(A sequel to the previous post, Multiplicity on Michaelmas.)
"Tony is on the couch . . ." Cf. The Analyst , Michaelmas evening.
"Tony Stark: That's how I wished it happened.
Binarily Augmented Retro-Framing, or BARF.
God, I gotta work on that acronym.
An extremely costly method of hijacking the
hippocampus to . . . clear traumatic memories. Huh."
"We need a multiplicity of viewpoints."
— Philip Pullman in a New Yorker interview
published yesterday
See as well Pullman's "Golden Compass"
in posts tagged
"The analyst, by freeing himself from the 'enchainment to past and future',
casts off the arbitrary pattern and waits for new aesthetic form to emerge,
which will (it is hoped) transform the content of the analytic encounter."
— From Psychoanalytic Aesthetics: The British School ,
by Nicola Glover, Chapter 4
"The 15 Puzzle and the Magic Cube
are spiritual kin …."
— "Metamagical Themas" column,
Douglas R. Hofstadter, Scientific American ,
Vol. 244, No. 3 (March 1981), pp. 20-39
As are the 15 Schoolgirls and the Eightfold Cube.
The previous post dealt with “magic” cubes, so called because of the
analogous “magic” squares. Douglas Hofstadter has written about a
different, physical , object, promoted as “the Magic Cube,” that Hofstadter
felt embodied “a deep invariant”:
Related literary remarks — Raiders of the Lost Birthday.
For Dan Brown fans — See posts now tagged Masonic Bricks.
Richard Sandomir in this evening's online New York Times —
|
On Sept. 24, 1950, Jimmy Nelson, a skinny 21-year-old ventriloquist, was introduced by Ed Sullivan on his Sunday night variety show, “Toast of the Town,” as “the greatest I’ve ever seen in his field.” Mr. Nelson was clean-cut and genial, with an air of boyish mischief. His dummy was a smart aleck in a suit and bow tie. “My name is Danny O’Day,” the dummy said to the audience. “This schnookle standing next to me is Jimmy Nelson. The kid thinks he’s a ventrickolist.” “That’s ventriloquist,” Mr. Nelson said, starting a rapid-fire exchange with his dummy. “Ventrickolist,” Danny said. “Ventriloquist,” Mr. Nelson said. It was an auspicious national debut…. |
Nelson reportedly died at 90 on Tuesday, September 24, 2019.
The remarks on Harvard existential nihilism posted here on that date
suggest a graphic illustration …
Venn trick o'list —
Nothing Galore
See as well a post from the preceding day,
Rabbit Hole Meets Memory Hole.
"… Max Black, the Cornell philosopher, and others have pointed out
how 'perhaps every science must start with metaphor and end with
algebra, and perhaps without the metaphor there would never have
been any algebra' …."
— Max Black, Models and Metaphors, Cornell U. Press, 1962,
page 242, as quoted in Dramas, Fields, and Metaphors, by
Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25
Metaphor —
Algebra —
|
The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):
1.
2.
3.
4.
5.
6. SEE ALSO: Pauli Matrices REFERENCES: Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 211-217, 1985. Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed. Oxford, England: Pergamon Press, pp. 80-84, 1982. Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms. New York: Plenum, pp. 47-48, 1977. Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics. New York: McGraw-Hill, 1964. Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed. Oxford, England: Oxford University Press, 1982. Goldstein, H. Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, p. 580, 1980. Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955. Referenced on Wolfram|Alpha: Dirac Matrices CITE THIS AS: Weisstein, Eric W. "Dirac Matrices."
From MathWorld— A Wolfram Web Resource. |
Desiring the exhilarations of changes:
The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being,
The ruddy temper, the hammer
Of red and blue, the hard sound—
Steel against intimation—the sharp flash,
The vital, arrogant, fatal, dominant X.
The 15 points of the finite projective 3-space PG(3,2)
arranged in tetrahedral form:
The letter labels, but not the tetrahedral form,
are from The Axioms of Projective Geometry , by
Alfred North Whitehead (Cambridge U. Press, 1906).
The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."
Screen Rant on July 31, 2019:
A Google Search sidebar this morning:
Apocalypse Soon! —
For Dan Brown
“It’s a combination of elation and fear, a certain kind of terror,”
Dr. Scott-Warren, a lecturer at Cambridge University, said
Thursday [Sept. 19] in an interview, describing his feelings.
“As a scholar, you get a sense of the fixed landmarks,” he said.
“Suddenly to have a new landmark to come right up through
the ground is quite disconcerting; there’s something alarming
about that.”
"A scholar in England suspected annotations in a First Folio
at the Free Library of Philadelphia were John Milton’s, so he
connected the dots . . . ." — The New York Times last Thursday
“It’s a combination of elation and fear, a certain kind of terror,”
Dr. Scott-Warren, a lecturer at Cambridge University, said
Thursday in an interview, describing his feelings.
“As a scholar, you get a sense of the fixed landmarks,” he said.
“Suddenly to have a new landmark to come right up through
the ground is quite disconcerting; there’s something alarming
about that.”
. . . .
"Dr. Scott-Warren … studies the history of books as material objects …."
"The sad truth is that, by and large, mathematics is feared
and perhaps even openly disliked in the popular culture of
the majority of countries across the globe. At the very least,
math is often perceived as 'hard' and 'sterile,' pehaps even
remote, and unforgiving."
— James Tanton, Halloween 2018
Related material —
Previous posts now tagged Pyramid Game suggest …
A possible New Yorker caption: " e . . . (ab) . . . (cd) . "
Caption Origins —
Playing with shapes related to some 1906 work of Whitehead:
"Robert Hunter, the man behind the poetic and mystical
words for many of the Grateful Dead’s finest songs, died
Sept. 23 at at his home in San Rafael, Calif. He was 78."
— By John Rogers in The Washington Post ,
September 24, 2019, at 5:58 p.m. EDT
In memoriam: The Annotated "Ripple."
|
Thursday, September 12, 2019
Tetrahedral Structures
|
Playing with shapes related to some 1906 work of Whitehead:
From a Log24 search for Dolgachev —
"The purpose of mathematics cannot be derived from
an activity inferior to it but from a higher sphere of
human activity, namely, religion."
— Igor Shafarevitch, 1973 remark published in 1982.
"Perhaps."
— Steven H. Cullinane, February 13, 2019
"Specifically, on May 6 of this year …." …
The "Dom" of the title is the cathedral of Cologne.
The DOM is the Document Object Model of HTML:
For more-recent existential vibrations, see yesterday morning's post
on a Crimson philosopher's "Finding Purpose Through Nihilism."
|
“We shall now give a brief summary of the beginnings of the Glass Bead Game…. The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads." |
Images from this journal related to the above cartoon —
(Click images for related posts.)
A sketch adapted from Girl Scouts of Palo Alto —
There is also finding purpose through dating —
(from the source code for the above Crimson article)
Related material — D8ing.
The disappearance of "Christo et Ecclesiae" at Harvard
Rabbit Hole
Memory Hole
The above Harvard seal in a PDF —
The same page, minus the seal, today at the Internet Archive —
For a larger image of the seal-less page, click here.
Click to enlarge.
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
"The bond with reality is cut."
— Hans Freudenthal, 1962
From page 180, Logicomix — It was a dark and stormy night …
"This is the relativity problem: to fix objectively a class of
equivalent coordinatizations and to ascertain the group of
transformations S mediating between them."
— Hermann Weyl, The Classical Groups,
Princeton University Press, 1946, p. 16
(Continued from November 27, 2010.)
The previous post suggests a review of a Tilman Piesk
illustration, with the general form of a 4-simplex, from
the Wikipedia article titled Simplex . As the article
notes, the lines shown connecting points are those of a
tesseract.
For Dan Brown fans …
… and, for fans of The Matrix, another tale
from the above death date: May 16, 2019 —
An illustration from the above
Miracle Octad Generator post:
Related mathematics — Tetrahedron vs. Square.
Detail from an OpenScholar tutorial —
The above phrase from Cicero means, according to
the usual translation, "explorer of truth."
Some may prefer a different translation of "inventore."
Related material —
See also A Counting-Pattern.
See other posts now tagged Six Dots.
Related narrative: Raiders of the Lost Ring .
"Mr. Dalachinsky was in his element on Sept. 14 at the Islip Art Museum
on Long Island, where he gave a reading after having attended a concert
by the Sun Ra Arkestra earlier that afternoon in Manhattan. Not long after
the reading, his wife said, he had a stroke and a cerebral hemorrhage.
He died the next day at Southside Hospital in Bay Shore. He was 72."
— Neil Genzlinger in The New York Times today
Also on Sept. 14 —
See as well Curse of the Fire Temple.
In the spirit of the Linz website in the previous post,
the title refers to New Yorker writer Adam Gopnik:
|
Tuesday, November 7, 2017
Polarities and Correlation
|
See also a search in this journal for Polarity + Correlation.
From the above aldaily.com link —
|
https://www.nybooks.com/articles/2019/10/10/ From a review of …
Trick Mirror: Reflections on Self-Delusion … as she grew up in Texas. In a way, she was primed for the illimitable expanse of the Internet by her Christian upbringing, which teaches its followers that everyone on earth is being watched by God. It gave her a flight of optimism, before this same system slowly but surely “metastasize[d] into a wreck”: “this feverish, electric, unlivable hell.” While the Internet was meant to allow you to reach out to any- and everyone without a hint of the cruel discriminations that blight our world, it turned into the opposite, a forum where individuals are less speaking to other people than preening and listening to themselves—turning themselves into desirable objects to be coveted by all. It became, that is, the perfect embodiment of consumer capitalism, where everything can be touted in the marketplace. How, Tolentino asks, did the idea take hold that “ordinary personhood would seamlessly adjust itself around whatever within it would sell”? How did our basic humanity come to be “reframed as an exploitable viral asset”? |
Related course — "History and Human Capital" at Harvard, a course
taught last spring by professors Claudia Goldin and Lawrence Katz —
Related reading — "Human Capital," by Claudia Goldin:
The above material suggested this post's title, "Das Humankapital ."
The same phrase is also the title of a perceptive website from Linz, Austria.
* For the alternative title, see a Wikipedia article on The Jew of Linz .
"… objects have a notion of 'this' or 'self.' " — Wikipedia
For related notions, see other posts tagged Quark Rock and …
"Before time began, there was the Cube." — Optimus Prime
See also this journal on the above date (Jan. 27, 2012).
Backstory: Search this journal for sciencenews.
Screen Rant on July 31, 2019 —
The above space PG(3,2), because of its close association with
Kirkman's schoolgirl problem, might be called "schoolgirl space."
See as well a Log24 post from the above Screen Rant date —
The above story's conclusion —
" … the current state of the art in quantum computing is still
not quite ready for solving anything but toy problems and
testing basic algorithms."
From "Annals of Square Space" (Log24, Sept. 3, 2019) —
" 'Before I go somewhere for a story, I have a certain understanding of
what form it will take, and when I get there, it’s always far, far more
complicated,' says the journalist and poet Eliza Griswold, over lunch
in Gramercy Park. 'They begin with a neat little bow' — she pantomimes
tying it, her wide blue eyes growing wider — 'and then: kaboom.' ”
— VOGUE Lives: Eliza Griswold, August 27, 2010, 9:10 AM,
by Megan O'Grady
"There is such a thing as a 4-set." — Saying adapted
from a 1962 young-adult novel.
Midrash — An image posted here on August 6 —
* A reference to a Harvard Crimson article from February 28, 1963.
Excerpt from a long poem by Eliza Griswold
in the current New Yorker —
Related material:
See as well, from the fiftieth anniversary of Gropius's death,
Log24 posts now tagged Gropius Moritat.
"Elementary particles are the most fundamental building blocks
of nature, and their study would seem to be an expression of
simplification in its purest form. The essence of complexity
research, by contrast, is the emergence of new kinds of order
that are only manifest when systems are large and messy."
— Sean Carroll in an opinion piece that concludes as follows:
The above plug for Sean Carroll's book
The Big Picture : On the Origins of
Life, Meaning, and the Universe Itself suggests…
"Changes interlock…." — John Dewey
Indeed they do.
See also Log24 remarks from the date of Greene's death
in posts now tagged Bregnans.
A page related to Eleanor Cook's "wonderful first line"
quoted above from A Reader's Guide to Wallace Stevens :
A Reader's Guide to Eleanor Cook —
From "Six Significant Landscapes," by Wallace Stevens (1916) —
VI
Rationalists, wearing square hats,
Think, in square rooms,
Looking at the floor,
Looking at the ceiling.
They confine themselves
To right-angled triangles.
If they tried rhomboids,
Cones, waving lines, ellipses —
As, for example, the ellipse of the half-moon —
Rationalists would wear sombreros.
But see "cones, waving lines, ellipses" in Kummer's Quartic Surface
(by R. W. H. T. Hudson, Cambridge University Press, 1905) and their
intimate connection with the geometry of the 4×4 square.
See "Politics of Experience" and "Blue Guitar."
"Behold, I stand at the door, and knock." — Rev. 3:20
For Harlan Kane — The 3:20 Midrash:
|
"… the walkway between here and there would be colder than a witch’s belt buckle. Or a well-digger’s tit. Or whatever the saying was. Vera had been hanging by a thread for a week now, comatose, in and out of Cheyne-Stokes respiration, and this was exactly the sort of night the frail ones picked to go out on. Usually at 4 a.m. He checked his watch. Only 3:20, but that was close enough for government work."
— King, Stephen (2013-09-24). |
In memory of a Church emissary who reportedly died on September 4,
here is a Log24 flashback reposted on that date —
Related poetry —
"To every man upon this earth,
Death cometh soon or late.
And how can man die better
Than facing fearful odds,
For the ashes of his fathers,
and the temples of his gods…?"
— Macaulay, quoted in the April 2013 film "Oblivion"
Related fiction —
From the previous post —
" . . . Only by the form, the structure,
Can words or music reach
The stillness . . . ."
— Adapted from T. S. Eliot's Four Quartets
by replacing "pattern" with "structure."
In memory of George F. Simmons, a mathematician
who reportedly died Aug. 6 at the age of 94 —
"It seems to me that a worthwhile distinction can be made
between two types of pure mathematics. The first …
centers attention on particular functions and theorems
which are rich in meaning and history…. The second is
concerned primarily with form and structure."
— George F. Simmons, Introduction to Topology and
Modern Analysis (1963)
" . . . Only by the form, the structure,
Can words or music reach
The stillness . . . ."
— Adapted from T. S. Eliot's Four Quartets
by replacing "pattern" with "structure."
Two posts related to Eliot's theological interests:
Form: Jan. 10, 2012.
Structure: June 6, 2016.
… Continued from previous posts now tagged Art Logos.
"Logos," a Greek word used in philosophy and theology,
is, in modern usage, also a brief form of "logotypes,"
a name for the branding symbols used by businesses.
For some less commercial aspects of the philosophical
concept, see Logo in this journal.
See also this morning's previous post, Peacock News.
"And all of the colors are black." — Paul Simon
* The title of course refers to the NBC logo.
See also other instances of "Peacock" in this journal.
* From earlier posts containing the title phrase.
Neil Montanus, a Kodak Colorama Photographer, Dies at 92
His colossal pictures, depicting an idealized American life,
greeted travelers at Grand Central Terminal for decades.
Katharine Q. Seelye in The New York Times —
Mr. Montanus was 92 when he died on Friday
under hospice care in Rochester, his son Jim said.
Robert Frank Dies; Pivotal Documentary Photographer Was 94
Mr. Frank, who was best known for his groundbreaking book,
“The Americans,” had a visually raw and personally expressive
style that made him one of the most influential photographers
of the 20th century.
Philip Gefter in The New York Times —
Robert Frank, one of the most influential photographers
of the 20th century, whose visually raw and personally
expressive style was pivotal in changing the course of
documentary photography, died on Monday in Inverness,
Nova Scotia. He was 94.
"And everything looks worse in black and white." — Paul Simon
For Harlan Kane
From this journal on Feb. 5, 2009:
"In the garden of Adding
live Even and Odd…
And the song of love's recision
is the music of the spheres."
— The Midrash Jazz Quartet in
City of God , by E. L. Doctorow (2000).
From this journal on the date of
the above post by Gavaler:
See as well an obituary for Mrs. Wertham from 1987.
Related art —
Friday, July 11, 2014
|
For further details, search the Web for "Wertham Professor" + Eck.
(For Harlan Kane)
"While digging in the grounds for the new foundation,
the broken fragments of a marble statue were unearthed."
— From Thomas Hardy, "Barbara of the House of Grebe,"
quoted in an epigraph to Paul de Man's "Shelley Disfigured,"
in turn quoted by Barbara Johnson on page 231 of Persons
and Things (Harvard paperback, 2010).
From "the world of the unintentional, the contingent, the minute,
and the particular" (Kovacevic, U. of Montenegro, 2011) —
Yes, we received your payment. No, it wasn't late, but it was for $78.13, and the bill was for $78.31. Okay, great. Read more: https://www.springfieldspringfield.co.uk/ movie_script.php?movie=the-circle
Another such transposition: Pages 213 and 231 in a search
for "gaps" in a 2010 paperback discussion of Lacan —
These pages are as follows —
(The above title was suggested by today's "Child-Resistant 4×4.")
* Specifically, resistant to the above revelation attributed to Barbara Johnson
by Harvard University Press —
"Deconstruction calls attention to gaps and reveals
that their claims upon us are fraudulent."
A related search at Amazon.com:
Barbara Johnson explains Lacan:
" The 'gap' in the real is the leap
from the empirical to
the signifying articulation
of the object of desire;
it cannot be perceived empirically.
It is 'nothing.' "
— Persons and Things , paperback (2010),
Harvard University Press, page 213
“By groping toward the light we are made to realize
how deep the darkness is around us.”
— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118
"Fury: OK. Your turn. Prove you're not a Skrull.
[Carol calmly blasts energy out of her fists towards a jukebox
on the opposite side of the room before resting her head
back on her fist. Fury continues to look towards the jukebox,
both concerned and confused]
Fury: And how is that supposed to prove to me that you're not a Skrull?
Carol: It's a photon blast.
Fury: And…?
Carol: A Skrull can't do that. So a full-bird colonel turned spy turned
SHIELD agent must have pretty high security clearance. Where's Pegasus?
[The scene changes to a black car driving through an empty highway
next to a mountain, before changing to the inside of the car showing Fury
driving and Carol in the passenger seat]
Fury: So the Skrulls are alien races which infiltrate and overtake alien planets.
And you're a Kree, a race of noble warriors.
Carol: Heroes. Noble warrior heroes."
* See also this morning's post in memory of guitarist Jimmy Johnson,
as well as . . .
"New York Fashion Week is scheduled Friday, September 6 through
Wednesday, September 11. View the preliminary schedule here. …
UPDATED AS OF: Thu 08/29/19"
— https://cfda.com/fashion-calendar/official-nyfw-schedule
View also a fashion photo from this journal on 08/29/19 —
I do not know where the above tank top can be purchased.
In memoriam: Guitarist, studio engineer Jimmy Johnson, 1943-2019 .
Johnson reportedly died on Thursday, Sept. 5.
See also, from the first of the seven posts of Thursday, August 29 —
* See a reference to that literary saloon from June 11, 2013.
The title, from Doreen St. Félix (previous post),
is irresistible. Details to flesh it out will follow.
Update of 12:41 PM – See Brosnan in Urge .
"Letting someone speak does not mean we condone
what they are saying, and it does not absolve that person
or group from consequences. And when we disagree,
we have an obligation to respond earnestly."
— Harvard College dean Rakesh Khurana in an undated
"Welcome Home" message to returning students (Fall, 2019)
An earnest response from this journal —
See as well a webpage from 2000,
"Symmetry from Plato to the
Four-Color Conjecture."
"When you come to a fork . . . ." — Yogi Berra (?)
The Observable site does not work in my Chrome browser.
To play with it, use Firefox. For a more straightforward
JavaScript program see the Diamond 16 Puzzle.
A link, observablehq.com/demo, (not functioning in my Chrome
browser at the present time but apparently OK in Firefox) in the
previous post suggests . . .
"Physically meaningful observables must also satisfy
transformation laws which relate observations
performed by different observers in different
frames of reference. These transformation laws are
automorphisms of the state space, that is
bijective transformations which preserve certain
mathematical properties of the space in question."
— Wikipedia, Observable
Those who prefer narrative to mathematics may read
"automorphisms" as "auto morphisms."
"Before time began . . . ." — "Transformers" first line, 2007
At present, the above Ajna page is not functioning in my Chrome browser
and is only partly functioning in Edge, but seems OK in Firefox.
Illustration from other posts now tagged
Cervantes Meets Pascal.
See as well Verhexung in this journal.
This post was suggested by . . .
Down the Up Ladder
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