Teaser head from the
online NY Times
this morning:
online NY Times
this morning:
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Month: January 2009
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Religion and Narrative, continued:
Report of ArrivalA PBS broadcast of Cyrano de Bergerac was shown yesterday nationally and this evening, a day late, by WNED TV, Buffalo.
From the translation by Anthony Burgess:
Cyrano speaks of falling leaves–
They fall well. With a sort of panache.
They plume down in their last
Loveliness, disguising their fear
Of being dried and pounded to ash
To mix with the common dust.
They go in grace, making their fall appear
Like flying.
ROXANE You’re melancholy today.
CYRANO Never. I’m not the melancholy sort.
ROXANE Very well, then. We’ll let
The leaves of the fall fall while you
Turn the leaves of my gazette.
What’s new at court?
CYRANO … There have been some scandals
To do with witches. A bishop went to heaven,
Or so it’s believed: there’s been as yet no report
Of his arrival….”Later….
CYRANO … See it there, a white plume
Over the battle– A diamond in the ash
Of the ultimate combustion–
My panache.”
Related material:Today’s previous entry
and the Epiphany
link to the
four-diamond symbol
in Jung’s Aion
with an epigraph by
Gerard Manley Hopkins: -
Religion and Narrative, continued:
A Public Square
In memory of
Richard John Neuhaus,
who died today at 72:“It seems, as one becomes older,
That the past has another pattern,
and ceases to be a mere sequence….”— T. S. Eliot, Four Quartets
See also The Folding.
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Epiphany 2009:
Archetypes, Synchronicity,
and Dyson on JungThe current (Feb. 2009) Notices of the American Mathematical Society has a written version of Freeman Dyson’s 2008 Einstein Lecture, which was to have been given in October but had to be canceled. Dyson paraphrases a mathematician on Carl Jung’s theory of archetypes:
“… we do not need to accept Jung’s theory as true in order to find it illuminating.”
The same is true of Jung’s remarks on synchronicity.
For example –
Yesterday’s entry, “A Wealth of Algebraic Structure,” lists two articles– each, as it happens, related to Jung’s four-diamond figure from Aion as well as to my own Notes on Finite Geometry. The articles were placed online recently by Cambridge University Press on the following dates:
R. T. Curtis’s 1974 article defining his Miracle Octad Generator (MOG) was published online on Oct. 24, 2008.
Curtis’s 1987 article on geometry and algebraic structure in the MOG was published online on Dec. 19, 2008.
On these dates, the entries in this journal discussed…
Oct. 24:
Cube Space, 1984-2003Material related to that entry:
Dec. 19:
Art and Religion: Inside the White CubeThat entry discusses a book by Mark C. Taylor:
The Picture in Question: Mark Tansey and the Ends of Representation (U. of Chicago Press, 1999).
In Chapter 3, “Sutures of Structures,” Taylor asks –
“What, then, is a frame, and what is frame work?”
One possible answer —
Hermann Weyl on the relativity problem in the context of the 4×4 “frame of reference” found in the above Cambridge University Press articles.
“Examples are the stained-glass
windows of knowledge.”
– Vladimir Nabokov -
Annals of Geometry:
A 1987 article by R. T. Curtis on the geometry of his Miracle Octad Generator (MOG) as it relates to the geometry of the 4×4 square is now available online ($20):
Further elementary techniques using the miracle octad generator, by R. T. Curtis. Abstract:“In this paper we describe various techniques, some of which are already used by devotees of the art, which relate certain maximal subgroups of the Mathieu group M24, as seen in the MOG, to matrix groups over finite fields. We hope to bring out the wealth of algebraic structure* underlying the device and to enable the reader to move freely between these matrices and permutations. Perhaps the MOG was mis-named as simply an ‘octad generator’; in this paper we intend to show that it is in reality a natural diagram of the binary Golay code.”
(Received July 20 1987)
– Proceedings of the Edinburgh Mathematical Society (Series 2) (1989), 32: 345-353, doi:10.1017/S0013091500004600.
(Published online by Cambridge University Press 19 Dec 2008.)
In the above article, Curtis explains how two-thirds of his 4×6 MOG array may be viewed as the 4×4 model of the four-dimensional affine space over GF(2). (His earlier 1974 paper (below) defining the MOG discussed the 4×4 structure in a purely combinatorial, not geometric, way.)
For further details, see The Miracle Octad Generator as well as Geometry of the 4×4 Square and Curtis’s original 1974 article, which is now also available online ($20):
A new combinatorial approach to M24, by R. T. Curtis. Abstract:
“In this paper, we define M24 from scratch as the subgroup of S24 preserving a Steiner system S(5, 8, 24). The Steiner system is produced and proved to be unique and the group emerges naturally with many of its properties apparent.”
(Received June 15 1974)
– Mathematical Proceedings of the Cambridge Philosophical Society (1976), 79: 25-42, doi:10.1017/S0305004100052075.
(Published online by Cambridge University Press 24 Oct 2008.)
* For instance:
Click for details.
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Literature and…
“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“
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A Mystery for Westlake:
Signs and Symbolscontinued…
from the five entries
ending on June 3, 2008
and from yesterday,
New Year’s DayThe end of a story by Vladimir Nabokov in The New Yorker of May 15, 1948:
“You have the incorrect number. I will tell you what you are doing: you are turning the letter O instead of the zero.”
They sat down to their unexpected festive midnight tea. The birthday present stood on the table. He sipped noisily; his face was flushed; every now and then he imparted a circular motion to his raised glass so as to make the sugar dissolve more thoroughly. The vein on the side of his bald head where there was a large birthmark stood out conspicuously and, although he had shaved that morning, a silvery bristle showed on his chin. While she poured him another glass of tea, he put on his spectacles and re-examined with pleasure the luminous yellow, green, red little jars. His clumsy moist lips spelled out their eloquent labels: apricot, grape, beech plum, quince. He had got to crab apple, when the telephone rang again.
Click for details.
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A Stitch in Time:
Out with
the Old Year…
Click to enlarge. In with
the New…
Click to enlarge. Escritorio
Sept. 15, 2008
A Stitch in Time… -
Elective Concurrences:
Feliz Cumpleaños
See also Log24 on the date
this picture was uploaded:
November 16, 2008. -
With Honors:
The Becket ListMonday, Dec. 29, 2008, was St. Thomas Becket’s Day.
On that day in this journal there was a note from the New York Times on the screenwriter of the 1969 film “A Walk With Love and Death”–
“He feuded with… John Huston, who gave the lead female role in ‘Walk’ to his teenage daughter… against Mr. Wasserman’s wishes.”Liz Evett
WEST RICHLAND, Wash. (AP) – Liz Evett, a teen who inspired people across the nation by creating a “bucket list” of things she wanted to do before she died, has died. She was 18.
Her mother, Angie Ivey, said Evett died Monday [Dec. 29, 2008] of leukemia. The West Richland teen was diagnosed with cancer nearly three years ago and relapsed in April.
When she stopped responding to treatment in June, Evett created a “bucket list” of things she wanted to do before dying and spent the last six months crossing them off.
Her list included feeding giraffes, meeting Seattle Mariner Ichiro Suzuki and graduating from high school.
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