Funding: This work was funded by the Office of the Assistant Secretary of Defense Research & Engineering through a Vannevar Bush Faculty Fellowship, ONR N00014-16-1-2010.
HANSEN — Department of Mathematics, University of Pennsylvania, Philadelphia, PA (jhansen@math.upenn.edu)
GHRIST — Department of Mathematics and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA (ghrist@math.upenn.edu)
See as well this journal on the above date (26 May 2020) —
Related literary notes — On April 28 The New York Times reported a death from the above date (Tuesday, April 26, 2022).
See a followup in the Times today on "New York literary royalty."
"Engelhardt’s goal in this study is to put the interplay
between fiction and mathematical conceptualizations
of the world into its historical context. She sees her work
as a beginning for further studies on the role of mathematics,
not only modern, in fiction in the wider field of literature and
science. It is fair to say that in her book Nina Engelhardt does
succeed in giving us an inspiring tour d’horizon of this interplay."
Another such tour —
On the title of Westworld Season 4 Episode 5, "Zhuangzi" —
"Dorothea by this time had looked deep into the ungauged reservoir of Mr. Casaubon's mind, seeing reflected there in vague labyrinthine extension every quality she herself brought; had opened much of her own experience to him, and had understood from him the scope of his great work, also of attractively labyrinthine extent. For he had been as instructive as Milton's 'affable archangel;' and with something of the archangelic manner he told her how he had undertaken to show (what indeed had been attempted before, but not with that thoroughness, justice of comparison, and effectiveness of arrangement at which Mr. Casaubon aimed) that all the mythical systems or erratic mythical fragments in the world were corruptions of a tradition originally revealed. Having once mastered the true position and taken a firm footing there, the vast field of mythical constructions became intelligible, nay, luminous with the reflected light of correspondences. But to gather in this great harvest of truth was no light or speedy work."
Geoffrey Block, Distinguished Professor of Music History at the University of Puget Sound, is the author of Enchanted Evenings: The Broadway Musical From Show Boat to Sondheim and Lloyd Webber. The book offers theater lovers an illuminating behind-the-scenes tour of some of America’s best loved, most admired, and most enduring musicals, as well as a riveting history. In the excerpt below we learn about how Hammerstein mentored Sondheim.
Sondheim, a native New Yorker whose father could play harmonized show tunes by ear after hearing them once or twice, was the beneficiary of a precocious, suitably specialized musical education. While still a teenager and shortly after the premiere of Carousel , Sondheim had the opportunity to be critiqued at length by the legendary Hammerstein, who, by a fortuitous coincidence that would be the envy of Show Boat’s second act, happened to be a neighbor and the father of Sondheim’s friend and contemporary, James Hammerstein. Sondheim’s unique apprenticeship with the first of his three great mentors, Oscar Hammerstein 2nd, one of the giants of the Broadway musical from the 1920s until long after his death in 1960, might serve as a Hegelian metaphor for Sondheim’s thesis, antithesis, and synthesis of modernism and traditionalism, high-brow and low-brow.
Note the above Oxford University Press date. Also on that date —
“Not games. Puzzles. Big difference. That’s a whole other matter.
All art — symphonies, architecture, novels — it’s all puzzles.
The fitting together of notes, the fitting together of words have
by their very nature a puzzle aspect. It’s the creation of form
out of chaos. And I believe in form.”
— Stephen Sondheim, in Stephen Schiff,
“Deconstructing Sondheim,” The New Yorker, issue of March 8, 1993, p. 76
"Sean Kelly, a wry master of literary and musical parodies
who helped infuse National Lampoon with the sharp-edged
and often crude humor it became known for, died on July 11
in Manhattan. He was 81."
“Somehow, a message had been lost on me. Groups act .
The elements of a group do not have to just sit there,
abstract and implacable; they can do things, they can
‘produce changes.’ In particular, groups arise
naturally as the symmetries of a set with structure.”
"Similar to the 15+35 construction of the Hoffman-Singleton graph is the 30+70 construction of the Higman-Sims graph. In the former the starting point was that the lines of PG(3,2) can be labeled with the triples in a 7-set such that lines meet when the corresponding triples have 1 element in common. This time we label the lines of PG(3,2) with the 4+4 splits of an 8-set, where intersecting lines correspond to splits with common refinement 2+2+2+2. Clearly, both descriptions of the lines of PG(3,2) are isomorphic. Take as vertices of the Higman-Sims graph the 15 points and 15 planes of PG(3,2) together with the 70 4-subsets of an 8-set. Join two 4-sets when they have 1 element in common. A 4-set determines a 4+4 split and hence a line in PG(3,2), and is adjacent to the points and planes incident with that line. A plane is adjacent to the nonincident points. This yields the Higman-Sims graph."
(Pips are the dots on dice. The above "choose us" image in the form of a
St. Bridget's cross is from Twirly Industries, a sportswear maker in Pakistan.)
See as well a Polish poet's meditation
quoted here on St. Bridget's Day, 2012:
— You think I like being here on Christmas eve, Alan ?
— No. Well, maybe.
— Okay… Okay, maybe I do have a touch of tunnel vision this holiday season. But in two days we're going to announce one of the largest mergers in U.S. corporate history.
When a deal like this turns up, you get on it and you ride it.
You don't ask it for a vacation.
December 26. After that there'll be so much money floating around here it'll be like Christmas every day.
December 26, people. If you'd like to celebrate that day, you all have my blessing.
"Now all they need is to resurrect Superman (Henry Cavill),
stop Steppenwolf from reuniting his three Mother Cubes
(sure, whatever) and wrap things up in under two cinematic
hours (God bless)."
A New Yorker writer on why he wanted to
learn mathematics at an advanced age —
"The challenge, of course, especially in light of the collapsing horizon, since I was sixty-five when I started. Also, I wanted especially to study calculus because I never had. I didn’t even know what it was—I quit math after feeling that with Algebra II I had pressed my luck as far as I dared. Moreover, I wanted to study calculus because Amie told me that when she was a girl William Maxwell had asked her what she was studying, and when she said calculus he said, 'I loved calculus.' Maxwell would have been about the age I am now. He would have recently retired after forty years as an editor of fiction at The New Yorker , where he had handled such writers as Vladimir Nabokov, Eudora Welty, John Cheever, John Updike, Shirley Hazzard, and J. D. Salinger. When Salinger finished Catcher in the Rye , he drove to the Maxwells’ country house and read it to them on their porch. I grew up in a house on the same country road that Maxwell and his wife, Emily, lived on, and Maxwell was my father’s closest friend."
— Wilkinson, Alec. A Divine Language (p. 5). Published
July 12, 2022, by Farrar, Straus and Giroux. Kindle Edition.
See as well two versions of
a very short story, "Turning Nine."
Wilkinson's title is of course deplorable.
Related material: "Night Hunt" in a
Log24 search for the phrase "Good Question."
"The successful artist shares with the politician
a recurrent temptation to indulge in emotional claptrap.
Bernard Bosanquet in Three Lectures on Aesthetic (1915)
proposed that this urge to chase after tears or laughter
could be quelled by attaching the art-emotion to a particular object
and not a set of reactions. His consequent definition of art was
'feeling expressed for expression’s sake.' Notice, however, that
this is something only the deranged would dream of wanting in
real life. Our everyday expressions of feeling are spontaneous and
practical; they are never 'for expression’s sake.' By contrast,
aesthetic feeling is self-sufficient."
Francis X. Clines, a reporter, columnist and foreign correspondent
for The New York Times whose commentaries on the news and
lyrical profiles of ordinary New Yorkers were widely admired as a
stylish, literary form of journalism, died on Sunday at his home in
Manhattan. He was 84.
. . . .
As a national correspondent … he tracked political campaigns
and the Washington scene, taking occasional trips through the
hills and hollows of Appalachia to write of a largely hidden
Other America.
The sound of that student’s holler tale remains — how to say? — precious or cool or awesome, worthy of preserving. A good phrase was offered by Kathy Williams, the teacher who invited Dr. Hazen to deal with her students’ inferiority complex. She quoted her 93-year-old grandmother’s version of “cool!” “Grandma Glenna always says, ‘Forever more !’ ” “Forever more !” she shouted, offering the youngsters something old that sounded new.
"A version of this article appears in print on Aug. 23, 2010, Section A, Page 22 of the New York edition with the headline: Say It Loud."
From Piligrimage: The Book of the People by Zenna Henderson
(a 1961 collection, published by Doubleday, of earlier stories) —
But all things have to end, and I sat one May afternoon,
staring into my top desk drawer, the last to be cleaned out,
wondering what to do with the accumulation of useless
things in it. But I wasn’t really seeing the contents of the
drawer, I was concentrating on the great weary emptiness
that pressed my shoulders down and weighted my mind.
“It’s not fair,” I muttered aloud and illogically, "to show
me Heaven and then snatch it away.”
“That’s about what happened to Moses, too, you know.”
My surprised start spilled an assortment of paper clips
and thumb tacks from the battered box I had just picked up.
“Well forevermore!” I said, righting the box. "Dr. Curtis!
What are you doing here?”
"Returning to the scene of my crime,” he smiled, coming
through the open door.
This is from Henderson's "Pottage," a story first published in 1955.
"It is night on the fourth of the curving terraces, high above the sea.
The stars are full out, known and unknown. Dante is halfway up the mountain….
It is half through the poem; half the whole is seen and said: hell, where grace
is not known but as a punishment; purgatory where grace and punishment are
two manners of one fact."
— Charles Williams, The Figure of Beatrice, Faber and Faber, 1943
"As of 2022, it is the oldest web browser still being maintained,,,,"
"The speed benefits of text-only browsing are most apparent
when using low bandwidth internet connections, or older computer
hardware that may be slow to render image-heavy content."
— Wikipedia [“Older” link added.]
Lyche, whose art often incorporates mathematical notions,
has not yet, as far as I know, explored the Borromean link
(three rings, linked mutually but not pairwise) in her art.
"I have had a thing for the Borromean rings for years now.
There’s something so poetic about them. The three rings
are strong together, but they fall apart if any one of them
is removed. Alternatively, the three rings are trapped together
until one of them leaves and sets the others free. I’m kind of
surprised there isn’t a Wisława Szymborska poem or Tom Stoppard play that explores the metaphorical possibilities
in the Borromean rings." — Scientific American , Sept. 30, 2016.
See also the Lamb date Sept. 30, 2016, as well as work
by Lyche, in Log24 posts tagged Star Cube.
"One of the most fascinating recent areas of research
is known as plasticity, which has shown that some
organisms have the potential to adapt more rapidly
and more radically than was once thought.
Descriptions of plasticity are startling, bringing to mind
the kinds of wild transformations you might expect to find
in comic books and science fiction movies."
"It’s important, as art historian Reinhard Spieler has noted,
that after a brief, unproductive stay in Paris, circa 1907,
Kandinsky chose to paint in Munich. That’s where he formed
the Expressionist art group Der Blaue Reiter (The Blue Rider) —
and where he avoided having to deal with cubism."
“If we ended Part 1 proud of our accomplishment—
perhaps even a little smug—then we will get reacquainted
with our humility in this article.” — Robert Jacobson
" 'Old Truths and New Clichés,' a collection of 19
prose articles, most appearing in English for the
first time, reveals that Singer was as consummate
an essayist as he was a teller of tales." — Benjamin Balint
"… the self-enclosing processes by which late 20th-century
American academics established and secured their status
(you painfully develop a thesis in competition with your peers,
then you keep on elaborating it until you die)."
"There are many places one can read about twistors
and the mathematics that underlies them. One that
I can especially recommend is the book Twistor Geometry
and Field Theory, by Ward and Wells."
For some musical background, see a Dec. 7, 1950, newspaper report of a church Christmas production. I was not active in any
church then, and am not now, but I later went to high school with,
and admired, several of the people from the church production.
So much for lookin' behind. For lookin' upstairs . . .
"There was cause to worry about the enemy occupying the
high ground on both sides of the MSR [Main Supply Route].
The resemblance to the 23rd Psalm's 'valley of the shadow
of death' was inescapable to us."
The musical accompaniment suggests a search in this journal
for "Reservoir." From that search, some remarks of perhaps
greater philosophical interest —
.
