Thursday, April 30, 2009
Wednesday, April 29, 2009
WW meets AA
Click on images for details.
Tuesday, April 28, 2009
The above symbol
does not stand for
Noah: Jenny, what's troubling you?
Jenny: Sigh. I was reading this book, but the words stopped in mid-sentence at the bottom! What… what do I do, Noah?
Noah: Turn the page.
Falls in love amidst turmoil.
The King and the Corpse, pp. 265-266:
"… the goddess at last bodily appeared to him, dark and slender, hair hanging free, and standing on the back of her tawny lion. He gave her greeting. And Kali, 'The Dark One,' addressed him with the voice of a
THE KING AND THE CORPSE
cloud of thunder: 'For what reason have you called? Make known your wish. Though it were unattainable, my appearance would guarantee its fulfillment.'"
United States Air Force.
Monday, April 27, 2009
with Julie Taymor
“On the producer side,
you may be working with
people you did not
hand-pick. Do the research.”
— Julie Taymor
— First of all we are in the country now, so no more black.
— No more black? Are you insane?
— You heard me. Only high-powered, neurotic, castrating, Manhattan career bitches wear black. Is that what you want to be?
— Ever since I was a little girl.
— Dialogue from remake of The Stepford Wives
Sunday, April 26, 2009
Saturday, April 25, 2009
by John Tierney
"Russell Crowe arrives at the Hotel Infinity looking tired and ornery. He demands a room. The clerk informs him that there are no vacancies…."
Footprints from California today
(all by a person or persons using Firefox browsers):
Concepts of Space: Euclid vs. Galois
Art Wars continued: Behind the Picture
A Riff for Dave: Me and My Shadow
A Death of Kings: In Memory of Bobby Fischer
Art Wars in review– Through the Looking Glass: A Sort of Eternity
3:28 PM and
Annals of Philosophy: The Dormouse of Perception
Epiphany for Roy, Part I
At the Still Point: All That Jazz
Where Entertainment is Not God: The Just Word
Happy New Yorker Day– Class Galore
The Politics of Change: Jumpers
"We are programmed to receive."
— Hotel California
Mathematics and Autism.
Welcome to the
Black Hole Café
"Our lifelong friendship made me not only an admirer of the depth, scholarship, and sheer energy of his mathematical work (and of his ceaseless activities as an editorial entrepreneur on behalf of mathematics) but one in awe of his status as the ultimate relaxed sophisticate."
by Alfred Bester
Friday, April 24, 2009
“Anakin Skywalker, otherwise known
as Darth Vader, is arguably
the central character in
George Lucas’s ‘Star Wars’….“
“Annakin’s last name
was the source
of the name for
“Contrary to previous reports that George Lucas named the ‘Star Wars’ character Anakin Skywalker (Darth Vader) after Annakin, Lucas said via his publicist Thursday that he did not.”
“Annakin inadvertently gave his own name to a film character, although the spelling is slightly different, when the actor Alec Guinness suggested the name to director George Lucas for a character in the Star Wars films.
At a screening of the film, Annakin asked Lucas about it.
‘He was running his picture with Anakin Skywalker in it, and I went over to him and said, “you know, you never got permission for this.” He said, “but I dropped an ‘n’ and therefore I got away with it,”‘ Annakin said.”
This morning’s NY Times
Passage O soul to India!
Eclaircise the myths Asiatic,
the primitive fables.
Not you alone proud truths of the world,
Nor you alone ye facts of modern science,
But myths and fables of eld,
Asia’s, Africa’s fables,
The far-darting beams of the spirit,
the unloos’d dreams,
The deep diving bibles and legends….
Thursday, April 23, 2009
“Timothy J. Holst, who joined the Ringling Brothers and Barnum & Bailey Circus as a lowly Keystone Kops clown, rose to the role of singing ringmaster, and ultimately became the show’s talent czar, died April 16 in São Paulo, Brazil, during a visit to sign up circus acts. He was 61.”
Sunday, April 19, 2009
Truth and Style)
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
The Crimson Passion
and the following
The Harvard Jesus
Crimson/Nancy K. Dutton
Friday, April 17, 2009
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.
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....
- Yesterday’s entry on Giordano Bruno and the Geometry of Language
- James Joyce and Heraldry
- “One might say that he [Joyce] invented a non-Euclidean geometry of language; and that he worked over it with doggedness and devotion….” —Unsigned notice in The New Republic, 20 January 1941
- Joyce’s “collideorscape” (scroll down for a citation)
- “A Hanukkah Tale” (Log24, Dec. 22, 2008)
- Stevens’s phrase from “An Ordinary Evening in New Haven” (Canto XXV)—
Some further context:
Thursday, April 16, 2009
Monday, April 13, 2009
Sunday, April 12, 2009
Is God, continued
Dialogue from the classic film Forbidden Planet—
“… Which makes it a gilt-edged priority that one of us gets into that Krell lab and takes that brain boost.”
(Cf. this journal on that date.)
Thanks to Professor Lavery for his detailed notes on his viewing experiences.
My own viewing recently included, on the night of Good Friday, April 10, the spiritually significant film Indiana Jones and the Kingdom of the Crystal Skull.
The mystic circle of 13 aliens at the end of that film, together with Leslie Nielsen’s Forbidden Planet remark quoted above, suggests the following:
“The aim of Conway’s game M13 is to get the hole at the top point and all counters in order 1,2,…,12 when moving clockwise along the circle.” —Lieven Le Bruyn
The illustration is from the weblog entry by Lieven Le Bruyn quoted below. The colored circles represent 12 of the 13 projective points described below, the 13 radial strokes represent the 13 projective lines, and the straight lines in the picture, including those that form the circle, describe which projective points are incident with which projective lines. The dot at top represents the “hole.”
“Let P3 denote the projective plane of order 3. The standard construction of P3 is to remove the zero point from a three-dimensional vector space over the field F3 and then identify each point x with -x, obtaining a space with
Conway  proposed the following game…. Place twelve numbered counters on the points… of P3 and leave the thirteenth point… blank. (The empty point will be referred to throughout as the “hole.”) Let the location of the hole be p; then a primitive move of the game consists of selecting one of the lines containing the hole, say
There is an obvious characterization of a move as a permutation in S13, operating on the points of P3. By limiting our consideration to only those moves which return the hole to its starting point…. we obtain the Conway game group. This group, which we shall denote by GC, is a subgroup of the symmetric group S12 of permutations of the twelve points…, and the group operation of GC is concatenation of paths. Conway  stated, but did not prove explicitly, that GC is isomorphic to the Mathieu group M12. We shall subsequently verify this isomorphism.
The set of all moves (including those not fixing the hole) is given the name M13 by Conway. It is important that M13 is not a group….”
 John H. Conway, “Graphs and Groups and M13,” Notes from New York Graph Theory Day XIV (1987), pp. 18–29.
Another exposition (adapted to Martin’s notation) by Lieven le Bruyn (see illustration above):
“Conway’s puzzle M13 involves the 13 points and 13 lines of P3. On all but one point numbered counters are placed holding the numbers 1,…,12 and a move involves interchanging one counter and the ‘hole’ (the unique point having no counter) and interchanging the counters on the two other points of the line determined by the first two points. In the picture [above] the lines are represented by dashes around the circle in between two counters and the points lying on this line are those that connect to the dash either via a direct line or directly via the circle. In the first part we saw that the group of all reachable positions in Conway’s M13 puzzle having the hole at the top position contains the sporadic simple Mathieu group M12 as a subgroup.”
For the religious significance of the circle of 13 (and the “hole”), consider Arthur and the 12 knights of the round table, et cetera.
From a professor’s weblog:
Saturday, April 11, 2009
“The novel should not be in any hurry. Once, hurry belonged to its sphere, now the film has taken that over; measured by the film, the hasty novel must always remain inadequate. The novel, as a creature of calmer times, may carry something of that old calm into our new hastiness. It could serve many people as slow-motion; it could induce them to tarry; it could replace the empty meditations of their cults.”
–Elias Canetti, The Human Province
Posted by David Lavery at 1:00 AM
Saturday, April 11, 2009
Friday, April 10, 2009
“There is a pleasantly discursive
treatment of Pontius Pilate’s
‘What is truth?’.”
— H. S. M. Coxeter, 1987,
introduction to Trudeau’s
remarks on the “Story Theory“
of truth as opposed to the
“Diamond Theory” of truth in
The Non-Euclidean Revolution
E. G. Beltrametti, “Can a finite geometry describe physical space-time?” Universita degli studi di Perugia, Atti del convegno di geometria combinatoria e sue applicazioni, Perugia 1971, 57–62.
“Can a finite geometry describe physical space?”
“Yes. Vide ‘The Eightfold Cube.'”
Thursday, April 9, 2009
“What wine does one drink?
What bread does one eat?”
Nature morte à l’échiquier
(les cinq sens),
“vers 1655, une narration
à valeur symbolique…”
Huile sur bois, 73 x 55 cm
Musée du Louvre, Paris
Wednesday, April 8, 2009
“For every kind of vampire,
there is a kind of cross.”
— Thomas Pynchon in
“Since 1963, when Pynchon’s first novel, V., came out, the writer– widely considered America’s most important novelist since World War II– has become an almost mythical figure,
(Click on images for their
source in past entries.)
“Plato’s Ghost evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”
— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics (by Jeremy Gray, September 2008)
“She’s a brick house…”
— Plato’s Ghost according to
Log24, April 2007
“First of all, I’d like
to thank the Academy.”
— Remark attributed to Plato
Irving John "I.J." Good died Sunday, April 5, 2009.
Information from Wikipedia:
"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.
Wikipedia states that "I. J. Good's vanity car license plate, hinting at his spylike wartime work, was
- 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."
"Some say the symbol
of Apple Computers,
the apple with a bite out of it,
is a nod to Alan Turing."
Tuesday, April 7, 2009
Bright Star and Dark Lady
“Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child.”
— Octavio Paz,
The same story on
May 11, 2005
with a different
Sunday, April 5, 2009
About the People:
Race to Witch Mountain
"George Bernard Shaw once wrote, 'Some people see things as they are and say why? I dream things that never were and say, why not?'"
— Robert Kennedy, University of Kansas, March 18, 1968
George Bernard Shaw:
THE SNAKE. I can talk of many things. I am very wise. It was I who whispered the word to you that you did not know. Dead. Death. Die.
EVE [shuddering] Why do you remind me of it? I forgot it when I saw your beautiful hood. You must not remind me of unhappy things.
THE SERPENT. Death is not an unhappy thing when you have learnt how to conquer it.
EVE. How can I conquer it?
THE SERPENT. By another thing, called birth.
EVE. What? [Trying to pronounce it] B-birth?
THE SERPENT. Yes, birth.
EVE. What is birth?
THE SERPENT. The serpent never dies. Some day you shall see me come out of this beautiful skin, a new snake with a new and lovelier skin. That is birth.
EVE. I have seen that. It is wonderful.
THE SERPENT. If I can do that, what can I not do? I tell you I am very subtle. When you and Adam talk, I hear you say 'Why?' Always 'Why?' You see things; and you say 'Why?' But I dream things that never were; and I say 'Why not?' I made the word dead to describe my old skin that I cast when I am renewed. I call that renewal being born.
EVE. Born is a beautiful word.
THE SERPENT. Why not be born again and again as I am, new and beautiful every time?
EVE. I! It does not happen: that is why.
THE SERPENT. That is how; but it is not why. Why not?
EVE. But I should not like it. It would be nice to be new again; but my old skin would lie on the ground looking just like me; and Adam would see it shrivel up and–
THE SERPENT. No. He need not. There is a second birth.
EVE. A second birth?
THE SERPENT. Listen. I will tell you a great secret….
Saturday, April 4, 2009
“As you read,
watch for patterns.”
"… in some autistic enchantment, pure as one of Bach's inverted canons or Euler's formula for polyhedra."
— George Steiner, "A Death of Kings," in The New Yorker, issue dated Sept. 7, 1968
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:
|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  (see also Conwell ) gives of certain isomorphisms between classical groups, namely
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 , 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…."
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.
Friday, April 3, 2009
Notes on Finite Geometry
The web pages at finitegeometry.org are currently down, but most of them are still available at the Internet Archive.
“Lord, I remember”
— Bob Seger
“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 of Monday, May 20, 1996
(pdf, 11 pages)
In this excellent analysis,
Holbo quotes Kierkegaard:
“… the knight of faith
‘has the pain of being unable to
make himself intelligible to others'”
(Kierkegaard, Fear and Trembling)
Thursday, April 2, 2009
"… in physics itself, there was what appeared, briefly, to be an ending, which then very quickly gave way to a new beginning: The quest for the ultimate building-blocks of the universe had been taken down to the molecular level in nineteenth-century kinetic theory… and finally to the nuclear level in the second and third decades of the twentieth century. For a moment in the 1920s the quest appeared to have ended…. However… this paradise turned out to be, if not exactly a fool's paradise, then perhaps an Eden lost."
— No Truth Except in the Details: Essays in Honor of Martin J. Klein, introduction by A.J. Kox and Daniel Siegel, June 25, 1994
New York Times obituary dated April 1, 2009:
"Martin J. Klein, a historian of modern physics…. died Saturday, [March 28, 2009] in Chapel Hill, N.C. He was 84 and lived in Chapel Hill."
Klein edited, among other things, Paul Ehrenfest: Collected Scientific Papers (publ. by North-Holland, Amsterdam, 1959).
— John Holbo,
Now We See
Wherein Lies the Pleasure
"The entire sequence of moves in these… chapters reminds one– or should remind one– of a certain type of chess problem where the point is not merely the finding of a mate in so many moves, but what is termed 'retrograde analysis'…."
— Vladimir Nabokov, foreword to The Defense
Wednesday, April 1, 2009
“For every kind of vampire,
there is a kind of cross.”
— Gravity’s Rainbow