Remember him to Herald Square.
Monday, November 10, 2014
Meanwhile, Back in 1962…
Thursday, September 27, 2012
April 9, 1962
The "1961" Oscars ceremony shown above was for the films of 1961.
The ceremony itself was held on April 9, 1962.
For a different Tiffany, see Tuesday's Another Day.
Saturday, April 10, 2021
Possibility
The previous post, on a Joyce symposium in
Utrecht on June 15-20, 2014, suggests a review
of this journal in June 2014. From June 21
of that year —
“Without the possibility that
an origin can be lost, forgotten,
or alienated into what springs
forth from it, an origin could
not be an origin. The possibility
of inscription is thus a necessary
possibility, one that must always
be possible.”
— Page 157 of The Tain of the Mirror:
Derrida and the Philosophy of Reflection ,
by Rodolphe Gasché, Harvard U. Press, 1986
Related art suggested by the above modal logic —
Wednesday, February 17, 2021
Raiders of the Lost Coordinates . . .
From posts tagged Tetrahedron vs. Square —
“There is such a thing as a 4-set.“
— Saying adapted from a 1962 young-adult novel.
Illustration (central detail a from the above tetrahedral figure) —
A Harvard Variation
from Timothy Leary —
The topics of Harvard and Leary suggest some other cultural
history, from The Coasters — “Poison Ivy“ and “Yakety Yak.”
Wednesday, February 3, 2021
Art of the Possible
Sunday, January 10, 2021
From Fly-Bottle
Illustrations from posts now tagged Ved Mehta in this journal —
Epigraph to Fly and the Fly-Bottle: Encounters with British Intellectuals ,
by Ved Mehta , remarks first published in The New Yorker in 1961 and 1962 —
See as well the Wallace Stevens phrase “The Ruler of Reality.”
Tuesday, December 29, 2020
Memorial by Kinbote for Cardin: WWW
A Harvard student* attempts to summarize Nabokov’s aesthetics —
“Take ‘Pale Fire,’ his 1962 poem-as-novel
bursting with butterfly as theme:
‘I can do what only a true artist can do —
pounce upon the forgotten butterfly of revelation …
see the web of the world,
and the warp and the weft of that web.’ “
“True artist” here refers to Kinbote, not Nabokov.
* Tessa K.J. Haining, Harvard Crimson Contributing Opinion Writer.
Tessa K.J. Haining ’23 lives in Adams House. Her column appears on
alternate Fridays. December 11, 2020.
Saturday, October 17, 2020
Modernist Cuts
“The bond with reality is cut.”
— Hans Freudenthal, 1962
Related screenshot of a book review
from the November AMS Notices —
Thursday, August 20, 2020
“One More Reality Show”
Monday, July 13, 2020
Unpoetic License
The above novel uses extensively the term “inscape.”
The term’s originator, a 19th-century Jesuit poet,
is credited . . . sort of. For other uses of the term,
search for Inscape in this journal. From that search —
A quote from a 1962 novel —
“There’s something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz.”
Addendum for the Church of Synchronology —
The Joe Hill novel above was published (in hardcover)
on Walpurgisnacht —April 30, 2013. See also this journal
on that date.
Thursday, June 11, 2020
Software Engineering I Prefer
Tuesday, May 12, 2020
Mehta Physics
Epigraph to Fly and the Fly-Bottle:
Encounters with British Intellectuals ,
by Ved Mehta , remarks first published
in The New Yorker in 1961 and 1962 —
See as well the Wallace Stevens phrase “The Ruler of Reality.”
Monday, February 24, 2020
Hidden Figure
Saturday, January 18, 2020
Interplay
"This interplay of necessity and contingency
produces our anxious— and highly pleasurable—
speculation about the future path of the story."
— Michel Chaouli in "How Interactive Can Fiction Be?"
(Critical Inquiry 31, Spring 2005, page 613.)
See also . . .
Continuing previous Modal Diamond Box posts:
Saturday, November 30, 2019
Thursday, November 7, 2019
For Connoisseurs of Insane Fantasy
From a 1962 young-adult novel —
"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."
Song adapted from a 1960 musical —
"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"
Friday, October 18, 2019
A Song for St. Luke’s Day
From a 1962 young-adult novel —
"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."
Song adapted from a 1960 musical —
"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"
Tuesday, October 15, 2019
Inside the Fire Temple
(The title refers to Log24 posts now tagged Fire Temple.)
In memory of a New Yorker cartoonist who
reportedly died at 97 on October 3, 2019 …
"Read something that means something."
— New Yorker advertising slogan
From posts tagged Tetrahedron vs. Square —
This journal on October 3 —
"There is such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.
Illustration (central detail a from the above tetrahedral figure) —
Thursday, October 3, 2019
The Overbye Metaphors
(For Harlan Kane)
"Once Mr. Overbye identifies a story, he said, the work is
in putting it in terms people can understand. 'Metaphors
are very important to the way I write,' he said. The results
are vivid descriptions that surpass mere translation."
— Raillan Brooks in The New York Times on a Times
science writer, October 17, 2017. Also on that date —
"There is such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.
See as well The Black List (Log24, September 27).
Friday, September 27, 2019
The Black List
"… 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.
Sunday, September 22, 2019
Colorful Tale
“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 …
Wednesday, September 18, 2019
The Perpetual Identity Crisis
"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 —
Sunday, August 25, 2019
Design Theory
"Mein Führer… Steiner…"
See Hitler Plans and Quadruple System.
"There is such a thing as a quadruple system."
— Saying adapted from a 1962 young-adult novel
Tuesday, August 6, 2019
Mathematics and Narrative: The Crosswicks Curse Continues.
"There is such a thing as a desktop."
— Saying adapted from a 1962 young-adult novel.
Monday, July 15, 2019
Possibility and Necessity: Kierkegaard Meets Nietzsche
The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —
See also . . .
Saturday, July 13, 2019
Which Roof?
Related material — Tetrahedron vs. Square and Cézanne's Greetings.
Compare and contrast:
A figure from St. Patrick's Day 2004 that might represent a domed roof …
Inscribed Carpenter's Square:
In Latin, NORMA
… and a cinematic "Fire Temple" from 2019 —
Monday, May 20, 2019
The Bond with Reality
Tuesday, April 9, 2019
Zero Dark Nine:
The Crosswicks Curse Continues . . .
"There is such a thing as geometry."
— Saying adapted from a 1962 young-adult novel.
Sunday, March 10, 2019
Friday, February 15, 2019
The Gifts Reserved for Age
"But, as the passage now presents no hindrance
To the spirit unappeased and peregrine
Between two worlds become much like each other…."
Related obituary:
https://www.nytimes.com/2019/02/15/obituaries/tom-cade-dead.html
Related date:
"as of Feb. 6, 2019" (from a post at 12 AM ET Feb. 7) —
"There is such a thing as a four-dimensional finite affine space."
— Saying adapted from a 1962 young-adult novel by Madeleine L'Engle
Wednesday, December 12, 2018
An Inscape for Douthat
Some images, and a definition, suggested by my remarks here last night
on Apollo and Ross Douthat's remarks today on "The Return of Paganism" —
In finite geometry and combinatorics,
an inscape is a 4×4 array of square figures,
each figure picturing a subset of the overall 4×4 array:
Related material — the phrase
"Quantum Tesseract Theorem" and …
A. An image from the recent
film "A Wrinkle in Time" —
B. A quote from the 1962 book —
"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."
Tuesday, November 13, 2018
Blackboard Jungle Continues.
From the 1955 film "Blackboard Jungle" —
From a trailer for the recent film version of A Wrinkle in Time —
Detail of the phrase "quantum tesseract theorem":
From the 1962 book —
"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."
Related mathematics from Koen Thas that some might call a
"quantum tesseract theorem" —
Some background —
See also posts tagged Dirac and Geometry. For more
background on finite geometry, see a web page
at Thas's institution, Ghent University.
Tuesday, August 28, 2018
Tuesday, August 7, 2018
The Search for Harmonic Analysis
Tuesday, June 19, 2018
Death on Father’s Day
From the University of Notre Dame in an obituary dated June 17 —
Timothy O’Meara, provost emeritus, Kenna Professor of Mathematics Emeritus and Trustee Emeritus at the University of Notre Dame, died June 17. He was 90.
A member of the Notre Dame faculty since 1962, O’Meara twice served as chairman of the University’s mathematics department and served as its first lay provost from 1978 to 1996.
He was graduated from the University of Cape Town in 1947 and earned a master’s degree in mathematics there the following year. Earning his doctoral degree from Princeton University in 1953, he taught at the University of Otago in New Zealand from 1954 to 1956 before returning to Princeton where he served on the mathematics faculty and as a member of the Institute for Advanced Study for the next six years.
In addition to his mathematical teaching and scholarship, he published magisterial works, including “Introduction to Quadratic Forms,” “Lectures on Linear Groups,” “Symplectic Groups” and “The Classical Groups and K-Theory,” co-authored with Alexander J. Hahn, professor of mathematics emeritus at Notre Dame and a former O’Meara doctoral student. |
Related material (update of 9:20 PM ET on June 19) —
Saturday, March 31, 2018
Cube Theory
For Greta Gerwig and Saoirse Ronan —
See also a Log24 post from the above Cube Theory date —
April 12, 2016 — Lyrics for a Cartoon Graveyard — as well as . . .
Notes for the Harrowing of Hell
Sunday, February 4, 2018
Logos for Sunday, February 4
"The walls in the back of the room show geometric shapes
that remind us of the logos on a space shuttle. "
— Web page on an Oslo art installation by Josefine Lyche.
See also Subway Art posts.
The translation above was obtained via Google.
The Norwegian original —
"På veggene bakerst i rommer vises geometriske former
som kan minne om logoene på en romferge."
Related logos — Modal Diamond Box in this journal:
Logos for Philosophers
(Suggested by Modal Logic) —
Thursday, January 25, 2018
Beware of Analogical Extension
"By an archetype I mean a systematic repertoire
of ideas by means of which a given thinker describes,
by analogical extension , some domain to which
those ideas do not immediately and literally apply."
— Max Black in Models and Metaphors
(Cornell, 1962, p. 241)
"Others … spoke of 'ultimate frames of reference' …."
— Ibid.
A "frame of reference" for the concept four quartets —
A less reputable analogical extension of the same
frame of reference —
Madeleine L'Engle in A Swiftly Tilting Planet :
"… deep in concentration, bent over the model
they were building of a tesseract:
the square squared, and squared again…."
See also the phrase Galois tesseract .
Thursday, December 21, 2017
Wrinkles
TIME magazine, issue of December 25th, 2017 —
" In 2003, Hand worked with Disney to produce a made-for-TV movie.
Thanks to budget constraints, among other issues, the adaptation
turned out bland and uninspiring. It disappointed audiences,
L’Engle and Hand. 'This is not the dream,' Hand recalls telling herself.
'I’m sure there were people at Disney that wished I would go away.' "
Not the dream? It was, however, the nightmare, presenting very well
the encounter in Camazotz of Charles Wallace with the Tempter.
From a trailer for the latest version —
Detail:
From the 1962 book —
"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."
Song adapted from a 1960 musical —
"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"
Friday, December 8, 2017
Logos (Continued)
"Denn die Welt braucht ewig die Wahrheit,
also braucht sie ewig Heraklit:
obschon er ihrer nicht bedarf.
Was geht ihn sein Ruhm an?
Der Ruhm bei »immer fortfließenden Sterblichen!«,
wie er höhnisch ausruft.
Sein Ruhm geht die Menschen etwas an, nicht ihn,
die Unsterblichkeit der Menschheit braucht ihn,
nicht er die Unsterblichkeit des Menschen Heraklit.
Das, was er schaute, die Lehre vom Gesetz im Werden
und vom Spiel in der Notwendigkeit , muß von jetzt
ab ewig geschaut werden: er hat von diesem größten
Schauspiel den Vorhang aufgezogen."
Logos for Philosophers
(Suggested by Modal Logic) —
Monday, September 4, 2017
Labor Date
(A sequel to the previous post, Up to Date)
"Dr. Sekler lectured around the world, but one trip proved life-changing.
In 1962, the year he married, Dr. Sekler made his first trip to Nepal.
'It was the way it had been for centuries — a beautiful valley filled with
happy, peaceful people. It seemed like Shangri-La,' he told the Harvard
Gazette in 2004."
— Bryan Marquard in The Boston Globe today
See also "Eight is a gate" in this journal.
Saturday, September 2, 2017
Try to Remember the Kind of September
(A prequel to an Ursula K. Le Guin story
in Fantastic magazine, September 1962)
Cover art by Lloyd Birmingham for "Plane Jane"
Knight Moves
Ursula K. Le Guin, in Amazing Stories , Sept. 1992, published
"The Rock That Changed Things" (pp. 9-13) and her story from
thirty years earlier, "April in Paris" (Fantastic Stories , Sept. 1962.)
The latter (pp. 14-19) was followed by some brief remarks (p. 19)
comparing the two stories.
For "The Rock," see Le Guin + Rock in this journal.
"April in Paris" is about time travel by means of an alchemist's
pentagram. The following figure from 1962 is in lieu of a pentagram —
See as well a search for 1962 in this journal.
Tuesday, May 23, 2017
In Memoriam
"From 1962 to 1969 Mr. Moore was Simon Templar . . . ."
— The New York Times online today
A related post — "Intruders for Mira" (Sept. 28, 2015).
Saturday, May 6, 2017
Talk Amongst Yourselves
A search for recent activity by the Liesl Schillinger of
the previous post yields …
Talk amongst yourselves.
Midrash for elitists —
The novel 2666 by Roberto Bolaño (see Bolaño in this journal
and Adam Kirsch in the above) and …
Matt Helm in Donald Hamilton's 1962 novel The Silencers —
"I cleaned up a little, went downstairs, and, rather than
get the pickup out of hock, paid sixty cents to have a taxi
take me to the international bridge. Two cents let me walk
across the Rio Grande into Mexico. The river bed was
almost dry. The usual skinny dark kids were playing their
usual incomprehensible games around the pools below
the bridge. Stepping off the south end of the span, I was
in a foreign country. Mexicans will tell you defensively that
Juarez isn't Mexico-that no border town is-but it certainly
isn't the United States of America, even though Avenida
Juarez, the street just south of the bridge, does bear a
certain resemblance to Coney Island. I brushed off a
purveyor of dirty pictures and shills for a couple of dirty
movie houses."
Midrash for populists —
The photo in the New York Times obituary
above is from the 1966 film based, very
loosely, on Donald Hamilton's The Silencers.
Saturday, March 25, 2017
Wednesday, March 22, 2017
Pulp Fiction Incarnate
Saturday, March 18, 2017
Back to the Past
"Old men ought to be explorers" — T. S. Eliot
"All on a Saturday night" — Johnny Thunder, 1962
Update of 8:25 PM ET on March 18 —
"Analysis." — Dr. Robert Ford in "Westworld"
"Master theorist and conceptual genius."
— Jon Pareles, front page, online New York Times tonight
Saturday, February 4, 2017
Time Loop
"On a Saturday night" — Johnny Thunder, 1962
"Only a peculiar can enter a time loop." — Tim Burton film, 2016
Highly qualified —
Saturday, January 14, 2017
1984: A Space Odyssey
See Eightfold 1984 in this journal.
Related material —
"… the object sets up a kind of
frame or space or field
within which there can be epiphany."
"… Instead of an epiphany of being,
we have something like
an epiphany of interspaces."
— Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self ,
Cambridge University Press, 1989
"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 University Press, Ithaca, NY, 1962
Click to enlarge:
Tuesday, January 10, 2017
Analogical Extension Meets Analytic Continuation
From Models and Metaphors , by Max Black,
Cornell University Press, 1962 —
I do not recommend the work of Lewin, nor that of a later
science groupie, Keith Devlin.
In September 2014, Devlin wrote an ignorant column about
a sort of bad mathematical joke based on a divergent infinite series.
He has now returned to the topic, this time writing more about
its proper mathematical background: analytic continuation .
Lewin is to Devlin as Lévi-Strauss is to Chomsky.
None of these four should be taken very seriously.
Max Black, however, should .
Monday, January 9, 2017
Diamond Song
From "Night Moves," by Bob Seger —
And oh, the wonder
Felt the lightning
Yeah, and we waited on the thunder
Waited on the thunder
I woke last night to the sound of thunder
How far-off, I sat and wondered
Started humming a song from 1962
Ain't it funny* how the night moves?
See as well Johnny Thunder on Diamond Records in 1962 —
Analogical Extension at Cornell
Click to enlarge the following (from Cornell U. Press in 1962) —
For a more recent analogical extension at Cornell, see the
Epiphany 2017 post on the eightfold cube and yesterday
evening's post "A Theory of Everything."
Friday, December 30, 2016
For the Accountant*
From "The Man Who Tried to Redeem the World with Logic" —
"To store the programs as data, the computer would need
something new: a memory. That’s where Pitts’ loops
came into play. 'An element which stimulates itself
will hold a stimulus indefinitely,' von Neumann wrote
in his report . . . ."
— Amanda Gefter, Nautilus , Feb. 5, 2015
Related material —
"Here we go loop de loop" — Johnny Thunder, 1962
* I.e., Ben Affleck in his new film.
Thursday, December 29, 2016
Tuesday, December 27, 2016
The Dark Side
"The record, released on the Diamond label,
became a big hit, rising to no. 4 on the
Billboard Hot 100 in early 1963." — Wikipedia
Saturday, December 3, 2016
SIAM Publication
For "the Trojan family" —
Related material on the late Solomon W. Golomb —
"While at JPL, Sol had also been teaching some classes
at the nearby universities: Caltech, USC and UCLA. In
the fall of 1962, following some changes at JPL—and
perhaps because he wanted to spend more time with
his young children— he decided to become a full-time
professor. He got offers from all three schools. He
wanted to go somewhere where he could 'make
a difference'. He was told that at Caltech 'no one has
any influence if they don’t at least have a Nobel Prize',
while at UCLA 'the UC bureaucracy is such that no one
ever has any ability to affect anything'. The result was
that—despite its much-inferior reputation at the time—
Sol chose USC. He went there in the spring of 1963 as
a Professor of Electrical Engineering—and ended up
staying for 53 years." — Stephen Wolfram, 5/25/16
See also Priority (Nov. 25) and "What's in a Name" (Dec. 1).
Thursday, June 2, 2016
Bullshit Studies
"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."
— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13
"What Shakespeare refers to in Lear as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."
— McLuhan, ibid. , page 241
This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned nonsense.
Epigraph by McLuhan —
"The Gutenberg Galaxy develops a mosaic or field
approach to its problems."
I prefer a different "mosaic or field" related to the movable
blocks of Fröbel, not the movable type of Gutenberg.
Wednesday, April 13, 2016
Black List
A search for "Max Black" in this journal yields some images
from a post of August 30, 2006 . . .
"Jackson has identified the seventh symbol." |
The "Jackson" above is played by the young James Spader,
who in an older version currently stars in "The Blacklist."
"… the memorable models of science are 'speculative instruments,' — Max Black in Models and Metaphors , Cornell U. Press, 1962 |
Saturday, March 26, 2016
Story Idea
From last evening's online New York Times —
"Mr. Hamner moved to California in 1962
and got his first break when 'The Twilight Zone'
accepted two of his story ideas. His eight scripts
for the series included 'The Hunt,' about a man
who is dead but does not realize it until his hunting
dog prevents him from wandering into hell . . . ."
— William Grimes
Hamner reportedly died on Thursday, March 24.
See this journal on that date.
Wednesday, February 24, 2016
The Media Message
See a link referencing The Gutenberg Galaxy (a Catholic's 1962 view of literacy)
in a Log24 post yesterday suggested by a New York Times obituary.
A different obituary this evening in that newspaper describes a Jew's 1979 view
of literacy. See "Elizabeth Eisenstein, Historian of Movable Type, Dies at 92."
Related material — McLuhan in Eisenstein's The Printing Press as an Agent
of Change , Cambridge University Press, 1979.
Eisenstein reportedly died on January 31, 2016. Synchronologists may
consult some media-related material reposted here on that date —
Fittingly, the Times concludes Eisenstein's obituary as follows —
"This article will be set in 8.7 point Imperial and printed on
one of several presses, including the Goss Colorliner."
For a perhaps more interesting printing press related to change,
see Despedida in this journal.
Sunday, November 22, 2015
Overlook Video
CALIFORNIA, UNITED STATES – OCTOBER 1962:
People watching President John F. Kennedy’s
TV announcement of Cuban blockade during the
missile crisis in a department store. (Photo by
Ralph Crane/Life Magazine/The LIFE Picture
Collection/Getty Images)
A Sunday opinion column from 2011,
"The Enduring Cult of Kennedy" —
"In this landscape, the death of J.F.K. looms up
like the Overlook Hotel." — Ross Douthat
on November 27, 2011
From this journal on that date —
Sunday, August 16, 2015
Sunday School
The title of the previous post, "For Quantum Mystics,"
suggests a search in this journal for Quantum + Mystic.
That search in turn suggests, in particular, a review of
a post of October 16, 2007 — a discussion of the
P.T. Barnum-like phrase "deep beauty" used to describe
a topic under discussion at Princeton by physicists.
Princeton, by the way, serves to illustrate the "gutter"
mentioned by Sir Laurence Olivier in a memorable
classroom scene from 1962.
Saturday, August 15, 2015
Schoolboy Problem
Sir Laurence Olivier, in "Term of Trial" (1962), dangles
a participle in front of schoolboy Terence Stamp:
"Walking to school today
my arithmetic book
fell into the gutter"
Were Stamp a Galois, the reply might be "Try this one, sir."
Friday, August 14, 2015
Schoolgirl Problem
But first, a word from our sponsa* …
Sir Laurence Olivier in "Term of Trial" (1962),
a film starring Sarah Miles as a schoolgirl —
* Bride in Latin. See also "bride's chair,"
a phrase from mathematical pedagogy.
Sunday, July 26, 2015
Sunday School
Hexagram 51:
"I woke last night to the sound of thunder,
How far off, I sat and wondered.
Started humming a song from 1962.
Ain't it funny how the night moves?"
Wednesday, December 17, 2014
Launched from Cuber
Continued from Nobel Note (Jan. 29, 2014).
From Tradition in Action , "The Missal Crisis of '62,"
remarks on the revision of the Catholic missal in that year—
"Neither can the claim that none of these changes
is heretical in content be used as an argument
in favor of its use, for neither is the employment of
hula girls, fireworks, and mariachis strictly speaking
heretical in itself, but they belong to that class of novel
and profane things that do not belong in the Mass."
— Fr. Patrick Perez, posted Sept. 11, 2007
See also this journal on November 22, 2014…
… and on Bruce Springsteen's birthday this year —
Tuesday, September 23, 2014
|
Thursday, September 11, 2014
A Class by Itself
The American Mathematical Society yesterday:
Harvey Cohn (1923-2014)
Wednesday September 10th 2014
Cohn, an AMS Fellow and a Putnam Fellow (1942), died May 16 at the age of 90. He served in the Navy in World War II and following the war received his PhD from Harvard University in 1948 under the direction of Lars Ahlfors. He was a member of the faculty at Wayne State University, Stanford University, Washington University in St. Louis, the University of Arizona, and at City College of New York, where he was a distinguished professor. After retiring from teaching, he also worked for the NSA. Cohn was an AMS member since 1942.
Paid death notice from The New York Times , July 27, 2014:
COHN–Harvey. Fellow of the American Mathematical Society and member of the Society since 1942, died on May 16 at the age of 90. He was a brilliant Mathematician, an adoring husband, father and grandfather, and faithful friend and mentor to his colleagues and students. Born in New York City in 1923, Cohn received his B.S. degree (Mathematics and Physics) from CCNY in 1942. He received his M.S. degree from NYU (1943), and his Ph.D. from Harvard (1948) after service in the Navy (Electronic Technicians Mate, 1944-46). He was a member of Phi Beta Kappa (Sigma Chi), won the William Lowell Putnam Prize in 1942, and was awarded the Townsend Harris Medal in 1972. A pioneer in the intensive use of computers in an innovative way in a large number of classical mathematical problems, Harvey Cohn held faculty positions at Wayne State University, Stanford, Washington University Saint Louis (first Director of the Computing Center 1956-58), University of Arizona (Chairman 1958-1967), University of Copenhagen, and CCNY (Distinguished Professor of Mathematics). After his retirement from teaching, he worked in a variety of capacities for the National Security Agency and its research arm, IDA Center for Computing Sciences. He is survived by his wife of 63 years, Bernice, of Laguna Woods, California and Ft. Lauderdale, FL, his son Anthony, daughter Susan Cohn Boros, three grandchildren and one great-granddaughter.
— Published in The New York Times on July 27, 2014
See also an autobiographical essay found on the web.
None of the above sources mention the following book, which is apparently by this same Harvey Cohn. (It is dedicated to "Tony and Susan.")
Advanced Number Theory, by Harvey Cohn
Courier Dover Publications, 1980 – 276 pages
(First published by Wiley in 1962 as A Second Course in Number Theory )
Publisher's description:
" 'A very stimulating book … in a class by itself.'— American Mathematical Monthly
Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.
The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.
Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.
In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory."
User Review –
"In a nutshell, the book serves as an introduction to Gauss' theory of quadratic forms and their composition laws (the cornerstone of his Disquisitiones Arithmeticae) from the modern point of view (ideals in quadratic number fields). I strongly recommend it as a gentle introduction to algebraic number theory (with exclusive emphasis on quadratic number fields and binary quadratic forms). As a bonus, the book includes material on Dirichlet L-functions as well as proofs of Dirichlet's class number formula and Dirichlet's theorem in primes in arithmetic progressions (of course this material requires the reader to have the background of a one-semester course in real analysis; on the other hand, this material is largely independent of the subsequent algebraic developments).
Better titles for this book would be 'A Second Course in Number Theory' or 'Introduction to quadratic forms and quadratic fields'. It is not a very advanced book in the sense that required background is only a one-semester course in number theory. It does not assume prior familiarity with abstract algebra. While exercises are included, they are not particularly interesting or challenging (if probably adequate to keep the reader engaged).
While the exposition is *slightly* dated, it feels fresh enough and is particularly suitable for self-study (I'd be less likely to recommend the book as a formal textbook). Students with a background in abstract algebra might find the pace a bit slow, with a bit too much time spent on algebraic preliminaries (the entire Part I—about 90 pages); however, these preliminaries are essential to paving the road towards Parts II (ideal theory in quadratic fields) and III (applications of ideal theory).
It is almost inevitable to compare this book to Borevich-Shafarevich 'Number Theory'. The latter is a fantastic book which covers a large superset of the material in Cohn's book. Borevich-Shafarevich is, however, a much more demanding read and it is out of print. For gentle self-study (and perhaps as a preparation to later read Borevich-Shafarevich), Cohn's book is a fine read."
Sunday, July 6, 2014
Game News
An essay linked to here on the date of Kuhn’s
death discussed the film “Good Will Hunting”:
“You can be sure that when an experienced movie director
like Gus Van Sant selects an establishing shot for the lead
character, he does so with considerable care, on the advice
of an expert.”
Establishing shots —
1. From a post of January 29, 2014:
2. From a post of April 12, 2011:
Parting shot —
From another post of January 29, 2014:
Note Watson‘s title advice.
Thursday, June 26, 2014
Study This Example, Part II
(Continued from 10:09 AM today)
The quotation below is from a webpage on media magnate
Walter Annenberg.
Annenberg Hall at Harvard, originally constructed to honor
the Civil War dead, was renamed in 1996 for his son Roger,
Harvard Class of ’62.
www.broadcastpioneers.com/
walterannenberg.html —
“It was said that Roger was ‘moody and sullen’
spending large parts of his time reading poetry
and playing classical music piano. It had been
reported that Roger attempted suicide at the
age of eleven by slitting his wrists. He recovered
and was graduated Magna Cum Laude from
Episcopal Academy in our area. For awhile,
Roger attended Harvard, but he was removed
from the school’s rolls after Roger stopped doing
his school work and spent almost all his time
reading poetry in his room. He then was sent to
an exclusive and expensive treatment center
in Bucks County, Pennsylvania. At that facility,
Roger became more remote. It was said that he
often didn’t recognize or acknowledge his father.
On August 7, 1962, Roger Annenberg died from
an overdose of sleeping pills.”
A more appropriate Annenberg memorial, an article
in The Atlantic magazine on June 25, notes that…
“Among those who ended up losing their battles
with mental illness through suicide are
Virginia Woolf, Ernest Hemingway, Vincent van Gogh,
John Berryman, Hart Crane, Mark Rothko, Diane Arbus,
Anne Sexton, and Arshile Gorky.”
Monday, May 26, 2014
Springtime for Vishnu
… Continues.
A post by Margaret Soltan this morning:
Links (in blue) from the above post:
Cane and Mondo Cane.
Bagger Vance — “Time for you to see the field.”
From Pictures for Kurosawa (Sept. 6, 2003) —
“As these flowing rivers that go towards the ocean,
when they have reached the ocean, sink into it,
their name and form are broken, and people speak of
the ocean only, exactly thus these sixteen parts
of the spectator that go towards the person (purusha),
when they have reached the person, sink into him,
their name and form are broken, and people speak of
the person only, and he becomes without parts and
immortal. On this there is this verse:
‘That person who is to be known, he in whom these parts
rest, like spokes in the nave of a wheel, you know him,
lest death should hurt you.’ “
— Prasna Upanishad
Related material — Heaven’s Gate images from Xmas 2012:
“This could be heaven or this could be hell.” — Hotel California
Those who prefer mathematics to narrative may consult Root Circle.
Thursday, January 30, 2014
Test
From Fritz Leiber's 1959 sci-fi classic "Damnation Morning" —
She drew from her handbag a pale grey
gleaming implement that looked by quick turns
to me like a knife, a gun, a slim sceptre, and a
delicate branding iron— especially when its tip
sprouted an eight-limbed star of silver wire.
“The test?” I faltered, staring at the thing.
“Yes, to determine whether you can live in the
fourth dimension or only die in it.”
Related 1962 drama from the Twilight Zone —
"He's a physicist, maybe he can help us out."
See also Step.
Wednesday, August 14, 2013
The Gift
"Give 'em hell." — Ben Bernanke at Princeton's Baccalaureate, 2013
Some background — Janet Leigh and the Museum of Modern Art
"The Varnedoe Debacle," by Hilton Kramer (Dec. 1991)
Hell… Hell. — Sinatra in The Manchuran Candidate
Wednesday, July 10, 2013
Diagon Alley
You say goodbye, I say …
A YouTube video uploaded on March 2, 2012—
This journal on the date of the above video's uploading— March 2, 2012:
"…des carreaux mi-partis de deux couleurs par une ligne diagonale…."
See also Josefine Lyche in Vril Chick and Bowling in Diagon Alley.
Saturday, March 16, 2013
The Crosswicks Curse
From the prologue to the new Joyce Carol Oates
novel Accursed—
"This journey I undertake with such anticipation
is not one of geographical space but one of Time—
for it is the year 1905 that is my destination.
1905!—the very year of the Curse."
Today's previous post supplied a fanciful link
between the Crosswicks Curse of Oates and
the Crosswicks tesseract of Madeleine L'Engle.
The Crosswicks Curse according to L'Engle
in her classic 1962 novel A Wrinkle in Time —
"There is such a thing as a tesseract."
A tesseract is a 4-dimensional hypercube that
(as pointed out by Coxeter in 1950) may also
be viewed as a 4×4 array (with opposite edges
identified).
Meanwhile, back in 1905…
For more details, see how the Rosenhain and Göpel tetrads occur naturally
in the diamond theorem model of the 35 lines of the 15-point projective
Galois space PG(3,2).
See also Conwell in this journal and George Macfeely Conwell in the
honors list of the Princeton Class of 1905.
Friday, January 18, 2013
Solomon’s Rep-tiles
"Rep-tiles Revisited," by Viorel Nitica, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics , American Mathematical Society,
"The goal of this note is to take a new look at some of the most amazing objects discovered in recreational mathematics. These objects, having the curious property of making larger copies of themselves, were introduced in 1962 by Solomon W. Golomb [2], and soon afterwards were popularized by Martin Gardner [3] in Scientific American…."
2. S. W. Golomb: "Replicating Figures in the Plane," Mathematical Gazette 48, 1964, 403-412
3. M. Gardner: "On 'Rep-tiles,' Polygons That Can Make Larger and Smaller Copies of Themselves," Scientific American 208, 1963, 154-157
Two such "amazing objects"—
Triangle |
Square |
For a different approach to the replicating properties of these objects, see the square-triangle theorem.
For related earlier material citing Golomb, see Not Quite Obvious (July 8, 2012; scroll down to see the update of July 15.).
Golomb's 1964 Gazette article may now be purchased at JSTOR for $14.
Saturday, December 1, 2012
Star Wars
Source: Rudolf Koch, The Book of Signs
The American Mathematical Society
(AMS) yesterday:
Lars Hörmander (1931-2012) Hörmander, who received a Fields Medal in 1962, |
Some related material:
- A 1990 AMS review of a book by another mathematician,
Harmonic Analysis in Phase Space , that is closely
related to Hörmander's research (and perhaps more
accessible to the nonspecialist than his books), - Mathematical Imagery (Log24, Jan. 19, 2012),
- The Eight-Pointed Star, and yesterday's
- Point.
See also posts on Damnation Morning and, from the
date of Hörmander's death,
- Will and Representation.
Sunday, November 18, 2012
Sermon
Happy birthday to…
Today's sermon, by Marie-Louise von Franz—
For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.
Another modern physicist, Niels Bohr, died
on this date in 1962…
The circle above is marked with a version For the square, see the diamond theorem. "Two things of opposite natures seem to depend — Wallace Stevens, |
Wednesday, July 18, 2012
Incommensurables
(Continued from Midsummer Eve)
"At times, bullshit can only be countered with superior bullshit."
— Norman Mailer, March 3, 1992, PBS transcript
"Just because it is a transition between incommensurables, the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience. Like the gestalt switch, it must occur all at once (though not necessarily in an instant) or not at all."
— Thomas Kuhn, The Structure of Scientific Revolutions , 1962, as quoted in The Enneagram of Paradigm Shifting
"In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry."
I have little respect for Enneagram enthusiasts, but they do at times illustrate Mailer's maxim.
My own interests are in the purely mathematical properties of the number nine, as well as those of the next square, sixteen.
Those who prefer bullshit may investigate non-mathematical properties of sixteen by doing a Google image search on MBTI.
For bullshit involving nine, see (for instance) Einsatz in this journal.
For non-bullshit involving nine, sixteen, and "asymmetry that resides at the very heart of symmetry," see Monday's Mapping Problem continued. (The nine occurs there as the symmetric figures in the lower right nine-sixteenths of the triangular analogs diagram.)
For non-bullshit involving psychological and philosophical terminology, see James Hillman's Re-Visioning Psychology .
In particular, see Hillman's "An Excursion on Differences Between Soul and Spirit."
Tuesday, June 12, 2012
Meet Max Black (continued)
Background— August 30, 2006—
In the 2006 post, the above seventh symbol 110000 was
interpreted as the I Ching hexagram with topmost and
next-to-top lines solid, not broken— Hexagram 20, View .
In a different interpretation, 110000 is the binary for the decimal
number 48— representing the I Ching's Hexagram 48, The Well .
“… 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
The algebra is certainly clearer than either I Ching
metaphor, but is in some respects less interesting.
For a post that combines both the above I Ching
metaphors, View and Well , see Dec. 14, 2007.
In memory of scholar Elinor Ostrom,
who died today—
Thursday, April 26, 2012
Rainbow People
(Mythopoetic continued)
Voice of America today—
Thousands of Norwegians Defy Confessed Killer Breivik in Song
"The demonstrators waved roses and flags
Thursday as they and Norwegian folk singer
Lillebjoern Nilsen sang an adaptation
of the children's song, 'My Rainbow Race,'
which Breivik in court last week called
an example of Marxist brainwashing."
[See also PETE SEEGER AND LILLEBJØRN NILSEN.
Click on the image below for Seeger's original version.]
Liberia Reacts to Taylor Conviction With Mixed Emotions
"As the verdict was read out, a rainbow was seen
in the sky, encircling the sun. For many Liberians,
superstition is a part of life. The rainbow heralded
a new era, they said, beginning with the verdict of Taylor."
["You're not the only one… with mixed emotions."]
Thursday, April 5, 2012
Leap Day of Faith
Presidential candidate Mitt Romney on Monday, April 2, 2012—
"I think there is in this country a war on religion.
I think there is a desire to establish a religion
in America known as secularism."
Nancy Haught of The Oregonian on Leap Day, Feb. 29, 2012—
William Hamilton, the retired theologian who declared in the 1960s that God was dead, died Tuesday [Feb. 28, 2012] in his downtown Portland apartment at 87. Hamilton said he'd been haunted by questions about God since he was a teenager. Years later, when his conclusion was published in the April 8, 1966, edition of Time Magazine, he found himself in a hornet's nest. Time christened the new movement "radical theology" and Hamilton, one of its key figures, received death threats and inspired angry letters to the editor in newspapers that carried the story. He encountered hostility at Colgate Rochester Crozer Divinity School, where he had been teaching theology, and lost his endowed chair in 1967. Hamilton moved on to teach religion at New College in Sarasota, Fla. |
(See also this journal on Leap Day.)
From New College: The Honors College of Florida—
Oct. 11, 1960: New College is founded as a private college 1961: Trustees obtain options to purchase the former Charles Ringling estate on Sarasota Bay and 12 acres of airport land facing U.S. 41 held by private interests. The two pieces form the heart of the campus Nov. 18, 1962: the campus is dedicated. Earth from Harvard is mixed with soil from New College as a symbol of the shared lofty ideals of the two institutions. |
See also, in this journal, "Greatest Show on Earth" and The Harvard Crimson—
The Harvard Crimson, Online Edition |
Sunday, Oct. 8, 2006 |
POMP AND
Friday, Oct. 6:
The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden. |
OPINION At Last, a By THE CRIMSON STAFF The Trouble By SAHIL K. MAHTANI |
Sunday, December 4, 2011
Code Wars
Steve Buscemi last night on Saturday Night Live
describing Christmas tree ornaments with his mate Sheila—
"This one's a little computer."
"Beep Boop Beep"
"This one's a little pinecone. … Beep Boop Beep"
Meanwhile…
In related news…
"Her name drives me insane."
— Rosetta Stone, 1978 cover of "Sheila," Tommy Roe's 1962 classic
Click image for sketch.
Saturday, November 26, 2011
Innermost Kernel (continued*)
A search on the word "innermost" in a PDF copy of a book
by Suzanne Gieser on Jung and Pauli yields no definite meaning
for the book's title, The Innermost Kernel (Springer, 2005).
The author does, however, devote a section (pp. 36-41) to the
influence of Schopenhauer on Jung and Pauli, and that section at least
suggests that the historical origin of her title is in Schopenhauer's
reformulation of Kant's "Ding an sich."
The Innermost Kernel , p. 37—
"… an expression of an underlying invisible world,
the one that forms the innermost essence of reality,
the thing-in-itself. This is the will, a blind existence
that forms an omnipresent entity beyond time, space
and individuality." *
* Arthur Schopenhauer, "Über die Vierfache Wurzel
des Satzes vom zureichenden Grunde" (1813),
Kleinere Schriften, SämtlicheWerke III
(Stuttgart, 1962), 805–806.
* See also Mann on Schopenhauer and an "innermost kernel."
Monday, October 10, 2011
The Aleph
COLLEGE OF THE DESERT
Minutes — Organization Meeting
11:00 a.m., Saturday, July 1, 1961—
15. Preparation of College Seal:
By unanimous consent preparation of a College
Seal to contain the following features was
authorized: A likeness of the Library building
set in a matrix of date palms, backed by
a mountain skyline and rising sun; before
the Library an open book, the Greek symbol
Alpha on one page and Omega on the other;
the Latin Lux et Veritas, College of the
Desert, and 1958 to be imprinted within or
around the periphery of the seal.
From the website http://geofhagopian.net/ of
Geoff Hagopian, Professor of Mathematics,
College of the Desert—
Note that this version of the seal contains
an Aleph and Omega instead of Alpha and Omega.
From another Hagopian website, another seal.
Thursday, April 28, 2011
Hard Bargain
Continued from Good Friday —
The New Yorker , in the above excerpt, says of David Deutsch that
"his books have titles of colossal confidence
('The Fabric of Reality,' 'The Beginning of Infinity')."
The Fabric of Reality — A post from Good Friday —
Friday, April 22, 2011
In memory of Hazel Dickens, two links — Weepin' like a willow, mournin' like a dove |
The Beginning of Infinity — Another Good Friday death—
Sidney Michaels, adapter of the 1962 play "Tchin-Tchin."
"At play's end they are Chaplinesque waifs living in the charmed circle
of innocents that includes saints, children, drunkards and madmen.
Subliminally, Tchin-Tchin is a Christian existential fable." — TIME
Saturday, October 30, 2010
Keanu vs. the Devil
(Continued from Little Buddha (1994), The Matrix (1999), and Constantine (2005))
This post was suggested by yesterday's post on Habermas and by his 1962 book The Structural Transformation of the Public Sphere (English translation, 1989).
The "public sphere" of Habermas has come to pass; it is, of course, the World-Wide Web.
For October 30, the day leading up to Devil's Night, a more private sphere—though in a public setting— seems appropriate…
The Day the Earth Stood Still (2008)
A Keanu Reeves scene related to this image—
"The low point of the movie’s persuasiveness is the single scene with Professor Barnhardt (John Cleese) — in the original an Einstein-like scientist who impresses Klaatu with his highly evolved thinking, here a caricature of professorial enlightenment. Helen decides to bring Klaatu to Professor Barnhardt when Klaatu professes his disappointment with earth’s leaders. 'Those aren’t our leaders!' she protests earnestly. 'Let me take you to one of our leaders!'"
A perhaps more persuasive scene, from today's New York Times—
Prize in Hand, He Keeps His Eye on Teaching
Nobel winner Mario Vargas Llosa teaches
a seminar on Borges at Princeton
(Photo by James Leynse for The New York Times )
Wednesday, August 25, 2010
That X
Martin Heidegger, Being and Time, translated by
John Macquarrie and Edward Robinson, Harper hardcover, 1962, p. 262—
"…the ultimate business of philosophy is to preserve
the force of the most elemental words…."
Heidegger was quoted, in a different translation, by Richard Rorty in 1998
in a review of Ein Meister aus Deutschland.
Related material: an August 18 death and this journal on that date—
"… it is impossible that there should be time if there is no soul,
except that there could be that X which time is…."
— Aristotle, Physics, IV.14, translated by Edward Hussey
See also Berlinerblau in this journal on August 10.
Monday, February 1, 2010
Frame by Frame
From "Time's Breakdown," September 17, 2003—
“… even if we can break down time into component Walsh functions, what would it achieve?” – The Professor, in “Passing in Silence,” by Oliver Humpage “Being is not a steady state but an occulting one: we are all of us a succession of stillness blurring into motion on the wheel of action, and it is in those spaces of black between the pictures that we find the heart of mystery in which we are never allowed to rest. The flickering of a film interrupts the intolerable continuity of apparent world; subliminally it gives us those in-between spaces of black that we crave.” – Gösta Kraken, Perception Perceived: an Unfinished Memoir (p. 9 in Fremder, a novel by Russell Hoban) |
This flashback was suggested by
- A review in next Sunday's New York Times Book Review of a new novel, Point Omega, by Don DeLillo. The review's title (for which the reviewer, Geoff Dyer, should not be blamed) is "A Wrinkle in Time." The review and the book are indeed concerned with time, but the only apparent connection to the 1962 novel of Madeleine L'Engle also titled A Wrinkle in Time is rather indirect– via the Walsh functions mentioned above.
- A phrase in the Times's review, "frame by frame," also appeared in this jounal on Saturday. It formed part of the title of a current exhibition at Harvard's Carpenter Center for the Visual Arts.
- The Carpenter Center exhibition will have an opening reception on February 4.
- February 4 is also the birthday of the above Russell Hoban, who will turn 85. See a British web page devoted to that event.
DeLillo is a major novelist, but the work of Hoban seems more relevant to the phrase "frame by frame."
Sunday, December 20, 2009
The Test
From the September 1953 Bulletin of the American Mathematical Society—
Emil Artin, in a review of Éléments de mathématique, by N. Bourbaki, Book II, Algebra, Chaps. I-VII–
"We all believe that mathematics is an art. The author of a book, the lecturer in a classroom tries to convey the structural beauty of mathematics to his readers, to his listeners. In this attempt he must always fail. Mathematics is logical to be sure; each conclusion is drawn from previously derived statements. Yet the whole of it, the real piece of art, is not linear; worse than that its perception should be instantaneous. We all have experienced on some rare occasions the feeling of elation in realizing that we have enabled our listeners to see at a moment's glance the whole architecture and all its ramifications. How can this be achieved? Clinging stubbornly to the logical sequence inhibits the visualization of the whole, and yet this logical structure must predominate or chaos would result."
Art Versus Chaos
From an exhibit,
"Reimagining Space"
The above tesseract (4-D hypercube)
sculpted in 1967 by Peter Forakis
provides an example of what Artin
called "the visualization of the whole."
For related mathematical details see
Diamond Theory in 1937.
"'The test?' I faltered, staring at the thing.
'Yes, to determine whether you can live
in the fourth dimension or only die in it.'"
— Fritz Leiber, 1959
See also the Log24 entry for
Nov. 26, 2009, the date that
Forakis died.
"There is such a thing
as a tesseract."
— Madeleine L'Engle, 1962
Tuesday, December 15, 2009
A Christmas Carol
“There are two silences.
One when no word is spoken.
The other when perhaps a torrent
of language is being employed.”
Stille Nacht…
Pinter died on December 24, 2008:
Heilige Nacht…
Also on Christmas Eve, 2008
(“24/12/08 3:23 pm”):
Wednesday, March 4, 2009
Wednesday March 4, 2009
— New York Times obituary of Jacob T. Schwartz dated Tuesday, March 3, 2009
John Markoff.
New York Lottery
March 3, 2009:
“Treatment of Autistic Schizophrenic Children with LSD-25 and UML-491“–
“Autistic schizophrenic children present challenging and baffling problems in treatment…. Many of the children have been followed subsequently into later childhood, adolescence, and adulthood…. Meanwhile, a new group of young autistic children are always available for new treatment endeavors as the new modes become available.”*
* by Lauretta Bender, M.D., Lothar Goldschmidt, M.D., and D.V. Siva Sankar, Ph.D., in Recent Advances in Biological Psychiatry, 1962, 4, 170-177.
Friday, June 20, 2008
Friday June 20, 2008
Drunkard’s Walk
In memory of Episcopal priest
and Jungian analyst
Brewster Yale Beach,
who died on Tuesday,
June 17, 2008
“A man walks down the street…”
Related material:
In the above screenshot of New York Times obituaries on the date of Brewster Beach’s death, Tim Russert seems to be looking at the obituary of Air Force Academy chapel architect Walter Netsch.
This suggests another chapel, more closely related to my own experience, in Cuernavaca, Mexico. Some background…
Walter Netsch in Oral History (pdf, 467 pp.):
“I also had a book that inspired me– this is 1947– called Communitas by Percival and Paul Goodman. Percival Goodman was the architect, and Paul Goodman was the writer and leftist. And this came out of the University of Chicago– part of the leftist bit of the University of Chicago….
I had sort of in the back of my mind, Communitas appeared from my subconscious of the new town out of town, and there were other people who knew of it….”
“God As Trauma”
by Brewster Yale Beach:
“The problem of crucifixion is
the beginning of individuation.”
“Si me de veras quieres,
deja me en paz.”
— Lucero Hernandez,
Cuernavaca, 1962
A more impersonal approach
to my own drunkard’s walk
(Cuernavaca, 1962, after
reading the above words):
Cognitive Blending
and the Two Cultures
An approach from the culture
(more precisely, the alternate
religion) of Scientism–
The Drunkard’s Walk:
How Randomness
Rules Our Lives—
is sketched in
Today’s Sermon:
The Holy Trinity vs.
The New York Times
(Sunday, June 8, 2008).
The Times illustrated its review
of The Drunkard’s Walk
with facetious drawings
by Jessica Hagy, who uses
Venn diagrams to make
cynical jokes.
A less cynical use of
a Venn diagram:
Saturday, July 14, 2007
Saturday July 14, 2007
Catholic University
of America
The August 2007 issue of Notices of the American Mathematical Society contains tributes to the admirable personal qualities and mathematical work of the late Harvard professor George Mackey. For my own tributes, see Log24 on March 17, 2006, April 29, 2006, and March 10, 2007. For an entry critical of Mackey’s reductionism– a philosophical, not mathematical, error– see Log24 on May 23, 2007 (“Devil in the Details”).
Here is another attack on reductionism, from a discussion of the work of another first-rate mathematician, the late Gian-Carlo Rota of MIT:
“Another theme developed by Rota is that of ‘Fundierung.’ He shows that throughout our experience we encounter things that exist only as founded upon other things: a checkmate is founded upon moving certain pieces of chess, which in turn are founded upon certain pieces of wood or plastic. An insult is founded upon certain words being spoken, an act of generosity is founded upon something’s being handed over. In perception, for example, the evidence that occurs to us goes beyond the physical impact on our sensory organs even though it is founded upon it; what we see is far more than meets the eye. Rota gives striking examples to bring out this relationship of founding, which he takes as a logical relationship, containing all the force of logical necessity. His point is strongly antireductionist. Reductionism is the inclination to see as ‘real’ only the foundation, the substrate of things (the piece of wood in chess, the physical exchange in a social phenomenon, and especially the brain as founding the mind) and to deny the true existence of that which is founded. Rota’s arguments against reductionism, along with his colorful examples, are a marvelous philosophical therapy for the debilitating illness of reductionism that so pervades our culture and our educational systems, leading us to deny things we all know to be true, such as the reality of choice, of intelligence, of emotive insight, and spiritual understanding. He shows that ontological reductionism and the prejudice for axiomatic systems are both escapes from reality, attempts to substitute something automatic, manageable, and packaged, something coercive, in place of the human situation, which we all acknowledge by the way we live, even as we deny it in our theories.”
— Robert Sokolowski, foreword to Rota’s Indiscrete Thoughts
![]() Fr. Robert Sokolowski, Ph.D., is Professor of Philosophy at The Catholic University of America in Washington, D.C. Ordained a Roman Catholic priest in 1962, he is internationally recognized and honored for his work in philosophy, particularly phenomenology. In 1994, Catholic University sponsored a conference on his work and published several papers and other essays under the title, The Truthful and the Good, Essays In Honor of Robert Sokolowski. |
The tributes to Mackey are contained in the first of two feature articles in the August 2007 AMS Notices. The second feature article is a review of a new book by Douglas Hofstadter. For some remarks related to that article, see Thursday’s Log24 entry “Not Mathematics but Theology.”
Monday, May 14, 2007
Monday May 14, 2007
Crossing Point
From Log24's
"Footprints for Baudrillard"–
"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?
— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"
"Oh, Euclid, I suppose."
— Madeleine L'Engle, A Wrinkle in Time,
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,
"The Tesseract"
From Log24's
Xanga footprints,
3:00 AM today:
Texas | /431103703/item.html | 5/14/2007 3:00 AM |
The link leads to a Jan. 23, 2006 entry
on what one philosopher has claimed is
"exactly that crossing point
of constraint and freedom
which is the very essence
of man's nature."
Wednesday, March 7, 2007
Wednesday March 7, 2007
Baudrillard
"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?
— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"
"Oh, Euclid, I suppose."
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,
"The Tesseract"
In memory of the French philosopher Jean Baudrillard, who died yesterday, Tuesday, March 6, 2007.
The following Xanga footprints may be regarded as illustrating Log24 remarks of Dec. 10, 2006 on the Library of Congress, geometry, and bullshit, as well as remarks of Aug. 28, 2006 on the temporal, the eternal, and St. Augustine.
From the District of Columbia–
Xanga footprints in reverse
chronological order from
the noon hour on Tuesday,
March 6, 2007, the date
of Baudrillard's death:
District of Columbia /499111929/item.html Beijing String |
3/6/2007 12:04 PM |
District of Columbia /497993036/item.html Spellbound |
3/6/2007 12:03 PM |
District of Columbia /443606342/item.html About God, Life, Death |
3/6/2007 12:03 PM |
District of Columbia /494421586/item.html A Library of Congress Reading |
3/6/2007 12:03 PM |
District of Columbia /500434851/item.html Binary Geometry |
3/6/2007 12:03 PM |
District of Columbia /404038913/item.html Prequel on St. Cecelia's Day |
3/6/2007 12:03 PM |
Thursday, March 1, 2007
Thursday March 1, 2007
Senior Honors
From the obituary in today's New York Times of historian Arthur M. Schlesinger Jr.–
"Mr. Schlesinger, partly through his appreciation of history, fully realized his good fortune. 'I have lived through interesting times and had the luck of knowing some interesting people,' he wrote.
A huge part of his luck was his father, who guided much of his early research, and even suggested the topic for his [Harvard] senior honors: Orestes A. Brownson, a 19th-century journalist, novelist and theologian. It was published by Little, Brown in 1938 as 'Orestes A. Brownson: A Pilgrim's Progress.'"
From The Catholic Encyclopedia:
"It is sufficient for true knowledge that it affirm as real that which is truly real."
From The Diamond Theory of Truth:
"Was there really a cherubim waiting at the star-watching rock…?
Was he real?
What is real?— Madeleine L'Engle, A Wind in the Door, Farrar, Straus and Giroux, 1973, conclusion of Chapter Three, "The Man in the Night"
"Oh, Euclid, I suppose."
— Madeleine L'Engle, A Wrinkle in Time, Farrar, Straus and Giroux, 1962, conclusion of Chapter Five, "The Tesseract"
Related material: Yesterday's first annual "Tell Your Story Day" at Harvard and yesterday's entry on Euclid.
Wednesday, January 31, 2007
Wednesday January 31, 2007
“At times, bullshit can only be
countered with superior bullshit.”
— Norman Mailer
“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962
— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)
Goguen does not give a source for this alleged “thoughts of God” statement.
A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.
Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.
Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.
Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.
Gudder may have been misquoting some other author’s blather about Kepler. Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature—
“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?
Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of Nature.
Sophia. Then these thoughts of Nature are also thoughts of God.
Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”
Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.
Sunday, November 12, 2006
Sunday November 12, 2006
Instance
From a review by Adam White Scoville of Iain Pears’s novel titled An Instance of the Fingerpost:
“Perhaps we are meant to see the story as a cubist retelling of the crucifixion, as Pilate, Barabbas, Caiaphas, and Mary Magdalene might have told it. If so, it is sublimely done so that the realization gradually and unexpectedly dawns upon the reader. The title, taken from Sir Francis Bacon, suggests that at certain times, ‘understanding stands suspended’ and in that moment of clarity (somewhat like Wordsworth’s ‘spots of time,’ I think), the answer will become apparent as if a fingerpost were pointing at the way.”
Another instance:
The film “Barabbas” (1962) shown on Turner Classic Movies at 8 PM Friday, Nov. 10.
Compare and contrast–
- Barabbas emerging from prison as if from Plato’s cave, and Barabbas’s vision of Christ in blinding sunlight: “Flung into the sunlight, he stands blinking at a young man in white robes; is it merely the unaccustomed light that dazzles his eyes, or does he really see a radiance streaming from the young man’s face?” —TIME Magazine, 1962
- 1 Peter 2 on Christ as the “living stone”
- The cover of the novel Stone 588 shown in Friday’s 11:20 PM entry
The film is based on the novel by Par Lagerkvist, winner of the Nobel Prize in Literature.
The Lagerkvist novel may be of more enduring interest than Stone 588, but, as Friday’s lottery numbers indicate, even lesser stories have their place.
Thursday, September 7, 2006
Thursday September 7, 2006
for Isak Dinesen,
who died in 1962
on this date
Meanwhile…
Click on pictures for details.
Thursday, August 31, 2006
Thursday August 31, 2006
(continued from 2001)
Glenn Ford in
“The 4 Horsemen
of the Apocalypse”:
A sneering review from TIME Magazine, March 23, 1962:
“Hero Ford, a playboy from Argentina, falls pampassionately in love with Heroine Thulin, a Parisienne married to a patriotic editor. When the editor joins the Resistance, the hero realizes his duty and secretly does the same. Unaware of his decision, the heroine decides that he is merely a lightweight, and goes back to her husband. At the fade, while the violins soar among the bomb bursts, the poor misunderstood playboy dies heroically in an attempt to weaken the Wehrmacht’s defenses in Normandy.
The tale is trite, the script clumsy, and the camera work grossly faked. Though the lovers wander all over Paris, the Cathedral of Notre Dame turns up in the background practically everywhere they go, almost as if it were following them around like a little dog.”
TIME Magazine is still wearing the Ivy League sneer it displayed so impressively in 1962.
A less dismissive summary from Answers.com:
“The World War I setting of the original Blasco-Ibanez novel has been updated to World War II, but the basic plot remains the same. A well-to-do Argentinian family, rent asunder by the death of patriarch Lee J. Cobb, scatters to different European countries in the late 1930s. Before expiring, Cobb had warned his nephew Carl Boehm that the latter’s allegiance to the Nazis would bring down the wrath of the titular Four Horsemen: War, Conquest, Famine and Death. Ford, Cobb’s grandson, has promised to honor his grandfather’s memory by thwarting the plans of Boehm. At the cost of his own life, Ford leads allied bombers to Boehm’s Normandy headquarters.”
In memory of Glenn Ford, a talented character actor who died at 90 yesterday, the opening paragraphs of an obituary in The Scotsman:
Screen icon Glenn Ford
dies at 90RHIANNON EDWARDGLENN Ford, one of the most enduring stars of the silver screen, has died at the age of 90.
Ford, who appeared in more than 200 films in a career spanning five decades, died at his home in Beverly Hills.
The actor’s health had been in decline for a number of years after he suffered a series of strokes.
Although he never achieved the superstardom he craved, Ford was widely acclaimed as one of the best character actors in the business.
The business of narrative:
From a narrative suggested by the name of The Scotsman‘s reporter and related, if only by association with Normandy, to Ford’s “Four Horsemen” film:
“The Vandaleurs are a family of Norman nobles with a heritable version of the mages’ Gift. They have been using magic covertly for what appears to have been a very long time…. Another branch of the family is known to hold a fief in Normandy, but it is not yet known if they are covert magicians as well.”
The Vandaleur narrative may be of interest to fans of The Da Vinci Code. (Ford is said to have been a Freemason, a charter member of Riviera Lodge No. 780, Pacific Palisades, California.)
For Catholics and others who prefer more traditional narratives:
Illuminated parchment,
1047 A.D.,
The Four Horsemen
of the Apocalypse
Related material:
Yesterday’s entries, and
an entry from April 7. 2003,
that they link to:
Wednesday, August 30, 2006
Wednesday August 30, 2006
A Multicultural Farewell
to a winner of the
Nobel Prize for Literature,
the Egyptian author of
The Seventh Heaven:
Supernatural Stories —
"Jackson has identified
the seventh symbol."
— Stargate
Other versions of
the seventh symbol —
"… 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
Sunday, August 27, 2006
Sunday August 27, 2006
Philosopher Max Black,
who died on this date
in 1988
“… 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
Wednesday, August 9, 2006
Wednesday August 9, 2006
Wikipedia on Mel Gibson:
“The arrest was supported by…
an open container… 75% full,
labeled ‘Cazador [sic] tequila‘
(a strong type of mezcal).”
Today’s New York Times:
Refined Tequilas,
Meant to be Savored:
Photo by Lars Klove for
The New York Times
— Essay by Eric Asimov,
“Spirits of the Times“
“Remember that we deal with
Herb Alpert–
cunning, baffling, and powerful.”
(Adapted from Chapter 5
of Alcoholics Anonymous)
“Tequila,”
by The Champs
(1958)
The Spirituality of
Addiction and Recovery
“Turns out she’s a party girl
who loves Tequila:
‘Time disappears with Tequila.
It goes elastic, then vanishes.'”
Yvonne returns to the Bella Vista
in Under the Volcano:
“… a glass partition
that divided the room
(from yet another bar,
she remembered now,
giving on a side street)”
David Sanborn
(a reply to Alpert’s
Lonely Bull ):
— Review of Sanborn’s album “Timeagain“
by Geoffrey Himes in Jazz Times,
June 2003
Robin Williams in Rehab
“It may be that Kylie is,
in her own way, an artist…
with a 357.”
Friday, May 19, 2006
Friday May 19, 2006
The Great Bartender
by Peter Viereck (1948)
Being absurd as well as beautiful,
Magic– like art– is hoax redeemed by awe.
(Not priest but clown,
the shuddering sorcerer
Is more astounded than
his rapt applauders:
“Then all those props and Easters
of my stage
Came true? But I was joking all the time!”)
Art, being bartender, is never drunk;
And magic that believes itself, must die.
My star was rocket of my unbelief,
Launched heavenward as
all doubt’s longings are;
It burst when, drunk with self-belief,
I tried to be its priest and shouted upward:
“Answers at last! If you’ll but hint
the answers
For which earth aches, that famous
Whence and Whither;
Assuage our howling Why? with final fact.”
— As quoted in The Practical Cogitator,
or The Thinker’s Anthology,
Selected and Edited by
Charles P. Curtis, Jr., and
Ferris Greenslet,
Third Edition, Revised and Enlarged,
With a new Introduction by
John H. Finley, Jr.,
Houghton Mifflin Company,
Boston, 1962
The dates of Viereck’s birth and death are according to this morning’s New York Times.
Five Log24 entries
ending May 13,
the date of Viereck’s death.
Friday, May 12, 2006
Friday May 12, 2006
"Does the word 'tesseract'
mean anything to you?"
— Robert A. Heinlein in
The Number of the Beast
(1980)
My reply–
Part I:
A Wrinkle in Time, by
Madeleine L'Engle
(first published in 1962)
Part II:
Diamond Theory in 1937
and
Geometry of the 4×4 Square
Part III:
"Wells and trees were dedicated to saints. But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden. Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy."
— Charles Williams, Witchcraft, Faber and Faber, London, 1941
A New Yorker profile of Madeleine L'Engle from April 2004, which I found tonight online for the first time. For a related reflection on truth, stories, and values, see Saint's Day. For a wider context, see the Log24 entries of February 1-15, 2003 and February 1-15, 2006.
Wednesday, November 2, 2005
Wednesday November 2, 2005
To Serve Man
Starring
Sir Anthony Hopkins
as Smithers
(See previous entry.)
In memory of Lloyd Bochner,
who died on Oct. 29, 2005:
Sunday, July 17, 2005
Sunday July 17, 2005
Dance
Yesterday’s AP “Thought for Today”–
“In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose.” – J. Robert Oppenheimer, American physicist (1904-1967).
From Log24 on Dec. 17, 2002:
The Dancing Wu Li Masters,
by Gary Zukav, Harvard ’64:
“The Wu Li Masters know that physicists are doing more than ‘discovering the endless diversity of nature.’ They are dancing with Kali [or Durga], the Divine Mother of Hindu mythology.”
“Eastern religions have nothing to say about physics, but they have a great deal to say about human experience. In Hindu mythology, Kali, the Divine Mother, is the symbol for the infinite diversity of experience. Kali represents the entire physical plane. She is the drama, tragedy, humor, and sorrow of life. She is the brother, father, sister, mother, lover, and friend. She is the fiend, monster, beast, and brute. She is the sun and the ocean. She is the grass and the dew. She is our sense of accomplishment and our sense of doing worthwhile. Our thrill of discovery is a pendant on her bracelet. Our gratification is a spot of color on her cheek. Our sense of importance is the bell on her toe.
This full and seductive, terrible and wonderful earth mother always has something to offer. Hindus know the impossibility of seducing her or conquering her and the futility of loving her or hating her; so they do the only thing that they can do. They simply honor her.”
How could I dance with another….?
— John Lennon and Paul McCartney, 1962-1963
Saturday, June 4, 2005
Saturday June 4, 2005
The 4×4 Square:
French Perspectives
Earendil_Silmarils:
Les Anamorphoses:
“Pour construire un dessin en perspective,
le peintre trace sur sa toile des repères:
la ligne d’horizon (1),
le point de fuite principal (2)
où se rencontre les lignes de fuite (3)
et le point de fuite des diagonales (4).”
_______________________________
Serge Mehl,
Perspective &
Géométrie Projective:
“… la géométrie projective était souvent
synonyme de géométrie supérieure.
Elle s’opposait à la géométrie
euclidienne: élémentaire…
La géométrie projective, certes supérieure
car assez ardue, permet d’établir
de façon élégante des résultats de
la géométrie élémentaire.”
Similarly…
Finite projective geometry
(in particular, Galois geometry)
is certainly superior to
the elementary geometry of
quilt-pattern symmetry
and allows us to establish
de façon élégante
some results of that
elementary geometry.
Other Related Material…
from algebra rather than
geometry, and from a German
rather than from the French:
“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 U. Press, 1946
Evariste Galois
Weyl also says that the profound branch
of mathematics known as Galois theory
relativity theory for the set Sigma,
a set which, by its discrete and
finite character, is conceptually
so much simpler than the
infinite set of points in space
or space-time dealt with
by ordinary relativity theory.”
— Weyl, Symmetry,
Princeton U. Press, 1952
Metaphor and Algebra…
“Perhaps every science must
start with metaphor
and end with algebra;
and perhaps without metaphor
there would never have been
any algebra.”
Max Black, Models and Metaphors, 1962
For metaphor and
algebra combined, see
in a diamond ring,”
A.M.S. abstract 79T-A37,
Notices of the
American Mathematical Society,
February 1979, pages A-193, 194 —
the original version of the 4×4 case
of the diamond theorem.
More on Max Black…
“When approaching unfamiliar territory, we often, as observed earlier, try to describe or frame the novel situation using metaphors based on relations perceived in a familiar domain, and by using our powers of association, and our ability to exploit the structural similarity, we go on to conjecture new features for consideration, often not noticed at the outset. The metaphor works, according to Max Black, by transferring the associated ideas and implications of the secondary to the primary system, and by selecting, emphasising and suppressing features of the primary in such a way that new slants on it are illuminated.”
— Paul Thompson, University College, Oxford,
The Nature and Role of Intuition
in Mathematical Epistemology
That intuition, metaphor (i.e., analogy), and association may lead us astray is well known. The examples of French perspective above show what might happen if someone ignorant of finite geometry were to associate the phrase “4×4 square” with the phrase “projective geometry.” The results are ridiculously inappropriate, but at least the second example does, literally, illuminate “new slants”– i.e., diagonals– within the perspective drawing of the 4×4 square.
Similarly, analogy led the ancient Greeks to believe that the diagonal of a square is commensurate with the side… until someone gave them a new slant on the subject.
Monday, January 24, 2005
Monday January 24, 2005
Old School Tie
“We are introduced to John Nash, fuddling flat-footed about the Princeton courtyard, uninterested in his classmates’ yammering about their various accolades. One chap has a rather unfortunate sense of style, but rather than tritely insult him, Nash holds a patterned glass to the sun, [director Ron] Howard shows us refracted patterns of light that take shape in a punch bowl, which Nash then displaces onto the neckwear, replying, ‘There must be a formula for how ugly your tie is.’ ”

have been extremely influential.”– Draft of
Computing with Modal Logics
(pdf), by Carlos Areces
and Maarten de Rijke
“Algebra in general is particularly suited for structuring and abstracting. Here, structure is imposed via symmetries and dualities, for instance in terms of Galois connections……. diamonds and boxes are upper and lower adjoints of Galois connections….”
and Applications: A Survey”
(pdf), by Jules Desharnais,
Bernhard Möller, and
Georg Struth, March 2004
Galois Correspondence
Evariste Galois
“Perhaps every science must
start with metaphor
and end with algebra;
and perhaps without metaphor
there would never have been
any algebra.”
— attributed, in varying forms
(1, 2, 3), to Max Black,
Models and Metaphors, 1962
For metaphor and
algebra combined, see
“Symmetry invariance
in a diamond ring,”
A.M.S. abstract 79T-A37,
Notices of the Amer. Math. Soc.,
February 1979, pages A-193, 194 —
the original version of the 4×4 case
of the diamond theorem.
Wednesday, January 5, 2005
Wednesday January 5, 2005
Death and the Spirit
A meditation for Twelfth Night
on "the whirligig of time"
- Frank Kelly Freas, who created, among other works, 400 portraits of saints for the Franciscans and the covers of Mad Magazine from 1958 through 1962. "I found it difficult to shift my artistic gears from the sublime to the ridiculous and back again," he said of his departure from Mad.
- Will Eisner, "an innovative comic-book artist who created the Spirit, a hero without superpowers, and the first modern graphic novel."
Yesterday's entry provided an approach to The Dark Lady, Kali, that was, in Freas's apt word, "ridiculous." The illustration below, "Mate," is an attempt to balance yesterday's entry with an approach that is, if not sublime, at least more serious. It is based on a similar illustration from Jan. 31, 2003, with actress Judy Davis playing The Dark Lady. Today it seems appropriate to replace Davis with another actress (anonymous here, though some may recognize her). I once knew her (unlike Davis) personally. One of my fondest memories of high school is reading Mad Magazine with her in the school lunch room. Our lives diverged after high school, but I could happily have spent my life in her company.
– S. H. Cullinane, Twelfth Night, 2005
A diamond and its dual "whirl" figure—
or a "jewel-box and its mate"
ending on Feb. 1, 2003, and the
perceptive remarks of Ryan Benedetti
on Sam Spade and Brigid O'Shaughnessy.
As for Eisner and "The Spirit,"
which has been called
"the quintessential noir detective series,"
those preferring non-graphic stories
may picture Spade or his creator,
Dashiell Hammett, in the title role.
Then, of course, there are Eisner's later
story, "A Contract With God,"
John 4:24, and 1916 4/24.
Sunday, October 31, 2004
Sunday October 31, 2004
A Triple Play
From today’s New York Times, in reverse order:
Vaughn Meader, Star as Kennedy Mimicker, Dies at 68 Sister Nancy Salisbury, 74, Headmistress, Dies |
For more background, see the Log24.net entry of 3 AM Friday, the date of Meader’s death. See also a Boston Globe obituary that quotes John F. Kennedy: “Vaughn Meader was busy tonight, so I came myself.”
Note that Rousmaniere was John F. Kennedy’s roommate at Harvard.
Note, too, that Kennedy’s daughter Caroline attended Sister Salisbury’s school.
A memorial Mass for Sister Salisbury will be held on Monday, November 22, 2004, at the Church of St. Ignatius Loyola, 980 Park Avenue, at 5:30 pm.
What does all this Camelot portend? I do not know, but the following quote seems appropriate.
“Flores, flores para los muertos.”
— Tennessee Williams, 1947
Monday, October 18, 2004
Monday October 18, 2004
Counting Crows
on the Feast of St. Luke
"In the fullness of time,
educated people will believe
there is no soul
independent of the body,
and hence no life after death."
— Francis Crick, who was awarded
a Nobel Prize on this date in 1962
"She went to the men on the ground and looked at them and then she found Inman apart from them. She sat and held him in her lap. He tried to talk, but she hushed him. He drifted in and out and dreamed a bright dream of a home. It had a coldwater spring rising out of a rock, black dirt fields, old trees. In his dream, the year seemed to be happening all at one time, all the seasons blending together. Apple trees hanging heavy with fruit but yet unaccountably blossoming, ice rimming the spring, okra plants blooming yellow and maroon, maple leaves red as October, corn crops tasseling, a stuffed chair pulled up to the glowing parlor hearth, pumpkins shining in the fields, laurels blooming on the hillsides, ditch banks full of orange jewelweed, white blossoms on dogwood, purple on redbud. Everything coming around at once. And there were white oaks, and a great number of crows, or at least the spirits of crows, dancing and singing in the upper limbs. There was something he wanted to say."
— Charles Frazier, Cold Mountain
Thursday, May 20, 2004
Thursday May 20, 2004
Parable
“A comparison or analogy. The word is simply a transliteration of the Greek word: parabolé (literally: ‘what is thrown beside’ or ‘juxtaposed’), a term used to designate the geometric application we call a ‘parabola.’…. The basic parables are extended similes or metaphors.”
— http://religion.rutgers.edu/nt/
primer/parable.html
“If one style of thought stands out as the most potent explanation of genius, it is the ability to make juxtapositions that elude mere mortals. Call it a facility with metaphor, the ability to connect the unconnected, to see relationships to which others are blind.”
— Sharon Begley, “The Puzzle of Genius,” Newsweek magazine, June 28, 1993, p. 50
“The poet sets one metaphor against another and hopes that the sparks set off by the juxtaposition will ignite something in the mind as well. Hopkins’ poem ‘Pied Beauty’ has to do with ‘creation.’ “
— Speaking in Parables, Ch. 2, by Sallie McFague
“The Act of Creation is, I believe, a more truly creative work than any of Koestler’s novels…. According to him, the creative faculty in whatever form is owing to a circumstance which he calls ‘bisociation.’ And we recognize this intuitively whenever we laugh at a joke, are dazzled by a fine metaphor, are astonished and excited by a unification of styles, or ‘see,’ for the first time, the possibility of a significant theoretical breakthrough in a scientific inquiry. In short, one touch of genius—or bisociation—makes the whole world kin. Or so Koestler believes.”
— Henry David Aiken, The Metaphysics of Arthur Koestler, New York Review of Books, Dec. 17, 1964
For further details, see
Speaking in Parables:
A Study in Metaphor and Theology
by Sallie McFague
Fortress Press, Philadelphia, 1975
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
“Perhaps every science must start with metaphor and end with algebra; and perhaps without metaphor there would never have been any algebra.”
— attributed, in varying forms (1, 2, 3), to Max Black, Models and Metaphors, 1962
For metaphor and algebra combined, see
“Symmetry invariance in a diamond ring,” A.M.S. abstract 79T-A37, Notices of the Amer. Math. Soc., February 1979, pages A-193, 194 — the original version of the 4×4 case of the diamond theorem.
Saturday, December 20, 2003
Saturday December 20, 2003
For St. Emil’s Day
On this date in 1962, Emil Artin died.
He was, in his way, a priest of Apollo, god of music, light, and reason.
The previous entry dealt with permutation groups, in the context of a Jan. 2004 AMS Notices review of a book on the mathematics of juggling.
It turns out that juggling is, in fact, related to Artin’s theory of “braid groups.” For details, see Juggling Braids.
For more on Apollo, see my entry of
1/09.
Friday, November 7, 2003
Friday November 7, 2003
Today in History:
The Comeback Kid
(Courtesy of Dr. Mac’s Cultural Calendar)
On this date:
In 1962, having lost the California governor’s race, Richard Nixon said to the press, “You won’t have Nixon to kick around any more.”
In 1972, Republican incumbent President Richard Nixon was re-elected, defeating Democratic candidate George McGovern, 520 electoral votes to 17.
From the archives of singer/songwriter Shannon Campbell (“voice of an angel, mouth of a truckdriver”)–
Feb. 6, 2002: The Essential Matrix
NEO: (whines) Who am I?
TRINITY: You are The One.
EVERYONE ELSE: Eh, he might be The One.
TRINITY: He is The One.
NEO: I am not The One.
TRINITY: You are The One.
THE ORACLE: You are not The One, but you can’t tell anybody.
NEO: (whines) But I wanted to be The One. I want to go home….
TRINITY: Fuck. He’s not The One.
EVERYONE ELSE: Told you so.
MORPHEUS: Sure wish someone was The One. I’m in deep shit.
Thursday, September 11, 2003
Thursday September 11, 2003
Particularity
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Upon learning of the recent death of Walter J. Ong, S. J., philosopher of language, I ordered a copy of his book
Hopkins, the Self, and God
University of Toronto Press, 1986.
As the reader of my previous entry will discover, I have a very low opinion of the literary skills of the first Christians. This sect’s writing has, however, improved in the past two millennia.
Despite my low opinion of the early Christians, I am still not convinced their religion is totally unfounded. Hence my ordering of the Ong book. Since then, I have also ordered two other books, reflecting my interests in philosophical fiction (see previous entry) and in philosophy itself:
Philosophical fiction —
The Hex Witch of Seldom,
by Nancy Springer,
Penguin Putnam Inc., 2002
(See 1 Corinthians 1:26-29)
Philosophy —
Definition,
by Richard Robinson,
Fellow of Oriel College, Oxford,
Oxford U. Press, 1954, reprinted 1962.
Following the scientific advice of Niels Bohr and Freeman Dyson, I articulated on April 25, 2003, a mad theory of the mystical significance of the number 162.
Here is that theory applied to the three works named above, all three of which I received, synchronistically, today.
Page 162 of Hopkins, the Self, and God is part of the long list of references at the back of the book. Undiscouraged by the seeming insignificance (vide my note Dogma) of this page, I looked more closely. Behold, there was Christ… Carol T. Christ, that is, author of The Finer Optic: The Aesthetic of Particularity in Victorian Poetry, Yale University Press, 1975. “Particularity” seemed an apt description of my “162” approach to literature, so I consulted Christ’s remarks as described in the main body of Ong’s book.
Particularity according to Christ —
“Victorian particularist aesthetics has prospered to the present time, and not only in novels. The isolated, particularized, unique ‘good moment’ [Christ, 105], the flash of awareness at one particular instant in just the right setting, which Hopkins celebrates….”
— Ong, Hopkins, the Self, and God, p. 14
I highly recommend the rest of Ong’s remarks on particularity.
Turning to the other two of the literary trinity of books I received today….
Page 162 of The Hex Witch of Seldom has the following:
“There was a loaf of Stroehmann’s Sunbeam Bread in the grocery sack also; she and Witchie each had several slices. Bobbi folded and compressed hers into little squares and popped each slice into her mouth all at once.”
The religious significance of this passage seems, in Ong’s Jesuit context, quite clear.
Page 162 of Definition has the following:
“Real Definition as the Search for a Key. Mr. Santayana, in his book on The Sense of Beauty, made the following extremely large demands on real definition:
‘A definition <of beauty> that should really define must be nothing less than the exposition of the origin, place, and elements of beauty as an object of human experience. We must learn from it, as far as possible, why, when, and how beauty appears, what conditions an object must fulfil to be beautiful, what elements of our nature make us sensible of beauty, and what the relation is between the constitution of the object and the excitement of our sensibility. Nothing less will really define beauty or make us understand what aesthetic appreciation is. The definition of beauty in this sense will be the task of this whole book, a task that can be only very imperfectly accomplished within its limits.’ ”
Here is a rhetorical exercise for Jesuits that James Joyce might appreciate:
Discuss Bobbi’s “little squares” of bread as the Body of Christ. Formulate, using Santayana’s criteria, a definition of beauty that includes this sacrament.
Refer, if necessary, to
the log24.net entries
Mr. Holland’s Week and Elegance.
Refrain from using the phrase
“scandal of particularity”
unless you can use it as well as
Annie Dillard.
Tuesday, July 1, 2003
Tuesday July 1, 2003
Jew’s on First
This entry is dedicated to those worshippers of Allah who have at one time or another cried
“Itbah al-Yahud!” … Kill the Jew!
(See June 29 entries).
Dead at 78 Comedian Buddy Hackett died on Tuesday, July First, 2003, according to the New York Times. According to Bloomberg.com, he died Sunday or Monday. |
![]() Associated Press
Buddy Hackett, |
Whatever. We may imagine he has now walked, leading a parade of many other stand-up saints, into a bar. |
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MIDRASH From my May 25 entry, Matrix of the Death God: R. M. Abraham’s Diversions and Pastimes, published by Constable and Company, London, in 1933, has the following magic square: The Matrix of Abraham A summary of the religious import of the above from Princeton University Press: “Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah. Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.” — Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72 Other appearances of this religious icon on the Web include:
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In the Picasso’s Birthday version, 22 of the 25 magic square cells are correlated with pictures on the “Class of ’91” cover of Rolling Stone magazine. Number 7 is Rod† Stewart. In accordance with the theological rhyme “Seven is heaven, eight is a gate,” our site music for today is “Forever Young,” a tune made famous by Stewart.
† Roderick, actually — the name of the hero in “Madwoman of Chaillot”