See also a Log24 search for "The Path."
Related material from a similar search
for "Nanavira Thera" —
"I am glad you have discovered that the situation is comical:
ever since studying Kummer I have been, with some difficulty,
refraining from making that remark."
— Nanavira Thera, Seeking the Path [Early Letters, 17 July 1958].
From the Aug. 30 post "A Brief Introduction to Ideas,"
an epigraph from Four Quartets —
Another view of the way up and the way down:
"Of course, presentation of the effect in the cause
is exactly what blending the Buddhist Monk's
two journeys provides. The cause is the dynamics
of the two input journeys; the effect is the existence
of a location on the path they occupy at the same time
of day. In the blend, the location and the encounter are
presented directly as part of the causal dynamics of motion."
— Page 78 in The Way We Think: Conceptual Blending ,
by Fauconnier and Turner, Basic Books, 2002.
The Source —
(The title is a reference to the previous post.)
"Pope Reminds Us The Devil Is Real"
— Catholic Online , Oct. 14, 2013
Related material:
The reported death of Justice Scalia …
… and posts on Scalia in this journal.
https://blacklistdeclassified.net/2022/04/15/
%f0%9f%94%b4-script-916-helen-maghi/ —
Red: If I may offer some counsel –
“Do not go where the path may lead.
Go instead where there is no path
and leave a trail.”
In the spirit of that, I bring an unusual case….
This post is in honor of Thandiwe Newton,
who left a Westworld trail —
Vide Bulk Apperception.
* Cf. a post from Day 3 of 2022.
"Howard Solomon was building the pharmaceutical company
Forest Laboratories, not by manufacturing drugs but by
licensing them. In his search for deals in the United States and
Europe, he learned about citalopram, a Danish antidepressant."
— Richard Sandomir, New York Times , Friday, Jan. 14, 2022
" '… he’d talk about Verdi writing "Falstaff" in his 80s,' Andrew Solomon
said. ' "Imagine that," he’d say, "in his 80s, he wrote some of the greatest
music ever written." That was the path he hoped to follow.' ”
From Atomicity and Quanta by James Jeans,
Cambridge University Press, 1926, pp. 55-56 —
| “So far as we can at present conjecture, the investigation of the structure which produces this atomicity appears to be the big problem in the path of the quantum-theory. To conform to the principle of relativity, the new atomicity must admit of expression in terms of the space-time continuum, although we have seen that it cannot be an atomicity of the continuum itself. It may conceivably be an atomicity of its metric properties, such as determine its curvatures. We may perhaps form a very rude picture of it by imagining the curvature of the continuum in the neighbourhood of an atom not to be of the continuous nature imagined by Weyl, but to occur in finite chunks—a straight piece, then a sudden bend, then another straight bit, and so on. A small bit of the continuum viewed through a five-dimensional microscope might look rather like a cubist picture; and, conversely, perhaps a cubist picture looks rather more like a little fragment of the continuum than like anything else.” |
This is, of course, not the “atomicity” of the previous post.
For examples of that atomicity, a concept of pure geometry
rather than of physics, see …
Faure, C. A., and Frölicher, A., “Fundamental Notions of
Lattice Theory,” in Modern Projective Geometry (2000).
(Mathematics and Its Applications, vol 521. Springer, Dordrecht.)
Related art (a “cubist picture”) —
Juan Gris, Fruit Dish and Carafe , 1914
Two images from a post of April 11, 2014 —
Tom Cruise at the Vatican in MI3
_____________________________________________________________________
Michelle Monaghan, star of "The Path," in MI3 —
From Nanavira Thera, "Early Letters," in Seeking the Path —
"nine possibilities arising quite naturally" —
Compare and contrast with Hudson's parametrization of the
4×4 square by means of 0 and the 15 2-subsets of a 6-set —
The revisiting, below, of an image shown here in part
on Spy Wednesday, 2016, was suggested in part by
a New York Times obituary today for a Nobel-prize
winning Hungarian novelist.
Note the references on the map to
"Devil's Gate" and "Pathfinder."
See also the following from a review of The Pathseeker , a novel
by the Nobel laureate (Imre Kertész), who reportedly died today —
|
… The commissioner is in fact not in search of a path, but rather of traces of the past (more literally the Hungarian title means ‘trace seeker’). His first shock comes at his realization that the site of his sufferings has been converted into a museum, complete with tourists “diligently carrying off the significance of things, crumb by crumb, wearing away a bit of the unspoken importance” (59). He meets not only tourists, however. He also comes across paradoxically “unknown acquaintances who were just as much haunted by a compulsion to revisit,” including a veiled woman who slowly repeats to him the inventory of those she lost: “my father, my younger brother, my fiancé” (79). The commissioner informs her that he has come “to try to redress that injustice” (80). When she asks how, he suddenly finds the words he had sought, “as if he could see them written down: ‘So that I should bear witness to everything I have seen’” (80). The act of bearing witness, however, proves elusive. In the museum he is compelled to wonder, “What could this collection of junk, so cleverly, indeed all too cleverly disguised as dusty museum material, prove to him, or to anyone else for that matter,” and adds the chilling observation, “Its objects could be brought to life only by being utilized” (71). As he touches the rust-eaten barbed wire fence he thinks, “A person might almost feel in the mood to stop and dutifully muse on this image of decay – were he not aware, of course, that this was precisely the goal; that the play of ephemerality was merely a bait for things” (66). It is this play of ephemerality, the possibility that the past will be consigned to the past, against which the commissioner struggles, yet his struggle is frustrated precisely by the lack of resistance, the indifference of the objects he has come to confront. “What should he cling on to for proof?” he wonders. “What was he to fight with, if they were depriving him of every object of the struggle? Against what was he to try and resist, if nothing was resisting?” (68) He had come with the purpose of “advertis[ing] his superiority, celebrat[ing] the triumph of his existence in front of these mute and powerless things. His groundless disappointment was fed merely by the fact that this festive invitation had received no response. The objects were holding their peace” (109). In point of fact The Pathseeker makes no specific mention either of the Holocaust or of the concentration camps, yet the admittedly cryptic references to places leave no doubt that this is its subject. Above the gate at the camp the commissioner’s wife reads the phrase, “Jedem das Seine,” to each his due, and one recalls the sign above the entrance to the camp at Buchenwald. Further references to Goethe as well as the Brabag factory, where Kertész himself worked as a prisoner, confirm this. Why this subterfuge on the part of the author? Why a third-person narrative with an unnamed protagonist when so many biographical links tie the author to the story? One cannot help but wonder if Kertész sought specifically to avoid binding his story to particulars in order to maintain the ultimately metaphysical nature of the quest. Like many of Kertész’s works,The Pathseeker is not about the trauma of the Holocaust itself so much as the trauma of survival. The self may survive but the triumph of that survival is chimerical. Translator Tim Wilkinson made the bold decision, in translating the title of the work, not to resort to the obvious. Rather than simply translate Nyomkereső , an allusion to the Hungarian translation of James Fenimore Cooper’s The Pathfinder , back into English, he preserves an element of the unfamiliar in his title. This tendency marks many of the passages of the English translation, in which Wilkinson has opted to preserve the winding and often frustratingly serpentine nature of many of the sentences of the original instead of rewriting them in sleek, familiar English. . . . — Thomas Cooper |
"Sleek, familiar English" —
"Those were the good old days!" — Applegate in "Damn Yankees"
(See previous post.)
Related material — Posts tagged Dirac and Geometry.
For an example of what Eddington calls "an open mind,"
see the 1958 letters of Nanavira Thera.
(Among the "Early Letters" in Seeking the Path ).
From Commentary magazine on Dec. 14, 2015 —
"Three significant American magazines started life in the 1920s.
The American Mercury , founded in 1924, met with the greatest
initial success, in large part because of the formidable reputations
of its editors, H.L. Mencken and George Jean Nathan, and it soon
became the country’s leading journal of opinion."
— Terry Teachout, article on the history of The New Yorker
A search for "American Mercury" in this journal yields a reference from 2003
to a book containing the following passage —
As Webern stated in "The Path to Twelve-Note Composition":
"An example: Beethoven's 'Six easy variations on a Swiss song.'
Theme: C-F-G-A-F-C-G-F, then backwards! You won't notice this
when the piece is played, and perhaps it isn't at all important,
but it is unity ."
— Larry J. Solomon, Symmetry as a Compositional Determinant ,
Chapter 8, "Quadrate Transformations"
This is the Beethoven piece uploaded to YouTube by "Music and such…"
on Dec. 12, 2009. See as well this journal on that same date.
Yesterday's online LA Times had an obituary for a
traveling salesman:
"Besides writing and teaching, Borg was a frequent speaker,
usually racking up 100,000 frequent flier miles a year.
He and Crossan, along with their wives, led annual tours
to Turkey to follow the path of the Apostle Paul and to give
a sense of his world. They also led tours to Ireland to
showcase a different brand of Christianity."
Borg and Crossan were members of the Jesus Seminar.
For Crossan, see remarks on "The Story Theory of Truth."
See also, from the date of Borg's death, a different salesman joke.
Some backstory —
"What we do may be small, but it has
a certain character of permanence."
— G. H. Hardy in A Mathematician's Apology
"Got to keep the loonies on the path."
— Lyrics to Dark Side of the Moon
For those who, like Tom Stoppard, prefer the dark side—
|
NEW ANGLE:
INT. OFFICE BUILDING – NIGHT
NIGHT WATCHMAN
Bateman wheels around and shoots him.
NEW ANGLE:
INT. PIERCE & PIERCE LOBBY – NIGHT
— AMERICAN PSYCHO |
Not quite so dark—
"And then one day you find ten years have got behind you."
— Lyrics to Dark Side of the Moon
This journal ten years ago, on August 25, 2003—
|
… We seek
The poem of pure reality, untouched
At the exactest point at which it is itself,
The eye made clear of uncertainty, with the sight
Everything, the spirit's alchemicana
The solid, but the movable, the moment,
— Wallace Stevens, "An Ordinary Evening |
"A view of New Haven, say…." —
"This is the garden of Apollo,
the field of Reason…."
John Outram, architect
A similar version of this Apollonian image —
Detail:
Related material for the loonies:
A quote from The Oxford Murders ,
a novel by Guillermo Martinez—
"Anyone can follow the path once it’s been marked out.
But there is of course an earlier moment of illumination,
what you called the knight’s move. Only a few people,
sometimes only one person in many centuries,
manage to see the correct first step in the darkness.”
“A good try,” said Seldom.
In memory of "Mr. Piano" Roger Williams, who died today—
Related material— A quote from The Oxford Murders ,
a novel by Guillermo Martinez—
"Anyone can follow the path once it’s been marked out.
But there is of course an earlier moment of illumination,
what you called the knight’s move. Only a few people,
sometimes only one person in many centuries,
manage to see the correct first step in the darkness.”
“A good try,” said Seldom.
From math16.com—
Quotations on Realism
|
The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)—
From The Search for Invariants (June 20, 2011):
The conclusion of Maja Lovrenov's
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—
"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."
— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241
Related material from Sunday's New York Times travel section—
In memory of Wu Guanzhong, Chinese artist who died in Beijing on Friday—
"Once Knecht confessed to his teacher that he wished to learn enough to be able to incorporate the system of the I Ching into the Glass Bead Game. Elder Brother laughed. 'Go ahead and try,' he exclaimed. 'You'll see how it turns out. Anyone can create a pretty little bamboo garden in the world. But I doubt that the gardener would succeed in incorporating the world in his bamboo grove.'"
— Hermann Hesse, The Glass Bead Game, translated by Richard and Clara Winston
"The Chinese painter Wu Tao-tzu was famous because he could paint nature in a unique realistic way that was able to deceive all who viewed the picture. At the end of his life he painted his last work and invited all his friends and admirers to its presentation. They saw a wonderful landscape with a romantic path, starting in the foreground between flowers and moving through meadows to high mountains in the background, where it disappeared in an evening fog. He explained that this picture summed up all his life’s work and at the end of his short talk he jumped into the painting and onto the path, walked to the background and disappeared forever."
— Jürgen Teichmann. Teichmann notes that "the German poet Hermann Hesse tells a variation of this anecdote, according to his own personal view, as found in his 'Kurzgefasster Lebenslauf,' 1925."
For Louise Fletcher
on her birthday
Fletcher in
Exorcist II: The Heretic
From Andrew Delbanco, the author of
The Death of Satan:
How Americans Have Lost the Sense of Evil:
— Andrew Delbanco in
The New York Review of Books, Nov. 4, 1999
Click on picture for details.
For Christ in a different context,
see the 9/11 entry of Log24
in a September 2003 archive.
For exorcism in a different context, see
Exorcism and Multiple Personality Disorder
from a Catholic Perspective,
by Fr. J. Mahoney.
"Got to keep the loonies on the path."
— Roger Waters
His Way
Suggested by George Steiner’s phrase in the previous entry, “as in inverse canons”–
| EXT. BLACK COVE FARM. DAY.
A beautiful day, MONROE INMAN MONROE Inman hovers, awkward. INMAN Ada comes forward, ****** LATER ******* INT. PARLOUR. At the piano, Ada unwraps
Ada picks them out on the piano. |
(Fourteen Canons on the First Eight Notes of the Goldberg Ground)
Bach in the original —
“Bach in the Original” —
One Ring to Rule Them All
In memory of J. R. R. Tolkien, who died on this date, and in honor of Israel Gelfand, who was born on this date.
Leonard Gillman on his collaboration with Meyer Jerison and Melvin Henriksen in studying rings of continuous functions:
“The triple papers that Mel and I wrote deserve comment. Jerry had conjectured a characterization of beta X (the Stone-Cech compactification of X) and the three of us had proved that it was true. Then he dug up a 1939 paper by Gelfand and Kolmogoroff that Hewitt, in his big paper, had referred to but apparently not appreciated, and there we found Jerry’s characterization. The three of us sat around to decide what to do; we called it the ‘wake.’ Since the authors had not furnished a proof, we decided to publish ours. When the referee expressed himself strongly that a title should be informative, we came up with On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. (This proved to be my second-longest title, and a nuisance to refer to.) Kolmogoroff died many years ago, but Gelfand is still living, a vigorous octogenarian now at Rutgers. A year or so ago, I met him at a dinner party in Austin and mentioned the 1939 paper. He remembered it very well and proceeded to complain that the only contribution Kolmogoroff had made was to point out that a certain result was valid for the complex case as well. I was intrigued to see how the giants grouse about each other just as we do.”
— Leonard Gillman: An Interview
This clears up a question I asked earlier in this journal….
|
Wednesday, May 14, 2003 Common Sense On the mathematician Kolmogorov: “It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.” — Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003 That this theorem is Kolmogorov’s is news to me. See
The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses. Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case. A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15. This is cited by Gillman and Jerison in the classic Rings of Continuous Functions. There ARE some references that indicate Kolmogorov may have done some work of his own in this area. See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”). Any other references to Kolmogorov’s work in this area would be of interest. Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone. I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968. |
A response by Richard Cudney:
|
“In regard to your entry, it is largely correct. The paper by Kolmogorov and Gelfand that you refer to is the one that I just read in his collected works. So, I suppose my entry was unfair to Gelfand. You’re right, the issue of credit is a bit touchy since Gelfand was his student. In a somewhat recent essay, Arnol’d makes the claim that this whole thread of early work by Gelfand may have been properly due to Kolmogorov, however he has no concrete proof, having been but a child at the time, and makes this inference based only on his own later experience as Kolmogorov’s student. At any rate, I had known about Gelfand’s representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them. And to clarify-where I speak of the credit for this theorem being obscured, I speak of my own experience as an algebraic geometer and not a functional analyst. In the textbooks on algebraic geometry, one sees no explanation of why we use Spec A to denote the scheme corresponding to a ring A. That question was answered when I took functional analysis and learned about Gelfand’s theorem, but even there, Kolmogorov’s name did not come up. This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras. In historical terms, this result precedes Gelfand’s theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique. That is to say, this whole vein of Gelfand’s work started in this joint paper. Of course, to be even more fair, I should say that Stone was the very first to prove a theorem like this, a debt which Kolmogorov and Gelfand acknowledge. Stone’s paper is the true starting point of these ideas, but this paper of Kolmogorov and Gelfand is the second landmark on the path that led to Grothendieck’s concept of a scheme(with Gelfand’s representation theorem probably as the third). As an aside, this paper was not Kolmogorov’s first foray into topological algebra-earlier he conjectured the possibility of a classification of locally compact fields, a problem which was solved by Pontryagin. The point of all this is that I had been making use of ideas due to Kolmogorov for many years without having had any inkling of it.” |
Powered by WordPress
