On St. Andrew's Day.
A Connery adventure in Kuala Lumpur—
For another Kuala Lumpur adventure, see today's update
to "In Defense of Plato's Realism"—
The July 5, 2007, post linked to
"Plato, Pegasus, and the Evening Star."
For related drama from Kuala Lumpur, see
"Occam's Razor, Plato's Beard."
Continued from October 30 (Devil’s Night), 2013.
“In a sense, we would see that change
arises from the structure of the object.”
— Theoretical physicist quoted in a
Simons Foundation article of Sept. 17, 2013
This suggests a review of mathematics and the
“Classic of Change ,” the I Ching .
The physicist quoted above was discussing a rather
complicated object. His words apply to a much simpler
object, an embodiment of the eight trigrams underlying
the I Ching as the corners of a cube.
See also…
(Click for clearer image.)
The Cullinane image above illustrates the seven points of
the Fano plane as seven of the eight I Ching trigrams and as
seven natural ways of slicing the cube.
For a different approach to the mathematics of cube slices,
related to Gauss’s composition law for binary quadratic forms,
see the Bhargava cube in a post of April 9, 2012.
"These are odd facts…." — G. H. Hardy,
quoted in the previous post, "Centered"
Other odd facts:
If n is odd, then the object at the center
of the n×n square is a square.
Similarly for the n×n×n cube.
Related meditation:
“In a sense, we would see that change
arises from the structure of the object,” he said.
“But it’s not from the object changing.
The object is basically timeless.”
— Theoretical physicist quoted in a
Simons Foundation article of Sept. 17, 2013,
"A Jewel at the Heart of Quantum Physics"
See also "My God, it's full of… everything."
"I have now come to the most difficult part of my story."
"265" — Page number and centered square number
"153" — Triangular number (as noted by St. Augustine)
"265/153" — Object Lesson
An accurate description of such number lore:
"These are odd facts, very suitable for puzzle columns
and likely to amuse amateurs, but there is nothing
in them which appeals much to a mathematician.
The proofs are neither difficult nor interesting—
merely a little tiresome. The theorems are not serious;
and it is plain that one reason (though perhaps not the
most important) is the extreme speciality of both the
enunciations and the proofs, which are not capable of
any significant generalization." — G. H. Hardy
See also some remarks on figurate numbers in this journal.
|
Nothing went wrong at the back of the north wind. "What a queer place it must be!" "It's a very good place." "Do you want to go back again?" "No; I don't think I have left it; I feel it here, somewhere." "Did the people there look pleased?" "Yes— quite pleased, only a little sad." "Then they didn't look glad?" "They looked as if they were waiting to be gladder some day." |
For the birth date of C. S. Lewis and Madeleine L'Engle.
|
THE GOLD KEY The speaker in this case |
"Now he believed that where there was a key, there must also be a lock…."
|
"We must find the country from which the shadows come," said Mossy. "We must, dear Mossy," responded Tangle. "What if your golden key should be the key to it?" "Ah! that would be grand," returned Mossy. |
From the cover of Anne Sexton's Transformations—
"Her metaphoric strength has never been greater —
really funny, among other things, a dark, dark laughter."
— C. K. Williams
Another dark lady:
See also Karr in this journal on the date of the above article—
May 24, 2012, the feast of the dark lady.
From "Why Was New Haven Divided into Nine Squares?"
"Of note on the Wadsworth Map of 1748 are…
the Grammar School, the 'Goal' or jail…."
Related material: Puritan in this journal.
Non-Puritans may prefer the following image—
Source: Yale English Department banner
Continued from Deo Gratias , a post at noon last Saturday
that featured blues singer R. L. Burnside.
"It is a fresh spiritual that he defines"
— "An Ordinary Evening in New Haven"
A Yale death between Saturday night and Sunday morning—
|
See is not believed to have committed suicide, according to
Judicial Department spokeswoman Rhonda Hebert
Mr. Samuel See was delivered to the |
Also known as Virgil the Geometer.
" Art, in other words, can speak to social conflicts,
and not always how you might think. Yvonne Scott,
a professor here at Trinity College, remarked
before the wake that in 1972 the invention of
Patrick Ireland was 'hard for people to grasp
because for a long while conceptual art wasn’t
understood here.' She added, 'Times have changed.' "
— Michael Kimmelman in The New York Times ,
May 22, 2008
Related art:
The "Square Round" link at the end of the previous post.
A story dated December 16, 2008, from the parish of Shannon.
A post dated December 16, 2008, from this journal.
Continued from Pensée (Feb. 10, 2012).*
Nick Paumgarten in The New Yorker of Dec. 2, 2013—
" When one speaks of Zwirner the gallerist, one is speaking
as much of a handful of women in their forties who have been
with the gallery fifteen or more years. Zwirner has made them
partners, meaning, he says, that they 'will participate in profits
as the gallery does well.' They are Angela Choon, who runs the
London gallery; Hanna Schouwink, from Holland; Bellatrix Hubert,
from France; and Kristine Bell, from outside Buffalo. Seeing them
all together, at an opening or a dinner, brings to mind David
Carradine’s gang of glamorous assassins in 'Kill Bill.' "
See also the previous post, on An Object of Beauty.
* For some related art, see Square Round.
In memory of a composer who reportedly died
on Thursday, November 21, 2013:
Related material, for mature audiences only, "based on the
confessional poetry of Anne Sexton," from Nov. 8, 2012:
See also Confessional : this journal on that date.
Peter Keepnews on the late jazz musician Chico Hamilton:
"He was a charter member of the baritone saxophonist
Gerry Mulligan’s quartet, which helped lay the groundwork
for the cool movement. His own quintet, which he formed
shortly after leaving the Mulligan group, came to be
regarded as the quintessence of cool."
Example: a recording uploaded on October 27, 2013,
and this journal on that date.
Related material: Working Backward.
Backstory: Frenkel's Metaphors and Waitressing for Godot.
In a recent vulgarized presentation of the Langlands program,
Edward Frenkel implied that number theory and harmonic
analysis were, before Langlands came along, quite unrelated.
This is false.
"If we think of different fields of mathematics as continents,
then number theory would be like North America and
harmonic analysis like Europe."
— Edward Frenkel, Love and Math , 2013
For a discussion of pre-Langlands connections between
these "continents," see…
"Fourier Analysis in Number Theory, my senior thesis, under the advisory of Patrick Gallagher.
This thesis contains no original research, but is instead a compilation of results from analytic
number theory that involve Fourier analysis. These include quadratic reciprocity (one of 200+
published proofs), Dirichlet's theorem on primes in arithmetic progression, and Weyl's criterion.
There is also a function field analogue of Fermat's Last Theorem. The presentation of the
material is completely self-contained."
— Shanshan Ding, University of Pennsylvania graduate student
Suggested by a theater review titled "Filling the Existential Void."
Companion piece: A Poem for Pinter.
"Waiting for Ogdoad" continues…
"You want Frye's with that?" — A recent humanities graduate.
Frye's backstory: Ogdoad.
Other material suggested by the previous post and by the time of this post…
No Man's Land, Gods and Monsters, and Forty and Eight.
From a slide show of Pinter's "No Man's Land"—
* Footnotes on the title—
For Hirst: Wikipedia.
For Spooner: Into the Woods.
For the groundlings: Urban Dictionary.
From the New York Times obituary of philanthropist
Fred Kavli, who died on Thursday, November 21—
” In 2005, when Mr. Kavli announced that
he planned to start the prizes, he recalled
skiing in the Norwegian mountains as a boy.
‘At times,’ he told a gathering in New York,
‘the whole sky was aflame with the Northern Lights
shifting and dancing across the sky down to the
white-clad mountaintops. In the stillness and
loneliness of the white mountains, I pondered the
universe, the planet, nature and the wonders of
man. I’m still pondering.’ “
“And we may see the meadow in December, icy white
and crystalline….” — Johnny Mercer, lyrics to Lionel
Hampton and Sonny Burke’s “Midnight Sun”
* Lyche
Ben Brantley reviewing a show by the X-Men patriarchs
that opened on Sunday:
"This isn’t just a matter of theatergoers chuckling
to show that they’re smart and cultured and had
damn well better be having a good time after
forking out all that money…."
I prefer reality (which includes the life of Fred Kavli) :
See also Saturday's posts Chess and Frame Tale.
Whether the patriarch Kavli, pictured above, is now having
a good time, I do not know. I hope so.
A scholium on the link to Pythagoras
in this morning's previous post Figurate Numbers:
For related number mysticism, see Chapter 8, "Magic Numbers,"
in Love and Math: The Heart of Hidden Reality,
by Edward Frenkel (Basic Books, Oct. 1, 2013).
(Click for clearer image.)
See also Frenkel's Metaphors in this journal.
* The wannabe of the title is of course not Langlands, but Frenkel.
The title refers to a post from July 2012:
The above post, a new description of a class of figurate
numbers that has been studied at least since Pythagoras,
shows that the "triangular numbers" of tradition are not
the only triangular numbers.
"Thus the theory of description matters most.
It is the theory of the word for those
For whom the word is the making of the world…."
— Wallace Stevens, "Description Without Place"
See also Finite Relativity (St. Cecilia's Day, 2012).
The search for 1984 at the end of last evening’s post
suggests the following Sunday meditation.
My own contribution to this genre—
A triangle-decomposition result from 1984:
| American Mathematical Monthly , June-July 1984, p. 382
MISCELLANEA, 129 Triangles are square “Every triangle consists of n congruent copies of itself” |
The Orwell slogans are false. My own is not.
* The “for Jews” of the title applies to some readers of Edward Frenkel.
“We’ll give the week-end to wisdom, to Weisheit, the rabbi….”
— Wallace Stevens in “Things of August” (see Storyville yesterday)
My choice for a rabbi would be George Steiner.
|
INTERVIEWER You once referred to the “patience of apprehension” and “open-endedness of asking” which fiction can enact, and yet you have described your fictions as “allegories of argument, stagings of ideas.” Do you still consider them to be “stagings of ideas”? GEORGE STEINER Very much so. My writing of fiction comes under a very general heading of those teachers, critics, scholars who like to try their own hand once or twice in their lives. |
For one such staging, see today’s earlier posts Chess and Frame Tale.
See The X-Men Tree, another tree, and Trinity MOG.
Norwegian, 22, Takes World Chess Title
Quoted here on Thursday, the date of Kavli‘s death:
Herbert Mitgang’s New York Times
obituary of Cleanth Brooks—
“The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background.”
See also Steiner, Chess, and Death.
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