized map of the prisoner’s mind. Both Security Fence and Cell, like Lou’s immense earlier installations Kitchen (1991-1995) and Back Yard (1995-1999) are characterized by the absence of their real human subject. But whereas the absent subject in Kitchen and Back Yard could be imagined through the details and accessories carefully laid out to view, in Lou’s two new installations the human body is implied simply through the empty volume created by the surrounding architecture. Both Cell and Security Fence are monochromatic and employ iconic forms that make direct reference to Minimalist art in its use of repetition, formal perfection and materiality. In contrast to this, the organic form of a gnarled tree trunk, Scaffold (2005-2006), its surface covered with shimmering golden beads, juts directly out from the wall.
Lou’s work has an immediate ‘shock’ content that works on different levels: first, an acknowledgement of the work’s sheer aesthetic impact and secondly the slower comprehension of the labour that underlies its construction. But whereas in Lou’s earlier works the startling clarity of the image is often a counterpoint to the lengthy process of its realization, for the execution of Cell, Lou further slowed down the process by using beads of the smallest variety with their holes all facing up in an exacting hour-by-hour approach in order to ‘use time as an art material’.
Concluding this body of work are three male figures in states of anguish. In The Seer (2005-2006), a man becomes the means of turning his body back in on himself. Bent over double, his body becomes an instrument of impending self-mutilation, the surface of his body covered with silver-lined beads, placed with the exactitude and precision of a surgeon. In Homeostasis (2005-2006) a naked man stands prostrate with his hands up against the wall in an act of surrender. In this work, the dissolution between inside and outside is explored as the ornate surface of Lou’s cell-like material ‘covers’ the form while exposing the systems of the body, both corporeal and esoteric. In The Vessel (2005-2006), Christ, the universal symbol of torture and agony holds up a broken log over his shoulders. This figure is beheaded, and bejewelled, with its neck carved out, becoming a vessel into which the world deposits its pain and suffering.
Lou has had numerous solo exhibitions internationally, including Museum Kunst Palast, Düsseldorf, Henie Onstad Kunstsenter, Oslo and Fondació Joan Miró, Barcelona. She was a 2002 recipient of the MacArthur Foundation Fellowship.
Liza Lou’s film Born Again (2004), in which the artist tells the compelling and traumatic story* of her Pentecostal upbringing in Minnesota, will be screened at 52 Hoxton Square from 3 – 25 March courtesy of Penny Govett and Mick Kerr.
Liza Lou will be discussing her work following a screening of her film at the ICA, The Mall, London on Friday 3 March at 7pm. Tickets are available from the ICA box office (+ 44 (0) 20 7930 3647).
A fully illustrated catalogue, with a text by Jeanette Winterson and an interview with Tim Marlow, will accompany the exhibition.
White Cube is open Tuesday to Saturday, 10.00 am to 6.00 pm.
For further information please contact Honey Luard or Susannah Hyman on + 44 (0) 20 7930 5373
* Warning note from Adrian Searle in The Guardian of March 21: “How much of her story is gospel truth we’ll never know.”
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Sunday, February 5, 2006
Catholic Schools Sermon
For those who might be tempted today, following yesterday’s conclusion of Catholic Schools Week, to sing (for whatever reason) “Ding Dong, the Witch is Dead”–
Here, from his classic Witchcraft (first published by Faber and Faber, London, 1941, reprinted by Apocryphile Press, Berkeley, CA, Oct. 1, 2005) is Charles Williams on the strong resemblance between witchcraft and the rituals of the Church:
Charles Williams on
Witchcraft and the Church
From Witchcraft, 2005 Apocryphile edition, pages 77-80–
[77] … The predisposition towards the idea of magic might be said to begin with a moment which seems to be of fairly common experience– the moment when it seems that anything might turn into anything else. We have grown used– and properly used– to regarding this sensation invalid because, on the whole, things do not turn into other things except by processes which we realize, or else at least so frequently that we appreciate the probability. But the occasional sensation remains. A room, a street, a field becomes unsure. The edge of a possibility of utter alteration intrudes. A door, untouched, might close; a picture might walk; a tree might speak; an animal might not be an animal; a man might not be a man. One may be with a friend, and a terror will take one even while his admirable voice is speaking; one will be with a lover and the hand will become a different and terrifying thing, moving in one’s own like a malicious intruder, too real for anything but fear. All this may be due to racial memories or to any other cause; the point is that it exists. It exists and can be communicated; it can even be shared. There is, in our human centre, a heart-gripping fear of irrational change, of perilous and malevolent change.
Secondly, there is the human body, and the movements of the human body. Even now, when, as a general rule, the human body is not supposed to mean [78] anything, there are moments when it seems, in spite of ourselves, packed with significance. This sensation is almost exactly the opposite of the last. There, one was aware that any phenomenon might alter into another and truer self. Here, one is aware that a phenomenon, being wholly itself, is laden with universal meaning. A hand lighting a cigarette is the explanation of everything; a foot stepping from a train is the rock of all existence. If the first group of sensations are due to racial fear, I do not know to what the second group are due– unless indeed to the Mercy of God, who has not left us without a cloud of witnesses. But intellectually they are both as valid or invalid as each other; any distinction must be a matter of choice. And they justify each other, at least to this extent, that (although the first suggests irrationality and the second rationality) they both at first overthrow a simple trust that phenomena are what phenomena seem.
But if the human body is capable of seeming so, so are the controlled movements of the human body– ritual movements, or rather movements that seem like ritual. A finger pointing is quite capable of seeming not only a significant finger, but a ritual finger; an evocative finger; not only a finger of meaning, but a finger of magic. Two light dancing steps by a girl may (if one is in that state) appear to be what all the Schoolmen were trying to express; they are (only one cannot quite catch it) an intellectual statement of beatitude. But two quiet steps by an old man may seem like the very speech of hell. Or the other way round. Youth and age have nothing to do with it, nor did the ages that defined and [79] denounced witchcraft think so. The youngest witch, it is said, that was ever burned was a girl of eleven years old.
Ordered movement, ritual, is natural to men. But some ages are better at it, are more used to it, and more sensitive to it, than others. The Middle Ages liked great spectacle, and therefore (if for no other reasons– but there were many) they liked ritual. They were nourished by ritual– the Eucharist exhibited it. They made love by ritual– the convention of courtly love preserved it. Certainly also they did all these things without ritual– but ritual (outside the inner experience) was the norm. And ritual maintains and increases that natural sense of the significance of movement. And, of course, of formulae, of words.
The value of formulae was asserted to be very high. The whole religious life ‘as generally necessary to salvation’ depended on formulae. The High God had submitted himself to formulae. He sent his graces. He came Himself, according to ritual movements and ritual formulae. Words controlled the God. All generations who have believed in God have believed that He will come on interior prayer; not all that He will come, if not visibly yet in visible sacraments, on exterior incantation. But so it was. Water and a Triune formula concentrated grace; so did oil and other formulae; so– supremely– did bread and wine and yet other formulae. Invocations of saints were assumed, if less explicitly guaranteed, to be effective. The corollaries of the Incarnation had spread, in word and gesture, very far.
The sense of alteration, the sense of meaning, the [80] evocation of power, the expectation of the God, lay all about the world. The whole movement of the Church had, in its rituals, a remarkable similarity to the other rites it denounced. But the other rites had been there first, both in the Empire and outside the Empire. In many cases the Church turned them to its own purposes. But also in many cases it entirely failed to turn them to its own purposes. In many cases it adopted statues and shrines. But in others it was adopted by, at least, the less serious spells and incantations. Wells and trees were dedicated to saints. But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden. Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.
Comments Off on Sunday February 5, 2006
Thursday, January 26, 2006
In honor of Paul Newman’s age today, 81:
On Beauty
“Something beautiful fills the mind yet invites the search for something beyond itself, something larger or something of the same scale with which it needs to be brought into relation. Beauty, according to its critics, causes us to gape and suspend all thought. This complaint is manifestly true: Odysseus does stand marveling before the palm; Odysseus is similarly incapacitated in front of Nausicaa; and Odysseus will soon, in Book 7, stand ‘gazing,’ in much the same way, at the season-immune orchards of King Alcinous, the pears, apples, and figs that bud on one branch while ripening on another, so that never during the cycling year do they cease to be in flower and in fruit. But simultaneously what is beautiful prompts the mind to move chronologically back in the search for precedents and parallels, to move forward into new acts of creation, to move conceptually over, to bring things into relation, and does all this with a kind of urgency as though one’s life depended on it.”
The above symbol of Apollo suggests, in accordance with Scarry’s remarks, larger structures. Two obvious structures are the affine 4-space over GF(3), with 81 points, and the affine plane over GF(32), also with 81 points. Less obvious are some related projective structures. Joseph Malkevitch has discussed the standard method of constructing GF(32) and the affine plane over that field, with 81 points, then constructing the related Desarguesian projective plane of order 9, with 92 + 9 + 1 = 91 points and 91 lines. There are other, non-Desarguesian, projective planes of order 9. See Visualizing GL(2,p), which discusses a spreadset construction of the non-Desarguesian translation plane of order 9. This plane may be viewed as illustrating deeper properties of the 3×3 array shown above. To view the plane in a wider context, see The Non-Desarguesian Translation Plane of Order 9 and a paper on Affine and Projective Planes (pdf). (Click to enlarge the excerpt beow).
See also
Miniquaternion Geometry: The Four Projective Planes of Order 9 (pdf), by Katie Gorder (Dec. 5, 2003), and a book she cites:
Miniquaternion geometry: An introduction to the study of projective planes, by T. G. Room and P. B. Kirkpatrick. Cambridge Tracts in Mathematics and Mathematical Physics, No. 60. Cambridge University Press, London, 1971. viii+176 pp.
For “miniquaternions” of a different sort, see my entry on Visible Mathematics for Hamilton’s birthday last year:
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Friday, December 30, 2005
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Friday, December 2, 2005
Proof 101
From a course description:
“This module aims to introduce the student to rigorous university level mathematics….
Syllabus: The idea of and need for mathematical statements and proofs…. proof by contradiction… proof by induction…. the infinite number of primes….”
In the December Notices of the American Mathematical Society, Brian (E. B.) Davies, a professor of mathematics at King’s College London, questions the consistency of Peano Arithmetic (PA), which has the following axioms:
From BookRags.com—
Axiom 1. 0 is a number.
Axiom 2. The successor of any number is a number.
Axiom 3. If a and b are numbers and if their successors are equal, then a and b are equal.
Axiom 4. 0 is not the successor of any number.
Axiom 5. If S is a set of numbers containing 0 and if the successor of any number in S is also in S, then S contains all the numbers.
It should be noted that the word “number” as used in the Peano axioms means “non-negative integer.” The fifth axiom deserves special comment. It is the first formal statement of what we now call the “induction axiom” or “the principle of mathematical induction.”
Peano’s fifth axiom particularly troubles Davies, who writes elsewhere:
I contend that our understanding of number should be placed in an historical context, and that the number system is a human invention. Elementary arithmetic enables one to determine the number of primes less than twenty as certainly as anything we know. On the other hand Peano arithmetic is a formal system, and its internal consistency is not provable, except within set-theoretic contexts which essentially already assume it, in which case their consistency is also not provable. The proof that there exists an infinite number of primes does not depend upon counting, but upon the law of induction, which is an abstraction from our everyday experience….
… Geometry was a well developed mathematical discipline based upon explicit axioms over one and a half millennia before the law of induction was first formulated. Even today many university students who have been taught the principle of induction prefer to avoid its use, because they do not feel that it is as natural or as certain as a purely algebraic or geometric proof, if they can find one. The feelings of university students may not settle questions about what is truly fundamental, but they do give some insight into our native intuitions.
— E. B. Davies in
“Counting in the real world,”
March 2003 (word format),
To appear in revised form in
Brit. J. Phil. Sci. as
“Some remarks on
the foundations
of quantum mechanics”
Exercise:
Discuss Davies’s claim that
The proof that there exists an infinite number of primes does not depend upon counting, but upon the law of induction.
Cite the following passage in your discussion.
It will be clear by now that, if we are to have any chance of making progress, I must produce examples of “real” mathematical theorems, theorems which every mathematician will admit to be first-rate.
… I can hardly do better than go back to the Greeks. I will state and prove two of the famous theorems of Greek mathematics. They are “simple” theorems, simple both in idea and in execution, but there is no doubt at all about their being theorems of the highest class. Each is as fresh and significant as when it was discovered– two thousand years have not written a wrinkle on either of them. Finally, both the statements and the proofs can be mastered in an hour by any intelligent reader, however slender his mathematical equipment.
I. The first is Euclid’s proof of the existence of an infinity of prime numbers.
The prime numbers or primes are the numbers
(A) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, …
which cannot be resolved into smaller factors. Thus 37 and 317 are prime. The primes are the material out of which all numbers are built up by multiplication: thus
666 = 2 . 3 . 3 . 37.
Every number which is not prime itself is divisible by at least one prime (usually, of course, by several). We have to prove that there are infinitely many primes, i.e. that the series (A) never comes to an end.
Let us suppose that it does, and that
2, 3, 5, . . . , P
is the complete series (so that P is the largest prime); and let us, on this hypothesis, consider the number
Q = (2 . 3 . 5 . . . . . P) + 1.
It is plain that Q is not divisible by any of
2, 3, 5, …, P;
for it leaves the remainder 1 when divided by any one of these numbers. But, if not itself prime, it is divisible by some prime, and therefore there is a prime (which may be Q itself) greater than any of them. This contradicts our hypothesis, that there is no prime greater than P; and therefore this hypothesis is false.
The proof is by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
— G. H. Hardy,
A Mathematician’s Apology,
quoted in the online guide for
Clear and Simple as the Truth:
Writing Classic Prose, by
Francis-Noël Thomas
and Mark Turner,
Princeton University Press
In discussing Davies’s claim that the above proof is by induction, you may want to refer to Davies’s statement that
Geometry was a well developed mathematical discipline based upon explicit axioms over one and a half millennia before the law of induction was first formulated
and to Hardy’s statement that the above proof is due to Euclid.
Comments Off on Friday December 2, 2005
Wednesday, November 30, 2005
Hobgoblin?
Brian Davies is a professor of mathematics at King’s College London. In the December Notices of the American Mathematical Society, he claims that arithmetic may, for all we know, be inconsistent:
“Gödel taught us that it is not possible to prove that Peano arithmetic is consistent, but everyone has taken it for granted that in fact it is indeed consistent.
Platonistically-inclined mathematicians would deny the possibility that Peano arithmetic could be flawed. From Kronecker onwards many consider that they have a direct insight into the natural numbers, which guarantees their existence. If the natural numbers exist and Peano’s axioms describe properties that they possess then, since the axioms can be instantiated, they must be consistent.”
“It is not possible to prove that Peano arithmetic is consistent”…?!
Where did Gödel say this? Gödel proved, in fact, according to a well-known mathematician at Princeton, that (letting PA stand for Peano Arithmetic),
“If PA is consistent, the formula expressing ‘PA is consistent’ is unprovable in PA.”
— Edward Nelson,
Mathematics and Faith (pdf)
Remarkably, even after he has stated correctly Gödel’s result, Nelson, like Davies, concludes that
“The consistency of PA cannot be concretely demonstrated.”
I prefer the argument that the existence of a model ensures the consistency of a theory.
For instance, the Toronto philosopher William Seager writes that
“Our judgement as to the consistency of some system is not dependent upon that system’s being able to prove its own consistency (i.e. generate a formula that states, e.g. ‘0=1’ is not provable). For if that was the sole basis, how could we trust it? If the system was inconsistent, it could generate this formula as well (see Smullyan,
Gödel’s Incompleteness Theorems, (Oxford, 1992, p. 109)). Furthermore, [George] Boolos allows that we do know that certain systems, such as Peano Arithmetic, are consistent even though they cannot prove their own consistency. Presumably, we know this because we can see that a certain model satisfies the axioms of the system at issue, hence that they are true in that model and so must be consistent.”
— Yesterday’s Algorithm:
Penrose and the Gödel Argument
The relationship between consistency and the existence of a model is brought home by the following weblog entry that neatly summarizes a fallacious argument offered in the AMS Notices by Davies:
The following is an interesting example that I came across in the article “Whither Mathematics?” by Brian Davies in the December issue of Notices of the American Mathematical Society.
Consider the following list A1 of axioms.
(1) There is a natural number 0.
(2) Every natural number a has a successor, denoted by S(a).
(3) There is no natural number whose successor is 0.
(4) Distinct natural numbers have distinct successors: a = b if and only if S(a) = S(b).
(5) If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all the natural numbers.
Now consider the following list A2 of axioms.
(1) G is a set of elements and these elements obey the group axioms.
(2) G is finite but not isomorphic to any known list of finite simple groups.
(3) G is simple, in other words, if N is a subset of G satisfying certain properties then N=G.
We can roughly compare A2 with A1. The second axiom in A2 can be thought of as analogous to the third axiom of A1. Also the third axiom of A2 is analogous to the fifth axiom of A1, insofar as it refers to an unspecified set with cetain properties and concludes that it is equal to G.
Now, as is generally believed by most group theorists, the system A2 is internally inconsistent and the proof its inconsistency runs for more than 10000 pages.
So who is to deny that the system A1 is also probably internally inconsistent! Particularly since Godel proved that you can not prove it is consistent (staying inside the system). May be the shortest proof of its inconsistency is one hundred million pages long!
— Posted by Krishna,
11/29/2005 11:46:00 PM,
at his weblog,
“Quasi-Coherent Ruminations”
An important difference between A1 (the set of axioms of Peano arithmetic) and A2 (a set of axioms that describe a new, unknown, finite simple group) is that A1 is known to have a model (the nonnegative integers) and A2 is not known to have a model.
Therefore, according to Seager’s argument, A1 is consistent and A2 may or may not be consistent.
The degree to which Seager’s argument invokes Platonic realism is debatable. Less debatable is the quasireligious faith in nominalism proclaimed by Davies and Nelson. Nelson’s own account of a religious experience in 1976 at Toronto is instructive.
I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.
— Edward Nelson,
Mathematics and Faith (pdf)
Nelson’s “Mathematics and Faith” was written for the Jubilee for Men and Women from the World of Learning held at the Vatican, 23-24 May 2000. It concludes with an invocation of St. Paul:
During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his
Pellegrino di Roma. “For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”
— Edward Nelson,
Mathematics and Faith (pdf)
Belief in the consistency of arithmetic may or may not be foolish, and therefore an Emersonian hobgoblin of little minds, but bullshit is bullshit, whether in London, in Princeton, in Toronto, or in Rome.
Comments Off on Wednesday November 30, 2005
Thursday, August 25, 2005
Analogical
Train of Thought
Part I: The 24-Cell
From S. H. Cullinane,
Visualizing GL(2,p),
March 26, 1985–
From John Baez, “This Week’s Finds in Mathematical Physics (Week 198),” September 6, 2003:
Noam Elkies writes to John Baez:
Hello again,
You write:
[…]
“I’d like to wrap up with a few small comments about last Week. There I said a bit about a 24-element group called the ‘binary tetrahedral group’, a 24-element group called SL(2,Z/3), and the vertices of a regular polytope in 4 dimensions called the ’24-cell’. The most important fact is that these are all the same thing! And I’ve learned a bit more about this thing from here:”
[…]
Here’s yet another way to see this: the 24-cell is the subgroup of the unit quaternions (a.k.a. SU(2)) consisting of the elements of norm 1 in the Hurwitz quaternions – the ring of quaternions obtained from the Z-span of {1,i,j,k} by plugging up the holes at (1+i+j+k)/2 and its <1,i,j,k> translates. Call this ring A. Then this group maps injectively to A/3A, because for any g,g’ in the group |g-g’| is at most 2 so g-g’ is not in 3A unless g=g’. But for any odd prime p the (Z/pZ)-algebra A/pA is isomorphic with the algebra of 2*2 matrices with entries in Z/pZ, with the quaternion norm identified with the determinant. So our 24-element group injects into SL2(Z/3Z) – which is barely large enough to accommodate it. So the injection must be an isomorphism.
Continuing a bit longer in this vein: this 24-element group then injects into SL2(Z/pZ) for any odd prime p, but this injection is not an isomorphism once p>3. For instance, when p=5 the image has index 5 – which, however, does give us a map from SL2(Z/5Z) to the symmetric group of order 5, using the action of SL2(Z/5Z) by conjugation on the 5 conjugates of the 24-element group. This turns out to be one way to see the isomorphism of PSL2(Z/5Z) with the alternating group A5.
Likewise the octahedral and icosahedral groups S4 and A5 can be found in PSL2(Z/7Z) and PSL2(Z/11Z), which gives the permutation representations of those two groups on 7 and 11 letters respectively; and A5 is also an index-6 subgroup of PSL2(F9), which yields the identification of that group with A6.
NDE
The enrapturing discoveries of our field systematically conceal, like footprints erased in the sand, the analogical train of thought that is the authentic life of mathematics – Gian-Carlo Rota |
Like footprints erased in the sand….
Log24, May 27, 2004 —
“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
“A theory…. predicts that space and time are indeed made of discrete pieces.”
— Lee Smolin in Atoms of Space and Time (pdf), Scientific American, Jan. 2004
“… a fundamental discreteness of spacetime seems to be a prediction of the theory….”
— Thomas Thiemann, abstract of Introduction to Modern Canonical Quantum General Relativity
“Theories of discrete space-time structure are being studied from a variety of perspectives.”
— Quantum Gravity and the Foundations of Quantum Mechanics at Imperial College, London
Disclaimer:
The above speculations by physicists
are offered as curiosities.
I have no idea whether
any of them are correct.
Related material:
Stephen Wolfram offers a brief
History of Discrete Space.
For a discussion of space as discrete
by a non-physicist, see John Bigelow‘s
Space and Timaeus.
Part III: Quaternions
in a Discrete Space
Comments Off on Thursday August 25, 2005
Friday, July 8, 2005
Comments Off on Friday July 8, 2005
Wednesday, July 6, 2005
Red and Blue
On the June 28 mock naval battle between “red” and “blue” fleets to mark the bicentenary year of the 1805 Battle of Trafalgar:
A spokeswoman for the Royal Navy said —
“Nelson is featured, but we are not billing it as Britain versus France… This will not be a French-bashing opportunity.”
Tuesday, June 7, 2005
“A SINGLE VERSE by Rimbaud,”
writes Dominique de Villepin,
the new French Prime Minister,
“shines like a powder trail
on a day’s horizon.
It sets it ablaze all at once,
explodes all limits,
draws the eyes
to other heavens.”
— Ben Macintyre,
The London Times, June 4:
When Rimbaud Meets Rambo
“Room 101 was the place where
your worst fears were realised
in George Orwell’s classic
Nineteen Eighty-Four.
[101 was also]
Professor Nash’s office number
in the movie ‘A Beautiful Mind.'”
— Prime Curios
Classics Illustrated —
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Monday, June 6, 2005
It was the best of times,
it was the worst of times.
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Saturday, March 12, 2005
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Friday, December 3, 2004
Crimson
on St. Cecilia’s Day
“… from the Age that is past,
To the Age that is waiting before.”
— Samuel Gilman, “Fair Harvard“
Published by The Harvard Crimson
on Monday, November 22, 2004:
Dylan Performs for Sold-Out Crowd
By KATHERINE CHAN Harvard Crimson Contributing Writer
Shouts of “Make way! Moses is here!” filled a restless crowd as legendary musician Bob Dylan closed off his College tour last night jamming in front of a sold out audience of Harvard undergraduates and Cambridge residents….
The turnout for last night’s two-hour show was greater than many of the student audience members anticipated…
But despite the legendary hits and massive crowds, several students said they were disappointed with the show.
“I love Bob Dylan. I just don’t know what he’s saying,” said Alexander A.C. De Carvalho ’08.
|
Recommended reading
for Harvard students:
Click on picture
for details.
From an entry of October 29, 2004:
“Each epoch has its singer.” — Jack London, Oakland, California, 1901
“Anything but the void. And so we keep hoping to luck into a winning combination, to tap into a subtle harmony, trying like lock pickers to negotiate a compromise with the ‘mystery tramp,’ as Bob Dylan put it….” — Dennis Overbye, Quantum Baseball, New York Times, Oct. 26, 2004
“You said you’d never compromise With the mystery tramp, but now you realize He’s not selling any alibis As you stare into the vacuum of his eyes And ask him do you want to make a deal?” — Bob Dylan, Like a Rolling Stone |
From The New York Times today:
“It’s official, I guess. Forty years after he recorded it, Bob Dylan’s ‘Like a Rolling Stone’ was just named the greatest rock ‘n’ roll song of all time….”
Comments Off on Friday December 3, 2004
Friday, October 29, 2004
Song
"Each epoch has its singer."
— Jack London, Oakland, California, 1901
"Anything but the void. And so we keep hoping to luck into a winning combination, to tap into a subtle harmony, trying like lock pickers to negotiate a compromise with the 'mystery tramp,' as Bob Dylan put it…."
— Dennis Overbye, Quantum Baseball,
New York Times, Oct. 26, 2004
"You said you'd never compromise
With the mystery tramp,
but now you realize
He's not selling any alibis
As you stare into
the vacuum of his eyes
And ask him do you want to
make a deal?"
— Bob Dylan, Like a Rolling Stone
"About a century ago scientists began to realize that beneath the too, too solid veneer of what had passed for reality for 2,000 years there was some pretty funny and fuzzy business going on….
Most of us, I suspect, would rather believe that the devil is running things than that no one is in charge, that our lives, our loves, World Series victories, hang on the whims of fate and chains of coincidences, on God throwing dice, as Einstein once referred to quantum randomness….
[But] we are people, with desires and memories and a sense of humor – not Ping Pong balls."
— Dennis Overbye, Quantum Baseball,
New York Times, Oct. 26, 2004
"You can be replaced by some Ping Pong balls and a dictionary."
— Anonymous source, March 29, 2001
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Sunday, October 10, 2004
Introduction to Aesthetics
“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology
“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases,’ indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.
A chess problem also has unexpectedness, and a certain economy; it is essential that the moves should be surprising, and that every piece on the board should play its part. But the aesthetic effect is cumulative. It is essential also (unless the problem is too simple to be really amusing) that the key-move should be followed by a good many variations, each requiring its own individual answer. ‘If P-B5 then Kt-R6; if …. then …. ; if …. then ….’ — the effect would be spoilt if there were not a good many different replies. All this is quite genuine mathematics, and has its merits; but it just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly*) which a real mathematician tends to despise.
* I believe that is now regarded as a merit in a problem that there should be many variations of the same type.”
(Cambridge at the University Press. First edition, 1940.)
Brian Harley in
Mate in Two Moves:
“It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver’s banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be.”
(London, Bell & Sons. First edition, 1931.)
Comments Off on Sunday October 10, 2004
Thursday, September 23, 2004
Aluminum, Your Shiny Friend
(Continued)
New York, NY 1977 $175 million 915 feet 59 Steel Aluminum, reflective glass
|
Click photo for larger image. |
“From the very beginning, the Citicorp Center (today, the Citigroup Center) in New York City was an engineering challenge. When planning for the skyscraper began in the early 1970s, the northwest corner of the proposed building site was occupied by
The church allowed Citicorp to build the skyscraper under one condition: a new church would have to be built on the same corner, with no connection to the Citicorp building and no columns passing through it.
How did the engineers do it? They set the 59-story tower on four massive columns, positioned at the center of each side, rather than at the corners. This design allowed the northwest corner of the building to cantilever 72 feet over the new church.”
Source: PBS, Building BIG.
Citigroup (NYSE:C) is said to be the largest financial services conglomerate in the world.
For more on the close relationship between churches and banks, see the works of T. S. Eliot and a description of the City of London,
The Square Mile.
For more on Eliot, architecture, and another Harvard man, use links in the previous entry.
Friday, September 10, 2004
Philosophy
For Samira Bellil,
who died in Paris on
Friday, Sept. 3, 2004…
From the link at
Symmetry and Change
in the Dreamtime,
Part 8, Friday,
Sept. 3, 2004,
Noon…
Under heaven
thunder rolls…
Log24 on Sept. 10, 2002—
Three songs from Sept. 10
in various preceding years–
“Good morning little schoolgirl
Good morning little schoolgirl
Can I come home with
Can I come home with you“
— Rod Stewart, Sept. 10, 1964
“Tell your mamma, girl, I can’t stay long
We got things we gotta catch up on
Mmmm, you know
You know what I’m sayin’ “
— Neil Diamond, Sept. 10, 1966
“A time of war, a time of peace
A time of love, a time of hate
A time you may embrace
A time to refrain from embracing“
— The Byrds, Sept. 10, 1965
Further verses from the Byrds
seem appropriate on this, the day
of Samira Bellil’s funeral:
To everything, turn, turn, turn,
there is a season, turn, turn, turn…
Tournante
“It’s not even called rape. They call it
a tournante, or pass-round.
The banality is deliberate:
a joint, a girl – same difference.”
… and a time to every purpose
under heaven.
“… The kind of school where teacher
Fabrice Genestal kept hearing
the word “tournante” and didn’t click
what it meant, till he and Sillam
sat the kids down in after-school
workshops, and got talking.”
— Metropolitan Police Service, London
Comments Off on Friday September 10, 2004
Tuesday, August 31, 2004
Iconography
For student
Anthony Fonseca,
Harvard ’04-’05:
Michael (Studio della Robbia, ca. 1475)
For teacher
Margaret Casey:
The Green and
Burning Tree, by
Chesca Potter
For the Voice of Gollum,
Peter Woodthorpe:
For further details, click on
any of the pictures above.
… y eres tú y soy yo
y es un caminarte en círculo
dar a tus hechos dimensión de arco
y a solas con tu impulso decirte la palabra.
— Homero Aridjis
For Lucero:
dimensión de arco
(This last picture, taken by
Andrew from London,
was added at
11:30 AM ET Aug. 31, 2004.
For the excellent story that
accompanies the picture, see
“Early Evening, the Light
Beginning to Fade.”)
Monday, August 30, 2004
Q.E.D.
A Log24 entry of Aug. 17, 2004, on the
three Semitic (or “Abrahamic”) religions:
“Looney.”
From Scotsman.com News Mon., 30 Aug., 2004 11:43 AM (UK)
Ex-Priest Sentenced for Disrupting Marathon
By Pat Hurst, PA News, in Athens
An ex-priest who lives in Britain was given a 12-month suspended sentence today for disrupting the men’s Olympic marathon in Athens.
Cornelius Horan, 57, a former Catholic priest living in London, appeared before a Greek judge this morning, local police said.
He was sentenced and released from custody but his whereabouts are unknown.
Irishman Horan, originally from Kerry, dashed from the sidelines to attack the marathon front-runner during yesterday’s event.
He told officers he staged the disruption to “prepare for the second coming”.
A police spokesman said: “He has got mental problems. He is not very well.
“His only explanation for his behaviour was that it was for the second coming.”
Horan also disrupted last year’s Silverstone Formula One Grand Prix by dashing across the track.
Leslie Broad, of Deunant Books, which publishes Mr Horan’s books on its website, said: “We publish two of his books on biblical prophecies and he seems to be fairly convinced that the second coming is due fairly shortly.
“After the incident at Silverstone, he did say he would never do anything like that again.
“He comes across as a shy, very intelligent and compassionate man but as is often the way with people who are very intelligent, it sometimes manifests itself in very strange ways.
“I think he found prison a fairly uplifting experience. He came out feeling that he had met a lot of people he wouldn’t normally have met, people who had committed serious crimes.”
Horan’s victim yesterday, Vanderlei De Lima, from Brazil, was at the head of the race just three miles from the finish.
Horan grabbed him and bundled him into spectators at the side of the road.
After a scuffle, the runner managed to get away, but he was clearly ruffled and finished third.
The Brazilian Olympic Committee put in an official complaint to the Greeks and at one point the final medal ceremony to be staged during the closing ceremony was in doubt.
Horan was arrested and taken to the General Police Division of Attica, where he stayed overnight.
|
Author biography
from Deunant Books:
Father Cornelius (“Neil”) Horan
Horan
“Neil Horan was born in 1947, in Scartaglen, County Kerry, in the Republic of Ireland. After schooling in Ireland he was ordained a Catholic Priest in Saint Mary’s Cathedral, Killarney, in 1973.
He has served all his priestly life in the Southwark Diocese, covering London south of the River Thames and Kent, his first Parish being Bexley in Kent. His interest in Bible prophecy began when he attended a lecture in 1974, given by the Apostolic Fellowship of Christ, a group which had originated with the Christadelphians. Meaning ‘Brothers in Christ’, the Christadelphians were a small Church formed in 1861 by Dr John Thomas. Father Horan says he owes a debt of gratitude to the Christadelphian tradition for the understanding of the Bible which they gave him. He regards the Bible as the greatest Book in the world and has devoted his life to making it better known, especially the Prophecies.
He is not a prophet, considering himself to be merely an interpreter, has never received a Divine message or vision, and God has never spoken to him. He feels that he is right only in so far as he interprets the Book of Books correctly.
He is still a Catholic Priest, listed in the Catholic Directory under his full name of Cornelius Horan. Cornelius, a Centurian [sic] in the Roman army, was the first Christian convert; Father Horan is proud to bear that name and hopes to meet his famous namesake soon, when Jesus comes.”
A Glorious New World
by Father Neil Horan
“Are there passages in the Bible that foretell events that were, at the time it was written, far in the future? Father Neil Horan argues eloquently, knowledgeably and persuasively in this book, first published in 1985, that this is so. It is easy to scoff at predictions of events that were, according to the book, to have taken place a few years ago but which have not happened, but to do that would be wrong. With only the most subtle changes of emphasis in interpretation, it could just as easily be argued that events in the Middle East particularly have to a large degree fulfilled the prophecies for the years since 1985.
Then there are the events yet to come. They are, according to the author and his sources, to be the most significant in the history of mankind, and are going to happen soon. With a little thought, certain current-day world figures are a disconcertingly comfortable match for some of the characters who will act out the earth-shattering dramas to come. Even the most hardened cynic will get that prickly feeling down the back of his neck as he reads this book.
Taken together with Father Horan’s later work ‘Christ Will Soon Take Power From All Governments’ (also available from Deunant Books) the two books represent one of the most remarkable and significant bodies of work seen in this field for many, many years.”
— Deunant Books on Theology
Comments Off on Monday August 30, 2004
Friday, April 9, 2004
We Call This Friday Good
— T. S. Eliot
Welcome to our imaginative and inspiring toy catalog! |
Today is Friday 9-April 2004. On this day in 1914 1st full color film shown “The World, The Flesh & the Devil” (London) |
What you will discover in this site is what we have been able to find in our everlasting search for the most original, innovative, amusing and mind bending toys from around the world.
Have Fun.
|
Comments Off on Friday April 9, 2004
Thursday, April 8, 2004
Triple Crown
“The tug of an art that unapologetically sees itself as on a par with science and religion is not to be underestimated…. Philosophical ambition and formal modesty still constitute Minimalism’s bottom line.”
— Michael Kimmelman, April 2, 2004
________________
From Hans Reichenbach‘s
The Rise of Scientific Philosophy:
Ch. 18 – The Old and the New Philosophy
“The speculative philosophers allotted to art a dignified position by putting art on a par with science and morality: truth, beauty and the good were for them the triple crown of human searching and longing.”
Ch. 15 – Interlude: Hamlet’s Soliloquy
“I have good evidence. The ghost was very conclusive in his arguments. But he is only a ghost. Does he exist? I could not very well ask him. Maybe I dreamed him. But there is other evidence….
It is really a good idea: that show I shall put on. It will be a crucial experiment. If they murdered him they will be unable to hide their emotions. That is good psychology. If the test is positive I shall know the whole story for certain. See what I mean? There are more things in heaven and earth than are dreamt of in your philosophy, my dear logician.
I shall know it for certain? I see your ironical smile. There is no certainty….
There I am, the eternal Hamlet. What does it help me to ask the logician….? His advice confirms my doubt rather than giving me the courage I need for my action. One has to have more courage than Hamlet to be always guided by logic.”
________________
On this Holy Thursday, the day of Christ’s Last Supper, let us reflect on Quine’s very pertinent question in Quiddities (under “Communication”):
“What transubstantiation?”
“It is easiest to tell what transubstantiation is by saying this: little children should be taught about it as early as possible. Not of course using the word…because it is not a little child’s word. But the thing can be taught… by whispering…”Look! Look what the priest is doing…He’s saying Jesus’ words that change the bread into Jesus’ body. Now he’s lifting it up. Look!”
From “On Transubstantiation” by Gertrude Elizabeth Margaret Anscombe, Collected Philosophical Papers, V.III: Ethics, Religion, and Politics, 1981, Univ. of Minnesota Press, as quoted in the weblog of William Luse, Sept, 28, 2003
A perhaps more credible instance of transubstantiation may be found in this account of Anscombe on the Feast of Corpus Christi:
“In her first year at Oxford, she converted to Catholicism. In 1938, after mass at Blackfriars on the Feast of Corpus Christi, she met Peter Geach, a young man three years her senior who was also a recent convert to Catholicism. Like her, Geach was destined to achieve eminence in philosophy, but philosophy played no role in bringing about the romance that blossomed. Smitten by Miss Anscombe’s beauty and voice, Geach immediately inquired of mutual friends whether she was ‘reliably Catholic.’ Upon learning that she was, he pursued her and, swiftly, their hearts were entangled.”
— John M. Dolan, Living the Truth
Christ plays in ten thousand places,
Lovely in limbs, and
lovely in eyes not his
To the Father through
the features of men’s faces.
— Gerard Manley Hopkins
Concluding reflections for Holy Thursday:
Truth, Beauty, and The Good
Art is magic delivered from
the lie of being truth.
— Theodor Adorno, Minima moralia,
London, New Left Books, 1974, p. 222
(First published in German in 1951.)
The director, Carol Reed, makes…
impeccable use of the beauty of black….
— V. B. Daniel on The Third Man
I see your ironical smile.
— Hans Reichenbach (see above)
Adorno, The Third Man, and Reichenbach
are illustrated below (l. to r.) above the names of cities with which they are associated.
In keeping with our transubstantiation theme, these three cities may be regarded as illustrating the remarks of Jimmy Buffett
on culinary theology.
Comments Off on Thursday April 8, 2004
Wednesday, February 18, 2004
Hard Core, Part II:
Star of Africa
In memory of St. Katharine Hepburn,
who died on St. Peter’s Day, 2003:
“Although the greater saints
are more acceptable to God
than the lesser,
it is sometimes profitable
to pray to the lesser.”
— St. Thomas Aquinas
From The Times, UK, Feb. 18, 2004:
Straw denies
a big-three takeover
at EU summit
Britain’s Foreign Secretary “said that there were no plans to set up a small body within the EU to take control of its affairs.
However, he told a news conference at the Foreign Office that it made sense for the three biggest economies to work ‘collaboratively’ on matters of common interest….
At tonight’s summit Mr Blair, Gerhard Schröder, the German Chancellor, and President Chirac of France will discuss initiatives to co-ordinate and strengthen the EU’s industrial policy….
German commentators regard the summit as a sea-change in British policy towards Europe — a signal that London’s main aim is no longer to split Paris and Berlin.”
Monday, February 9, 2004
Hermes and Folded Time
Yesterday’s entry on painter Ward Jackson and the philosopher Gadamer involved what is called hermeneutics, or the art of interpretation. Gadamer was a leader in this field. The following passage perhaps belabors the obvious, but it puts hermeneutics clearly in context.
From Daniel Chandler’s Semiotics for Beginners:
“The ‘tightness’ of semiotic codes themselves varies from the rule-bound closure of logical codes (such as computer codes) to the interpretative looseness of poetic codes. Pierre Guiraud notes that ‘signification is more or less codified,‘ and that some systems are so ‘open’ that they ‘scarcely merit the designation ‘code’ but are merely systems of “hermeneutic” interpretation’ (*Guiraud 1975, 24). Guiraud makes the distinction that a code is ‘a system of explicit social conventions’ whilst ‘a hermeneutics’ is ‘a system of implicit, latent and purely contingent signs,’ adding that ‘it is not that the latter are neither conventional nor social, but they are so in a looser, more obscure and often unconscious way’ (*ibid., 41). His claim that (formal) codes are ‘explicit’ seems untenable since few codes would be likely to be widely regarded as wholly explicit. He refers to two ‘levels of signification,’ but it may be more productive to refer to a descriptive spectrum based on relative explicitness, with technical codes veering towards one pole and interpretative practices veering towards the other. At one end of the spectrum are what Guiraud refers to as ‘explicit, socialized codes in which the meaning is a datum of the message as a result of a formal convention between participants’ (*ibid., 43-4). In such cases, he argues, ‘the code of a message is explicitly given by the sender’ (*ibid., 65). At the other end of the spectrum are ‘the individual and more or less implicit hermeneutics in which meaning is the result of an interpretation on the part of the receiver’ (*ibid., 43-4). Guiraud refers to interpretative practices as more ‘poetic,’ being ‘engendered by the receiver using a system or systems of implicit interpretation which, by virtue of usage, are more or less socialized and conventionalized’ (*ibid., 41). Later he adds that ‘a hermeneutics is a grid supplied by the receiver; a philosophical, aesthetic, or cultural grid which he applies to the text’ (*ibid., 65).”
* Pierre Guiraud, Semiology (trans. George Gross), London: Routledge & Kegan Paul, 1975
Related material:
From Michalinos Zembylas on Michel Serres:
“Serres’ use of Hermes is reminiscent of hermeneutics. The word derives from Hermes and implies that the idea of hermeneutics as a theory of interpretation (and consequently of communication) is necessary when there is a possibility for misunderstanding. Hermes translated the ‘word of Gods’; an interpreter translates the written text, and a teacher ‘translates’ the literature…. Understanding then is aided by the mediation of a hermeneut…. According to Gadamer (1975), the pleasure such understanding elicits is the joy of knowledge (which does not operate as an enchantment but as a kind of transformation). It is worth exploring this idea a bit more since there are interesting connections with Serres’ work.”
There is also an interesting connection with Guiraud’s work. As quoted above, Guiraud wrote that
“…a hermeneutics is a grid supplied by the receiver; a philosophical, aesthetic, or cultural grid which he applies to the text.”
Serres describes Hermes as passing through “folded time.” Precisely how time can be folded into a grid is the subject of my note The Grid of Time, which gives the context for the Serres phrase “folded time.”
For more on hermeneutics and Gadamer’s “joy of knowledge,” see Ian Lee in The Third Word War on “understanding the J.O.K.E.” (the Joy of Knowledge Encyclopedia).
Comments Off on Monday February 9, 2004
Wednesday, October 29, 2003
War of Ideas
US Defense Secretary Donald Rumsfeld recently declared a “war of ideas.”
Here is some background– notes made to help clarify my own thoughts.
Today, the 22nd “Socialist International Conference,” held every 4 years, concludes. This is a non-communist gathering of various countries’ Social Democratic parties. It has been called a gathering of “dinosaurs” (rather like the Democratic Party in the United States, or Tony Blair).
More relevant is the following history:
The First International
1864-1876
Founded in London, led by Karl Marx.
The Second International
1889-1914
Founded at a Paris congress, collapsed with the outbreak of World War I.
The Third International
1919-1939
Founded by the Russian revolution, also known as the Comintern. Said to have ended with the Hitler-Stalin nonaggression pact, officially dissolved in 1943. Succeeded by a Stalinist, hence non-international, organization.
The Fourth International
Founded by Trotsky in 1938. Ended in various splinter groups after World War II.
The Fifth International
In process of formation.
See Movement for a Socialist Future and
The Fifth International?.
Comments Off on Wednesday October 29, 2003
Tuesday, September 23, 2003
Intelligence Test
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At left: Reuters Offers IQ Test
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Today’s British Intelligence Award
goes to Reuters news agency:
Key Phrase Was Dropped from UK Iraq Dossier Tue September 23, 2003 12:33 PM ET By Katherine Baldwin and Janet McBride
LONDON (Reuters) – The British intelligence chief responsible for a pre-war dossier on Iraq’s weapons dropped a key sentence from it days before publication after prompting from Downing Street, an inquiry heard Tuesday.
He did it at the suggestion of Jonathan Powell, chief of staff to Prime Minister Tony Blair, the inquiry heard.
The offending sentence stated that former Iraqi President Saddam Hussein was prepared to use chemical and biological weapons “if he believes his regime is under threat.”
Powell argued that phrase suggested Iraq was only a threat if attacked.
The revelation that Powell ordered the sentence to be omitted raises fresh doubts over the intervention of Blair’s office in the compilation of the September dossier.
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Today’s British Stupidity Award goes,
of course, to Jonathan Powell.
Thursday, July 24, 2003
Intelligence Test
On July 17, my entry “British Intelligence” linked to a Guardian story about a bumbling amateur spy organization set up by the Bush administration. The headline of that entry, together with Tony Blair’s remark quoted there, implied that The Guardian was a much better example of real British intelligence than Blair’s minions.
On July 21, my entry “Meet D. B. Norton” attacked Blair as a puppet of media tycoon Rupert Murdoch.
Now The Guardian has come through with a story confirming the picture of puppetmaster Murdoch. See
For background on Rupert Murdoch, see
Murdoch’s Mean Machine
How Rupert uses his vast media power
to help himself and hammer his foes
in the Columbia Journalism Review
Edward Arnold portrays Rupert Murdoch
as he hears of
Wednesday’s 400-21 House vote
against media tycoons.
For more details, see
Congress Vote May Stymie Murdoch and
Scramble to Overturn House Media Bill.
Comments Off on Thursday July 24, 2003
Friday, July 18, 2003
Hideous Strength
On a Report from London:
Assuming rather prematurely that the body found in Oxfordshire today is that of David Kelly, Ministry of Defence germ-warfare expert and alleged leaker of information to the press, the Financial Times has the following:
“Mr Kelly’s death has stunned all the players involved in this drama, resembling as it does a fictitious political thriller.”
— Financial Times, July 18,
2003, 19:06 London time
I feel it resembles rather a fictitious religious thriller… Namely, That Hideous Strength, by C. S. Lewis. The use of the word “idea” in my entries’ headlines yesterday was not accidental. It is related to an occurrence of the word in Understanding: On Death and Truth, a set of journal entries from May 9-12. The relevant passage on “ideas” is quoted there, within commentary by an Oberlin professor:
“That the truth we understand must be a truth we stand under is brought out nicely in C. S. Lewis’ That Hideous Strength when Mark Studdock gradually learns what an ‘Idea’ is. While Frost attempts to give Mark a ‘training in objectivity’ that will destroy in him any natural moral sense, and while Mark tries desperately to find a way out of the moral void into which he is being drawn, he discovers what it means to under-stand.
‘He had never before known what an Idea meant: he had always thought till now that they were things inside one’s own head. But now, when his head was continually attacked and often completely filled with the clinging corruption of the training, this Idea towered up above him-something which obviously existed quite independently of himself and had hard rock surfaces which would not give, surfaces he could cling to.’
This too, I fear, is seldom communicated in the classroom, where opinion reigns supreme. But it has important implications for the way we understand argument.”
— “On Bringing One’s Life to a Point,” by Gilbert Meilaender, First Things, November 1994
The old philosophical conflict between realism and nominalism can, it seems, have life-and-death consequences. I prefer Plato’s realism, with its “ideas,” such as the idea of seven-ness. A reductio ad absurdum of nominalism may be found in the Stanford Encyclopedia of Philosophy under Realism:
“A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false….”
The claim that 7 is not prime is, regardless of its motives, dangerously stupid… A quality shared, it seems, by many in power these days.
Comments Off on Friday July 18, 2003
Saturday, July 12, 2003
Before and After
From Understanding the (Net) Wake:
24
A.
“Its importance in establishing the identities in the writer complexus….will be best appreciated by never forgetting that both before and after the Battle of the Boyne it was a habit not to sign letters always.”(114)
Joyce shows an understanding of the problems that an intertextual book like the Wake poses for the notion of authorship.
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G. H. Hardy in A Mathematician’s Apology:
“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases,’ indeed, is one of the duller forms of mathematical argument. A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.
A chess problem also has unexpectedness, and a certain economy; it is essential that the moves should be surprising, and that every piece on the board should play its part. But the aesthetic effect is cumulative. It is essential also (unless the problem is too simple to be really amusing) that the key-move should be followed by a good many variations, each requiring its own individual answer. ‘If P-B5 then Kt-R6; if …. then …. ; if …. then ….’ — the effect would be spoilt if there were not a good many different replies. All this is quite genuine mathematics, and has its merits; but it just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly*) which a real mathematician tends to despise.
* I believe that is now regarded as a merit in a problem that there should be many variations of the same type.”
(Cambridge at the University Press. First edition, 1940.)
Brian Harley in Mate in Two Moves:
“It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver’s banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be.”
(London, Bell & Sons. First edition, 1931.)
Comments Off on Saturday July 12, 2003
Tuesday, July 1, 2003
Jew’s on First
This entry is dedicated to those worshippers of Allah who have at one time or another cried
“Itbah al-Yahud!” … Kill the Jew!
(See June 29 entries).
Dead at 78
Comedian Buddy Hackett died on Tuesday, July First, 2003, according to the New York Times. According to Bloomberg.com, he died Sunday or Monday. |
Associated Press
Buddy Hackett,
on the set of
“It’s a Mad, Mad,
Mad, Mad World”
in 1962. |
Whatever. We may imagine he has now walked, leading a parade of many other stand-up saints, into a bar. |
Hepburn at Chaillot
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MIDRASH
for Buddy Hackett
From my May 25 entry,
Matrix of the Death God:
R. M. Abraham’s Diversions and Pastimes, published by Constable and Company, London, in 1933, has the following magic square:
The Matrix of Abraham
A summary of the religious import of the above from Princeton University Press:
“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah. Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”
— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72
Other appearances of this religious icon on the Web include:
On Linguistic Creation
Picasso’s Birthday
1991 Yearbook
Rolling Stone
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Hackett
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In the Picasso’s Birthday version, 22 of the 25 magic square cells are correlated with pictures on the “Class of ’91” cover of Rolling Stone magazine. Number 7 is Rod† Stewart. In accordance with the theological rhyme “Seven is heaven, eight is a gate,” our site music for today is “Forever Young,” a tune made famous by Stewart.
† Roderick, actually — the name of the hero in “Madwoman of Chaillot”
Comments Off on Tuesday July 1, 2003
Monday, May 26, 2003
Mental Health Month, Day 26:
Many Dimensions,
Part III — Why 26?
At first blush, it seems unlikely that the number 26=2×13, as a product of only two small primes (and those distinct) has any purely mathematical properties of interest. (On the other hand, consider the number 6.) Parts I and II of “Many Dimensions,” notes written earlier today, deal with the struggles of string theorists to justify their contention that a space of 26 dimensions may have some significance in physics. Let them struggle. My question is whether there are any interesting purely mathematical properties of 26, and it turns out, surprisingly, that there are some such properties. All this is a longwinded way of introducing a link to the web page titled “Info on M13,” which gives details of a 1997 paper by J. H. Conway*.
Info on M13
“Conway describes the beautiful construction of a discrete mathematical structure which he calls ‘M13.’ This structure is a set of 1,235,520 permutations of 13 letters. It is not a group. However, this structure represents the answer to the following group theoretic question:
Why do the simple groups M12 and L3(3) share some subgroup structure?
In fact, both the Mathieu group M12 and the automorphism group L3(3) of the projective plane PG(2,3) over GF(3) can be found as subsets of M13. In addition, M13 is 6-fold transitive, in the sense that it contains enough permutations to map any two 6-tuples made from the thirteen letters into each other. In this sense, M13 could pass as a parent for both M12 and L3(3). As it is known from the classification of primitive groups that there is no finite group which qualifies as a parent in this sense. Yet, M13 comes close to being a group.
To understand the definition of M13 let us have a look at the projective geometry PG(2,3)….
The points and the lines and the “is-contained-in” relation form an incidence structure over PG(2,3)….
…the 26 objects of the incidence structure [are] 13 points and 13 lines.”
Conway’s construction involves the arrangement, in a circular Levi graph, of 26 marks representing these points and lines, and chords representing the “contains/is contained in” relation. The resulting diagram has a pleasingly symmetric appearance.
For further information on the geometry of the number 26, one can look up all primitive permutation groups of degree 26. Conway’s work suggests we look at sets (not just groups) of permutations on n elements. He has shown that this is a fruitful approach for n=13. Whether it may also be fruitful for n=26, I do not know.
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There is no obvious connection to physics, although the physics writer John Baez quoted in my previous two entries shares Conway’s interest in the Mathieu groups.
* J. H. Conway, “M13,” in Surveys in Combinatorics, 1997, edited by R. A. Bailey, London Mathematical Society Lecture Note Series, 241, Cambridge University Press, Cambridge, 1997. 338 pp. ISBN 0 521 59840 0.
Comments Off on Monday May 26, 2003
Sunday, May 25, 2003
— ART WARS —
Mental Health Month, Day 25:
Matrix of the Death God
Having dealt yesterday with the Death Goddess Sarah, we turn today to the Death God Abraham. (See Jacques Derrida, The Gift of Death, University of Chicago Press, 1996.) For a lengthy list of pictures of this damned homicidal lunatic about to murder his son, see The Text This Week.
See, too, The Matrix of Abraham, illustrated below. This is taken from a book by R. M. Abraham, Diversions and Pastimes, published by Constable and Company, London, in 1933.
The Matrix of Abraham
A summary of the religious import of the above from Princeton University Press:
“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah. Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”
— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72
Other appearances of this religious icon on the Web:
On Linguistic Creation
Picasso’s Birthday
A less religious approach to the icon may be found on page 393 of R. D. Carmichael’s Introduction to the Theory of Groups of Finite Order (Ginn, Boston, 1937, reprinted by Dover, 1956).
This matrix did not originate with Abraham but, unlike Neo, I have not yet found its Architect.
Friday, May 23, 2003
Mental Health Month, Day 23:
The Prime Cut Gospel
On Christmas Day, 1949,
Mary Elizabeth Spacek was born in Texas.
Lee Marvin, Sissy Spacek in “Prime Cut”
Exercises for Mental Health Month:
Read this discussion of the phrase, suggested by Spacek’s date of birth, “God’s gift to men.”
Read this discussion of the phrase “the same yesterday, today, and forever,” suggested by the previous reading.
Read the more interesting of these discussions of the phrase “the eternal in the temporal.”
Read this discussion of eternal, or “necessary,” truths versus other sorts of alleged “truths.”
Read this discussion of unimportant mathematical properties of the prime number 23.
Read these discussions of important properties of 23:
- R. D. Carmichael’s 1937 discussion of the linear fractional group modulo 23 in
Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937 (reprinted by Dover in 1956), final chapter, “Tactical Configurations,” and
- Conway’s 1969 discussion of the same group in
J. H. Conway, “Three Lectures on Exceptional Groups,” pp. 215-247 in Finite Simple Groups (Oxford, 1969), edited by M. B. Powell and G. Higman, Academic Press, London, 1971….. Reprinted as Ch. 10 in Sphere Packings, Lattices, and Groups
Read this discussion of what might be called “contingent,” or “literary,” properties of the number 23.
Read also the more interesting of these discussions of the phrase “the 23 enigma.”
Having thus acquired some familiarity with both contingent and necessary properties of 23…
Read this discussion of Aquinas’s third proof of the existence of God.
Note that the classic Spacek film “Prime Cut” was released in 1972, the year that Spacek turned 23:
Essay question:
If Jesus was God’s gift to man, and (as many men would agree) so was the young Sissy Spacek (also born on Christmas Day), was young Sissy’s existence in her 23rd year contingent or necessary? If the latter, should she be recognized as a Person of the Trinity? Quaternity? N-ity?
Talk amongst yourselves.
Comments Off on Friday May 23, 2003
Sunday, February 9, 2003
Messe
Yesterday's entry, "Requiem for a Queen," suggested a certain resemblance between the Jedburgh death mask of Mary Queen of Scots and the face of actress Vivien Leigh. The following links are related to this resemblance.
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The first great stage success of Miss Leigh was in a play called "
The Mask of Virtue," which opened on May 15, 1935.
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Leigh was
educated for eight years at the Convent of the Sacred Heart in Roehampton.
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A
requiem mass for Miss Leigh
was held at the Roman Catholic Church of St. Mary's, Cadogan Street, London, on 12th July 1967, at 10 o'clock. On the coffin were her favorite white roses, picked from her garden at Tickerage Mill in Sussex.
Yesterday's site music, "The Water is Wide," was suggested by T. S. Eliot's language in Four Quartets. Whether Eliot's use of the motto of the Catholic queen Mary Stuart, "In my end is my beginning," was meant as a tribute to that monarch is debatable. As one web forum entry points out, the motto "Ma fin est ma [sic] commencement" is the title of a rondeau by Guillaume de Machaut written some two centuries earlier, and Eliot may have taken his motto from Machaut rather than Mary. Some evidence for this is provided by the lyrics for Machaut's rondeau, which include Eliot's phrase "in my beginning is my end" as well as the reversed version. At any rate, Machaut and Eliot share an interest in four-part compositions — as do I and as did, apparently, the compilers of the Gospels.
A search on the phrase Machaut Eliot "four part" yields an essay that to me seems like rainbow's-end gold:
ON TIME, ORIGINALITY, AND THE ART OF
MUSICAL COMPOSITION
by Joseph Dillon Ford
In honor of Ford, Eliot, Machaut, Leigh, and Stuart, today's site music is the "Kyrie" from Machaut's "Messe de Notre Dame."
Comments Off on Sunday February 9, 2003
Tuesday, January 7, 2003
Song of Bernadette
BROADWAY BABY!
In memory of Broadway’s Jean Kerr —
Recall the ending of the classic film “Michael.”
See also this review of a Bernadette Peters concert:
“Then comes the moment that you have been secretly waiting for all of your life and whisks you away to the other universe, where everyone is singing happy show-tunes and appreciating the good life. Has some religious leader taken over my life or what? No, nothing like that… I just attended the first ever London concert performance of Bernadette Peters at the Royal Festival Hall….
… Broadway Baby simply brought the house down for the first time.”
I’m just a Broad-way Ba-by,
walk-ing off my ti-red feet,
Pound-ing For-ty Sec-ond Street,
to be in a show.
Broad-way Ba-by,
Learn-ing how to sing and dance,
Wait-ing for that one big chance
to be in a show.
Gee, I’d like to be
On some mar-quee,
All twink-ling lights,
A spark to pierce the dark
from Bat-t’ry Park
to Wash – ing-ton Heights.
Some day may-be,
All my dreams will be re-paid.
Comments Off on Tuesday January 7, 2003
Saturday, January 4, 2003
ART WARS:
The Reader
Over Your Shoulder
See also last night’s entry on “Red Dragon” and
this news story on a Chinese cannibal-artist
from today’s Toronto Globe and Mail.
Comments Off on Saturday January 4, 2003
Monday, December 30, 2002
Homer
“No matter how it’s done, you won’t like it.”
— Robert Redford to Robert M. Pirsig in Lila
“The evening before Harriet injures Roy,
she asks him, in a restaurant car,
whether he has read Homer.”
— Oxford website on the film of The Natural
“Brush Up Your Shakespeare”
— Cole Porter lyric for a show that opened
on December 30, 1948
Judy Davis as Harriet Bird
Thine eyes I love…
Shakespeare, Sonnet 132
“Roy’s Guenevere-like lover is named Memo Paris,
presumably the face that launched a thousand strikes.”
— Oxford website on the film of The Natural
Nicole Kidman
as Memo Paris
“Iris is someone to watch over Roy.”
— Oxford website on the film of The Natural
Kate Winslet as young Iris Murdoch
From the second-draft screenplay
for The Sting,
with Robert Redford as Hooker:
HOOKER
(shuffling a little)
I, ah…thought you might wanna come out for a while. Maybe have a drink or somethin’.
LORETTA
You move right along, don’t ya.
HOOKER
(with more innocence than confidence)
I don’t mean nothin’ by it. I just don’t know many regular girls, that’s all.
LORETTA
And you expect me to come over, just like that.
HOOKER
If I expected somethin’, I wouldn’t be still standin’ out here in the hall.
Loretta looks at him carefully. She knows it’s not a line.
LORETTA
(with less resistance now)
I don’t even know you.
HOOKER
(slowly)
You know me. I’m just like you…
It’s two in the morning and I don’t know nobody.
The two just stand there in silence a second. There’s nothing more to say. She stands back and lets him in.
Iris Murdoch on Plato’s Form of the Good,
by Joseph Malikail:
“For Murdoch as for Plato, the Good belongs to Plato’s Realm of Being not the Realm of Becoming…. However, Murdoch does not read Plato as declaring his faith in a divine being when he says that the Good is
the universal author of all things beautiful and right, parent of light and the lord of light in the visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which [one who] would act rationally either in public or private life must have his eyes fixed (Republic…).
Though she acknowledges the influence of Simone Weil in her reading of Plato, her understanding of Plato on Good and God is not Weil’s (1952, ch.7)*. For Murdoch,
Plato never identified his Form of the Good with God (the use of theos in the Republic… is a façon de parler), and this separation is for him an essential one. Religion is above the level of the ‘gods.’ There are no gods and no God either. Neo-Platonic thinkers made the identification (of God with good) possible; and the Judaeo-Christian tradition has made it easy and natural for us to gather together the aesthetic and consoling impression of Good as a person (1992, 38)**.
As she understands Plato:
The Form of the Good as creative power is not a Book of Genesis creator ex nihilo … Plato does not set up the Form of the Good as God, this would be absolutely un-Platonic, nor does he anywhere give the sign of missing or needing a real God to assist his explanations. On the contrary, Good is above the level of the gods or God (ibid., 475)**.
Mary Warnock, her friend and fellow-philosopher, sums up Murdoch’s metaphysical view of the Vision of the Good:
She [Murdoch] holds that goodness has a real though abstract existence in the world. The actual existence of goodness is, in her view, the way it is now possible to understand the idea of God.
Or as Murdoch herself puts it, ‘Good represents the reality of which God is the dream.’ (1992, 496)**”
*Weil, Simone. 1952. Intimations of Christianity Among The Ancient Greeks. Ark Paperbacks, 1987/1952.
**Murdoch, Iris. 1992. Metaphysics As A Guide To Morals. London: Chatto and Windus.
From the conclusion of Lila,
by Robert M. Pirsig:
“Good is a noun. That was it. That was what Phaedrus had been looking for. That was the homer over the fence that ended the ballgame.”
Comments Off on Monday December 30, 2002
Friday, December 27, 2002
Another Opening of Another Show
"To die will be an awfully big adventure."
— Peter Pan
in "An Awfully
Big Adventure"
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On this date in 1904, "Peter Pan" opened to great applause at the Duke of York's theatre in London. A cinematic sequel, "An Awfully Big Adventure," is illustrated at left and below. I have always felt this film's soundtrack should include the classic Mac Davis song "Girl, you're a hot-blooded woman-child…."
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Comments Off on Friday December 27, 2002
Friday, December 6, 2002
Great Simplicity
Today
is the day that Daisetsu Suzuki attained satori,
according to the Zen Calendar. “Daisetsu” is
said to mean “Great Simplicity.”
For those who prefer Harry Potter and
Diagon Alley, here is another calendar:
To Have and Have Not
Those who prefer traditional Western religions may like a site on the Trinity that contains this:
“Zen metaphysics is perhaps most succinctly set forth in the words ‘not-two.” But even when he uses this expression, Suzuki is quick to assert that it implies no monism. Not-two, it is claimed, is not the same as one.* But when Suzuki discusses the relationship of Zen with Western mysticism, it is more difficult to escape the obvious monistic implications of his thinking. Consider the following:
We are possessed of the habit of looking at Reality by dividing it into two… It is all due to the human habit of splitting one solid Reality into two, and the result is that my ‘have’ is no ‘have’ and my ‘have not’ is no ‘have not.’ While we are actually passing, we insist that the gap is impassable.**”
*See: Daisetz T. Suzuki, ‘Basic Thoughts Underlying Eastern Ethical and Social Practice’ in Philosophy and Culture — East and West: East-West Philosophy in Practical Perspective, ed. Charles A. Moore (Honolulu: University of Hawaii Press, 1968), p. 429
** Daisetsu Teitaro Suzuki, Mysticism Christian and Buddhist (London: George Allen & Unwin, 1957, Unwin paperback, 1979), p. 57.
Personally, I am reminded by Suzuki’s satori on this date that today is the eve of the anniversary of Pearl Harbor. I am also reminded by the rather intolerant tract on the Trinity quoted above that the first atomic bomb was exploded in the New Mexico desert at a test site named Trinity. Of course, sometimes intolerance is justified.
Concluding unscientific postscript:
On the same day in 1896 that D. T. Suzuki attained satori,
lyricist Ira Gershwin was born.
Dies irae, dies illa.
Comments Off on Friday December 6, 2002
Friday, November 22, 2002
MAYA
Jack London died on this date. On the other hand, Hoagy Carmichael, Jamie Lee Curtis, and Mariel Hemingway were born.
Comments Off on Friday November 22, 2002
Friday, October 18, 2002
Readings for the Oct. 18
Feast of St. Luke
A fellow Xangan is undergoing a spiritual crisis. Well-meaning friends are urging upon her all sorts of advice. The following is my best effort at religious counsel, meant more for the friends than for the woman in crisis.
Part I… Wallace Stevens
From Brewer’s Dictionary of Phrase and Fable:
Ox Emblematic of St. Luke. It is one of the four figures which made up Ezekiel’s cherub (i. 10). The ox is the emblem of the priesthood….
The dumb ox. St. Thomas Aquinas; so named by his fellow students at Cologne, on account of his dulness and taciturnity. (1224-1274.)
Albertus said, “We call him the dumb ox, but he will give one day such a bellow as shall be heard from one end of the world to the other.” (Alban Butler.)
From Wallace Stevens, “The Latest Freed Man“:
It was how the sun came shining into his room:
To be without a description of to be,
For a moment on rising, at the edge of the bed, to be,
To have the ant of the self changed to an ox
With its organic boomings, to be changed
From a doctor into an ox, before standing up,
To know that the change and that the ox-like struggle
Come from the strength that is the strength of the sun,
Whether it comes directly or from the sun.
It was how he was free. It was how his freedom came.
It was being without description, being an ox.
Part II… The Rosy Cross
Readings:
Part III… Stevens Again
A major critical work on Wallace Stevens that is not unrelated to the above three works on the Rosicrucian tradition:
Leonora Woodman, Stanza My Stone: Wallace Stevens and the Hermetic Tradition, West Lafayette, Indiana: Purdue University Press, 1983
From the Department of English, Purdue University:
Leonora Woodman came to Purdue in 1976. In 1979, she became Director of Composition, a position she held until 1986…. At the time of her death in 1991, she was in the midst of an important work on modernist poetry, Literary Modernism and the Fourth Dimension: The Visionary Poetics of D.H. Lawrence, H.D., and Hart Crane.
For more on Gnostic Christianity, see
- Elaine Pagels, The Gnostic Gospels (Random House, 1979), and
- Harold Bloom, Omens of Millenium: The Gnosis of Angels, Dreams, and Resurrection (Riverhead Books, 1996).
Wednesday, October 9, 2002
To Apollo
On this date in 28 B.C. the Temple of Apollo
was dedicated on the Palatine Hill in Rome.
Horace, Odes, XXXI
Frui paratis et valido mihi,
Latoe, dones et precor integra
Cum mente nec turpem senectam
Degere nec cithara carentem.
O grant me, Phoebus, calm content,
Strength unimpaird, a mind entire,
Old age without dishonour spent,
Nor unbefriended by the lyre!
— The Odes and Carmen Saeculare of Horace,
John Conington, translator.
London, George Bell and Sons, 1882.
Representations of Apollo:
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See also
The Angel in the Stone
"Everything is found
and lost and buried
and then found again"
— Tanya Wendling
Comments Off on Wednesday October 9, 2002
Friday, September 13, 2002
Meditation for Friday the 13th
The 1946 British film below (released as “Stairway to Heaven” in the U.S.) is one of my favorites. I saw it as a child. Since costar Kim Hunter died this week (on 9/11), and since today is Friday the 13th, the following material seems relevant.
Kim Hunter in 1946
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R.A.F pilot and psychiatrist
Alan McGlashan
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Alan McGlashan has practiced as a psychiatrist in London for more than forty years. He also served as a pilot for the R.A.F. (with MC and Croix de Guerre decorations).
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The doctor in “A Matter of Life and Death” addresses a heavenly court on behalf of his patient, R.A.F pilot David Niven:
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In the film, David Niven is saved by mistake from a fated death and his doctor must argue to a heavenly court that he be allowed to live. |
In a similar situation, I would want Dr. Alan McGlashan, a real-life psychiatrist, on my side. For an excerpt from one of my favorite books, McGlashan’s The Savage and Beautiful Country,
click here.
As Walker Percy has observed (see my Sept. 7 note, “The Boys from Uruguay”), a characteristic activity of human beings is what Percy called “symbol-mongering.” In honor of today’s anniversary of the births of two R.A.F. fighter pilots,
Sir Peter Guy Wykeham-Barnes (b. 1915) and author
Roald Dahl (b. 1916),
here is one of the better symbols of the past century:
The circle is of course a universal symbol, and can be made to mean just about whatever one wants it to mean. In keeping with Clint Eastwood’s advice, in the soundtrack album for “Midnight in the Garden of Good and Evil,” to “accentuate the positive,” here are some positive observations on a circle from the poet (and perhaps saint) Dante, who died on the night of September 13-14:
In the sun, Dante and Beatrice find themselves surrounded by a circle of souls famous for their wisdom on earth. They appear as splendid lights and precious jewels who dance and sing as they lovingly welcome two more into their company. Their love for God is kindled even more and grows as they find more individuals to love. Among the blessed souls are St. Thomas Aquinas and one of his intellectual “enemies”, Siger of Brabant, a brilliant philosopher at the University of Paris, some of whose teachings were condemned as heretical. Conflicts and divisions on earth are now forgotten and absorbed into a communal love song and dance “whose sweetness and harmony are unknown on earth and whose joy becomes one with eternity.”
Dante compares their dance and song to God’s bride on earth, the Church, when she answers the morning bells to rise from bed and “woo with matins song her Bridegroom’s love.” Some critics consider this passage the most “spiritually erotic” of all the one hundred cantos of the Comedy. It is the ending of Canto 10, verses 139-148.
— Fr. James J. Collins, “The Spiritual Journey with Dante V,” Priestly People October 1997
The above material on Dante is from the Servants of the Paraclete website.
For more on the Paraclete, see
The Left Hand of God.
See also the illustration in the note below.
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Saturday, August 31, 2002
Today’s birthday: Dr. Maria Montessori
THE MONTESSORI METHOD: CHAPTER VI
HOW LESSONS SHOULD BE GIVEN
“Let all thy words be counted.”
Dante, Inf., canto X.
CONCISENESS, SIMPLICITY, OBJECTIVITY.
…Dante gives excellent advice to teachers when he says, “Let thy words be counted.” The more carefully we cut away useless words, the more perfect will become the lesson….
Another characteristic quality of the lesson… is its simplicity. It must be stripped of all that is not absolute truth…. The carefully chosen words must be the most simple it is possible to find, and must refer to the truth.
The third quality of the lesson is its objectivity. The lesson must be presented in such a way that the personality of the teacher shall disappear. There shall remain in evidence only the object to which she wishes to call the attention of the child….
Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale “block design” subtest.
Mathematicians mean something different by the phrase “block design.”
A University of London site on mathematical design theory includes a link to my diamond theory site, which discusses the mathematics of the sorts of visual designs that Professor Pope is demonstrating. For an introduction to the subject that is, I hope, concise, simple, and objective, see my diamond 16 puzzle.
Comments Off on Saturday August 31, 2002
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