From this journal on September 24, 2012—
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"A single self-transcendence" — Aldous Huxley
From an anonymous author at the website
"This little story… has that climactic moment of Kill Devil Hills also appears in a 1983 film—
"Suppose it were possible to transfer
— Trailer for "Brainstorm" (1983), |
"… that 'good' threshold . . . ." — See Threshold in this journal.
The "Where is the fourth?" question above is also by Plato.
One possible answer . . .
Other possible "fourth" locations . . .
Pizza photo credit: Marcela Nowak on Instagram
"Today, we are considered a joke."
— Red Party candidate in Schnecksville, PA
on Saturday, April 13, 2024.
See as well Schneck in this journal —
Ben Affleck sings "Aquellos Ojos Verdes"
at the end of "Hollywoodland."
This post was suggested by the death on a Beltane
of Solomon Golomb and by the appearance of
Prof. Colva M. Roney-Dougal in a CV linked to
here on yesterday's MIchaelmas morning.
For Neumann himself, see Planet Princeton.
https://www.cbsnews.com/news/book-excerpt-
revenge-of-the-tipping-point-by-malcolm-gladwell/
"In 2000, Malcolm Gladwell published the first of several bestselling books,
'The Tipping Point,' in which he applied the laws of epidemics to promote
positive social change. Now, he's returned to that optimistic book's lessons
in 'Revenge of the Tipping Point' (to be published October 1 by
Little, Brown & Co.), to examine the flip side of those theories."
That publication date suggests a review of "October the First is Too Late."
From The New York Times on Michaelmas 2024 —
Mathematician-programmer Lana Creal reportedly died on Sept. 14.
An image reposted in this journal on that date —
Notes on some other women in mathematics —
Embedded in the Sept. 26 New Yorker review of Coppola's
Megalopolis is a ghostly transparent pyramidal figure . . .
The pyramidal figure is not unrelated to Scandia.tech —
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American Mathematical Monthly, Vol. 92, No. 6 LETTERS TO THE EDITOR Material for this department should be prepared exactly the same way as submitted manuscripts (see the inside front cover) and sent to Professor P. R. Halmos, Department of Mathematics, University of Santa Clara, Santa Clara, CA 95053 Editor: Miscellaneum 129 ("Triangles are square," June-July 1984 Monthly ) may have misled many readers. Here is some background on the item. That n2 points fall naturally into a triangular array is a not-quite-obvious fact which may have applications (e.g., to symmetries of Latin-square "k-nets") and seems worth stating more formally. To this end, call a convex polytope P an n-replica if P consists of n mutually congruent polytopes similar to P packed together. Thus, for n ∈ ℕ, (A) An equilateral triangle is an n-replica if and only if n is a square. Does this generalize to tetrahedra, or to other triangles? A regular tetrahedron is not a (23)-replica, but a tetrahedron ABCD with edges AB, BC, and CD equal and mutually orthogonal is an n-replica if and only if n is a cube. Every triangle satisfies the "if" in (A), so, letting T be the set of triangles, one might surmise that (B) ∀ t ∈ T (t is an n-replica if and only if n is a square). This, however, is false. A. J. Schwenk has pointed out that for any m ∈ ℕ, the 30°-60°-90° triangle is a (3m2)-replica, and that a right triangle with legs of integer lengths a and b is an ((a2 + b2)m2)-replica. As Schwenk notes, it does not seem obvious which other values of n can occur in counterexamples to (B). Shifting parentheses to fix (B), we get a "square-triangle" lemma:
(C) (∀ t ∈ T, t is an n-replica) if and only if n is a square.
Steven H. Cullinane
501 Follett Run Road Warren, PA 16365 |
(Continued from May 2, 2023 and December 18, 2022)
Harmonic analysis based on the circle involves the
circular functions. Dyadic harmonic analysis involves …
Summary, as an illustration of a title by George Mackey —
From a Sept. 23 New York Times article headlined
"Is Math the Path to Chatbots
That Don’t Make Stuff Up?
Chatbots like ChatGPT get stuff wrong.
But researchers are building new A.I.
systems that can verify their own math
— and maybe more."
The article is about an AI startup named "Harmonic."
From a Times photo illustrating the article —
See also the word "harmonic" in this journal yesterday.
The word "whiteboard" in this journal is also instructive.
Iris Murdoch as above —
"… even Hamlet looks second-rate compared with Lear.
Only the very greatest art invigorates without consoling,
and defeats our attempts, in W. H. Auden's words,
to use it as magic."
"Francis Ford Coppola
Re-enters a Changed Hollywood.
It Could Be Rough."
Brooks Barnes in The New York Times today —
"Hollywood marketers tend to use a playbook that begins with
boiling a movie down to a single, salable genre. Is this a comedy
or a drama? It can’t be both, they will tell you. Consumers want
a clear idea of what they are getting. Strong reviews can help,
but only to a degree.
But 'Megalopolis' is unboilable. It’s an avant-garde, dystopian,
science-fiction fable that veers into satire, fever dream, mystery,
romance and comedy."
The New York Times today reports the Oct. 17, 2023,
death of a man who "flipped, violating the mafia’s solemn
oath of loyalty, Omertà."
And then there is academic Omertà.
See
Hemispheres: The Old Up-Down Flip
and
For more amusement from Toronto, see today's Toronto Sun .
Related material — Last Sunday's post in this journal
From a post on "Matrix Bingo" —
From a Log24 search for "Women's Night" —
The Mackey material, from St. Patrick's Day 2006, suggests a look
at the angels of Noah Jacobs' 1958 classic Naming Day in Eden —
Jacobs on angels —
"Their sensuous functions have been extinguished so that they
have no idea of sensible images, metaphor, tones or gestures.
They have no need in their noumenal sphere of these seductive
and puzzling artifices. Their penchant for unashamed abstraction
is the deepest strain in their make-up."
Compare and contrast —
Quilts (for instance) as "seductive and puzzling artifices"
that embody symmetry.
Quilt geometry as the exploitation of symmetry.
From the post Belgian Puzzle Art —
Related reading . . .
— "The Devil, unlike the angels, was at home in the world of phenomena.
He knew how to combine pure concepts with empirical intuitions …
which is the basic principle of linguistic creation."
(Noah Jonathan Jacobs, Naming-Day in Eden, Macmillan, 1958 …
In Macmillan 1969 revised edition, page 21.)
The figure of 25 parts discussed in
"On Linguistic Creation"–
— "Such is the square dance of Numbers."
(Jacques Derrida, Dissemination, 1972)
— "It all adds up."
(Saul Bellow, book title, 1994)
For related rotations, see
"Turn your head around."
(Now tagged as "The Turning")
Related geometric meditations —
The Narnia Catechism: Is it Time Variants or Time Variance ?
Welcome to the Time Variance Authority!
Vide, from the above Jesuit date, the post
"Catchphrases from the city of Angels."
The "Cara.app" name in the previous post suggests . . .
Other "techniques d'avant garde" in 1985 —
85-03-26… Visualizing GL(2, p)
85-04-05… Group actions on partitions
85-04-05… GL(2, 3) actions on a cube
85-04-28… Generating the octad generator
85-08-22… Symmetry invariance under M12
85-11-17… Groups related by a nontrivial identity
The previous post, on art theory, suggests a look at art practice.
See as well a rather different look at Aiello on the above YouTube date.
"Asteras eisathreis . . . ." — Plato
This figure from a post of April 29, 2008 is related to remarks
by art theorist Rosalind Krauss in tonight's previous post.
Related language —
"Kernel" in mathematics and "Innerste Kern." elsewhere.
Related philosophy —
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
— Wittgenstein, Philosophical Investigations (1953), Section 109
The New York Times yesterday reported that Marxist theorist
Fredric Jameson died on Sunday.
Related material from a search for Jameson in this journal —
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Rosalind Krauss in The Optical Unconscious
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"The personalities come and go in kaleidoscopic succession,
many changes often being made in the course of twenty-four hours."
"By a breaking up of the original personality at different moments
along different lines of cleavage, there may be formed several different
secondary personalities which may take turns with one another."
— Morton Prince, The Dissociation of a Personality ,
Longmans, Green, and Co., 1906, pages 2 and 3.
Related reading . . .
"Sometimes a wind comes before the rain
and sends birds sailing past the window,
spirit birds that ride the night,
stranger than dreams."
— The end of DeLillo's Point Omega
Meanwhile on that YouTube date . . .
"You probably couldn't come up with a more stinging metaphor for how
fame, for all its sensation and glitter, ultimately becomes a tombstone."
The black rectangle below is
known as the "end-of-proof symbol,"
"Halmos," or "tombstone."
* See the previous post, "Raiders of the Lost Box."
The "Facets" tag in this morning's previous post,
"The Portable Divinity Box," suggests a look at
Box759.
In 1978, Harvard moved a structure known as the Morton Prince House
from Divinity Avenue to Prescott Street, where it occupies the former Hurlbut
Parking Lot, which was the vista from my 1960-61 freshman room.
From the Log24 post "Very Stable Kool-Aid" —
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A Letter from Timothy Leary, Ph.D., July 17, 1961
Harvard University July 17, 1961
Dr. Thomas S. Szasz Dear Dr. Szasz: Your book arrived several days ago. I've spent eight hours on it and realize the task (and joy) of reading it has just begun. The Myth of Mental Illness is the most important book in the history of psychiatry. I know it is rash and premature to make this earlier judgment. I reserve the right later to revise and perhaps suggest it is the most important book published in the twentieth century. It is great in so many ways–scholarship, clinical insight, political savvy, common sense, historical sweep, human concern– and most of all for its compassionate, shattering honesty. . . . . |
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Morton Prince, a Boston neurologist, founded the Journal of Abnormal Psychology in 1906 as an outlet especially for those who took a psychogenic view of neurotic disorders. Through experiments with hypnotism, he added appreciably to knowledge of subconscious and coconscious mental processes; The Dissociation of a Personality (Prince, 1905) still ranks as a classic. He early saw that studying normal people in the depth and detail with which one studied patients could make significant contributions to our whole understanding of human nature. Before his death he established and briefly directed the Harvard Psychological Clinic, devising the research environment out of which presently sprang major contributions to the study of personality.
— "Who Was Morton Prince?," by R. W. White, |
See as well Who Was R. W. White?
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CBS Sunday Morning today suggests a review of an old post featuring Pearl Jam. From that post . . . Mathematics and Narrative, continued… Out of What Chaos, a novel by Lee Oser— "This book is more or less what one would expect if Walker Percy wrote about a cynical rock musician who converts to Catholicism, and then Nabokov added some of his verbal pyrotechnics, and then Buster Keaton and the Marquis de Sade and Lionel Trilling inserted a few extra passages. It is a loving and yet appalled description of the underground music scene in the Pacific Northwest. And it is a convincing representation of someone very, very smart." "If Evelyn Waugh had lived amid the American Northwest rock music scene, he might have written a book like this." –Anonymous Amazon.com reviewer A possible source for Oser's title– "…Lytton Strachey described Pope's theme as 'civilization illumined by animosity; such was the passionate and complicated material from which he wove his patterns of balanced precision and polished clarity.' But out of what chaos did that clarity and precision come!" —Authors at Work, by Herman W. Liebert and Robert H. Taylor, New York, Grolier Club, 1957, p. 16 |
"Before time began . . . ." — Optimus Prime
I noticed this favicon on Sept. 18 (see post) at a publisher's webpage.
It turns out that it is not specific to the publisher, but rather to sites
hosted by Squarespace.com. For instance . . .
See also a post on Christmas Day, 2013.
Related material from the Sept. 18 post mentioned above —
"When things go bonkers, you have to adapt."
— Chris Hemsworth as Dementus in "Furiosa" (2024)
"Before time began, there was the Cube."
— Optimus Prime in "Transformers" (2007)
Today, an animated Transformers opens, with
Chris Hemsworth as the voice of Optimus Prime.
Also today: The new tag "Cubehenge" in this journal.
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The Ring and the Stone
From Many Dimensions, a novel "This Holy Thing has been kept in seclusion," Ibrahim answered, "through many centuries, and in all that time none of its keepers have approached or touched it. And since Giles Tumulty stole it men have grasped at it in their own wisdom. But this woman has put her will at its disposal, and between it and her the union may be achieved by which the other Hiddenness is made manifest." "What is the other Hiddenness?" Lord Arglay asked. The Hajji hesitated, then he turned his eyes back to Chloe and seemed to ask a question of her. What answer he saw on the forehead at which he gazed she could not guess, but he spoke then in a low and careful voice. "In the Crown of Suleiman the Wise-the Peace be upon him!-" he said, "there was a Stone, and this Stone was that which is the First Matter of Creation, holy and terrible. But on the hand of the King there was a Ring and in the Ring was another secret, more holy and terrible than the Stone. For within the Ring there was a point of that Light which is the Spirit of Creation, the Adornment of the Unity, the Knowledge of the Loveliness, the Divine Image in the mirror of the worlds just and true. This was the justice and the Wisdom of Suleiman, by which all souls were made manifest to him and all causes rightly determined. Also when within the Holy of Holies in the Temple that the King made he laid his crown upon the Ark and between the wings of the Cherubim, and held his hand over it, the Light of the Ring shone upon the Stone and all things had peace. But when the King erred, building altars to strange gods, he dared no longer let the Light fall upon the Stone; also he put aside the Ring and it is told that Asmodeus sat upon his throne seven years. But I think that perhaps the King himself had not all that time parted from his throne, how closely soever Asmodeus dwelt within his soul. And of the hiding place of the Ring I do not know, nor any of my house; if it is on earth it is very secret. But the Light of it is in the Stone and all the Types of the Stone-and the Power of it is in the soul and body of any who have sought the union with the Stone, so that whoever touches them in anger or hatred or evil desire is subjected to the Light and Power of the Adornment of the Unity. And this I think my nephew did, and this is the cause of his blasting and hurling out." He looked straight at Chloe. "But woe, woe, woe to you," he said, "if from this time forth for ever you forget that you gave your will to the Will of That which is behind the Stone." |
This post was suggested by a Friday the Thirteenth death.
From August 10 —
Earlier . . .
Still earlier . . .
"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."
— Wittgenstein, Philosophical Investigations (1953), Section 109
Brooke Shields at the 2024 Tony awards —
"As the newly elected president of Actors Equity Association,
I am so proud to be here to celebrate the entire theatrical community,"
the actress, 59, said." — People online, June 16, 2024 11:13 PM EDT
Continuing yesterday's "Bell, Book and Candle" theme . . .
[Such lines and planes have not been, in mathematical language,
"translated."]
— Paul R. Halmos, Finite Dimensional Vector Spaces,
Princeton University Press, 1948, page 14
Candle from Sense8, Season 1, Episode 1: “Limbic Resonance”
"When things go bonkers, you have to adapt." — From "Furiosa" (2024)
Click the "timelessness" quote below for the "Bell, Book and Candle" scene
with Kim Novak and James Stewart atop the Flatiron Building.
"Before time began . . . ." — Optimus Prime
The writer whose elegance was reportedly described as above
by Rolling Stone was Nick Tosches.
Related reading . . .
Here Drucker is promoting a merchandiser of magic crystals.
I prefer the artist on the right.
* For the Omensetter of the title, see a post of Oct. 10, 2018.
Continued from August 9, 2024.
Today 's previous post was on Ch. 6 of Selig's Geometric Fundamentals.
Ch. 9 is on Clifford Algebra.
"Living out my Audrey in Charade fantasies"
— Lily Collins on Instagram yesterday.
This journal on the Ides of March, 2006 —
Gallia est omnis divisa in partes tres,
quarum unam incolunt Belgae,
aliam Aquitani, tertiam qui ipsorum
lingua Celtae, nostra Galli appellantur.
Some less stressful material . . .
"a medley cobbled together" —
By Adam Gopnik
February 27, 2012
The New Yorker
Gopnik says that a female figure from the Book of Revelation,
"The Big Reveal,"
"suggests the women evangelists who were central
to Paul’s version of the movement and anathema
to a pious Jew like John. She is the original
shiksa goddess."
Related imagery —
"The state of Florida will be
conducting its own investigation . . . ."
As will Miss Minutes.
Dædalus, the Journal
of the American Academy of Arts & Sciences
Related readings —
Clicking the Xbox icon on a Windows lockscreen today yielded . . .
See as well . . .
See the previous post as well as posts
now tagged Hard Gray Stone.
Related art notes:
A passage accessed via the new URL Starbrick.art* —
Thursday, February 25, 2021
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A related cultural note suggested by the New York Times obituary today
of fashion designer Mary McFadden, who reportedly died yesterday
(a Friday the Thirteenth) and is described by the Times as a late-life
partner of "eightfold-way" physicist Murray Gell-Mann —
* A reference to the 2-column 4-row matrix (a "brick") that underlies
the patterns in the Miracle Octad Generator of R. T. Curtis. The only
connection of this eight-part matrix to Gell-Mann's "Eightfold Way"
that I know of is simply the number 8 itself.
The previous post's Wired reference to a seven-year AI project
suggests a review of this journal seven years ago . . .
From "Inside Google's 7-Year Mission
to Give AI a Robot Body" —
Or not.
Welcome to the towel room.
From a Log24 post of February 26, 2024 —
The URL https://tri.be
of the design firm Modern Tribe . . .
Some will prefer other digital gateways . . .
Amy Adams in The Master
From Yeats's sequel to "Sailing to Byzantium,"
titled simply "Byzantium" —
Astraddle on the dolphin's mire and blood,
Spirit after spirit! The smithies break the flood,
The golden smithies of the Emperor!
Marbles of the dancing floor
Break bitter furies of complexity,
Those images that yet
Fresh images beget,
That dolphin-torn, that gong-tormented sea.
The New York Times asks above,
"Are art and science forever divided?
Or are they one and the same?"
A poet's approach . . .
“The old man of ‘Sailing to Byzantium’ imagined the city’s power
as being able to ‘gather’ him into ‘the artifice of eternity’—
presumably into ‘monuments of unageing intellect,’ immortal and
changeless structures representative of or embodying all knowledge,
linked like a perfect machine at the center of time.”
— Karl Parker, Yeats’ Two Byzantiums
A mathematician's approach . . .
Compare and contrast the 12-dimensional extended binary Golay code
with the smaller 8-dimensional code below, which also has minimum
weight 8 . . .
From Sept. 20, 2022 —
Perhaps someone can prove there is no way that adding more generating
codewords can turn the cube-motif code into the Golay code, or perhaps
someone can supply such generating codewords.
See also other posts tagged Farago in this journal.
Three properties of space — interlocking, interlacing, interweaving.
— "One, two, three … but where is the fourth?"
— "Socrates, the fourth, intertwining, is at . . .
http://m759.net/wordpress/?p=93725 ."
Musical accompaniment — "Will the circle be unbroken?"
A hymn I personally prefer —
"The stuff that dreams are made of."
The above YouTube date — June 3, 2018 —
in this journal leads to . . .
https://openprocessing.org/sketch/105458 . . .
Diamonds Studio Generative Identity
by Radamés Ajna
And then there is another quiet flow . . .
A rumored work in progress from East Berlin . . .
Softly Flows the Conewago
by East Berlin author Nancy Springer
Also by Springer —
“They are the horses of a dream.
They are not what they seem.”
— The Hex Witch of Seldom, page 16
See as well a dies natalis — January 6, 2016 —
that shares an Epiphany with the Guardian's
"Nobel losers" article . . .
Today's previous post presented historic logos of
the ABC that is the Australian Broadcasting Corporation.
An exact quote from tonight's broadcast on an American
ABC network —
"I meet with people all the time who tell me,
can we please just have discourse about
how we're going to invest in the aspirations and
the ambitions and the dreams of the American people…."
— Blue Party candidate
Her debate opponent, the Red Party candidate,
might well have replied . . .
"I meet with people all the time who tell me,
I'm mad as hell and I'm not going to take it any more!"
Related art from this journal:
The September 5 post Make Hollywood Sane Again —
"… dum frater sororis suae automata per clostellum miratur …."
Related reading . . .
"At the end of a long road was a drive that led to a large house . . . ."
Orthodox:
Unorthodox:
Related mathematical vocabulary . . .
OH, A COVER IS NOT THE BOOK
SO OPEN IT UP AND TAKE A LOOK
CAUSE UNDER THE COVERS ONE DISCOVERS . . . .
Now added to a Likewise.com list —
The Portage to San Cristobal of A. H.
Related reading —
On a letter from Hebrew, the fentanyl of languages —
Today's host for a special political edition of CBS Sunday Morning
is Ted Koppel. Vocabulary review:
Koppel's appearance today was backed by the usual CBS Sunday Morning
sun-disk Apollo symbol. An Apollo symbol that some may prefer —
The Ninefold Square
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Rosalind Krauss "If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete. Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal— or, according to Krauss,
"This is the garden of Apollo, the field of Reason…." |
… in posts tagged Kummer-Sept-2013.
Musical accompaniment suggested by
tonight's earlier Paradise Dreams —
I have my own dreams of paradise, but will settle for companionship that is
merely purgatorial.
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Jessica H: My parents' usual ritual was that shortly before Dad's expected arrival at home, Mom would freshen up in preparation. She put on a little lipstick, take off her apron sometimes, and maybe change her blouse, splash on some perfume, and when Dad was home and settled in his favorite chair in the living room, they'd pour drinks and discuss the events of the day, his day. Some months ago my mother gave me an article that she'd found from the 1950's that offered tips to women on the proper way to welcome your man at home after a hard day's work. She read me those guidelines and her comments on them revealed that she had fooled us all. While back in the day she had seemed to be that era's model of a perfect housewife, she was actually downright subversive. Eleanor H: "Prepare yourself, take 15 minutes to rest so you will be refreshed when he arrives." Meanwhile, the kids are throwing their blocks out the window. Jessica H: (laughs) Eleanor H: "Touch up your makeup, put a ribbon in your hair." If I put a ribbon in my hair my husband would leave home. "Be fresh looking, be a little gay and a little more interesting." If he's so bored he should change jobs. "He Probably needs a lift." Eleanor H: "Prepare the children." Make sure you have just one. (laughs) Jessica H: (laughs) Eleanor H: "Take a few minutes to wash their hands and faces. They are little treasures, and he would like to see them like that." Well, wouldn't we all. (laughs) Jessica H: (laughs) Eleanor H: "Be happy to see him, greet him with a smile, and be glad to see him." One more mouth to feed. "Have dinner (laughs) have dinner ready." He doesn't care a thing about dinner, he wants his drink. "Most men are hungry when they come home." Here you are meat loaf, mashed potatoes. Stuff it down 'cause I worked hard on it. Jessica H: (laughs) Eleanor H: "Have him lean back into a comfortable chair, or suggest that he lie down in the bedroom." How about suggesting that we both lie down in the bedroom? Jessica H: (laughs) Eleanor H: "Make the evening his. Never complain if he doesn't take you out to dinner or to other places of entertainment." You could just rot instead. (laughs) "Try to understand his world of strain and pressure." What about my world of strain and pressure? "Try to make your home a place of peace and order, where your husband can renew himself in body and spirit," while you go down the tubes. Jessica H: (laughs) As mom said, she understood that what Dad really required was a drink. He needed to be defused, and we kids steered clear of that living room until that essential transition from sober to tipsy had taken place. Sometimes when my brother Charlie was a little older, nine or ten, he'd venture into their space, but only very cautiously. — http://www.winnetkapodcast.com/episode-6-transcript
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