Monday, November 10, 2014

Meanwhile, Back in 1962

Filed under: Uncategorized — Tags: — m759 @ 11:59 PM

Remember him to Herald Square.

Thursday, September 27, 2012

April 9, 1962

Filed under: Uncategorized — m759 @ 1:01 AM

IMAGE- Andy Williams sings 'Moon River' from 'Breakfast at Tiffany's' at the Academy Awards on 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, March 31, 2018

Cube Theory

Filed under: Uncategorized — m759 @ 9:00 PM

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 . . .

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Notes for the Harrowing of Hell

Filed under: Uncategorized — Tags: — m759 @ 12:18 PM

From a post of April 15, 2006

From elsewhere

Sunday, February 4, 2018

Logos for Sunday, February 4

Filed under: Uncategorized — m759 @ 10:00 AM

"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:

Nietzsche, 'law in becoming' and 'play in necessity'

Logos for Philosophers
(Suggested by Modal Logic) —

Nietzsche, 'law in becoming' and 'play in necessity'

Thursday, January 25, 2018

Beware of Analogical Extension

Filed under: Uncategorized — Tags: — m759 @ 11:29 AM

"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' …."

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


Filed under: Uncategorized — Tags: — m759 @ 1:00 PM

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 —


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)

Filed under: Uncategorized — Tags: — m759 @ 3:00 PM

Nietzsche, 'law in becoming' and 'play in necessity'

"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) —

Nietzsche, 'law in becoming' and 'play in necessity'

Monday, September 4, 2017

Labor Date

Filed under: Uncategorized — m759 @ 2:00 PM

(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
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

Filed under: Uncategorized — m759 @ 3:07 PM

(A prequel to an Ursula K. Le Guin story
in Fantastic  magazine, September 1962)

Cover art by Lloyd Birmingham for "Plane Jane"

Knight Moves

Filed under: Uncategorized — m759 @ 12:42 PM

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 —

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

See as well a search for 1962 in this journal.

Tuesday, May 23, 2017

In Memoriam

Filed under: Uncategorized — m759 @ 11:26 AM

"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

Filed under: Uncategorized — m759 @ 1:45 PM

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

Security Complex

Filed under: Uncategorized — m759 @ 9:36 PM

"All on a Saturday night" — Johnny Thunder, 1962

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Wednesday, March 22, 2017

Pulp Fiction Incarnate

Filed under: Uncategorized — m759 @ 2:20 PM

From Log24 earlier —

More recently, an image from the above March 18 VUDU date —

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Saturday, March 18, 2017

Back to the Past

Filed under: Uncategorized — Tags: — m759 @ 7:35 PM

"Old men ought to be explorers" — T. S. Eliot

"All on a Saturday night" — Johnny Thunder, 1962

'Loop De Loop,' Johnny Thunder, Diamond Records, 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

Filed under: Uncategorized — m759 @ 10:09 PM

"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

Filed under: Uncategorized — m759 @ 2:40 PM

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

Epiphany 2017 —

Click to enlarge:

Tuesday, January 10, 2017

Analogical Extension Meets Analytic Continuation

Filed under: Uncategorized — m759 @ 7:35 PM

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

Filed under: Uncategorized — m759 @ 8:40 PM

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

'Loop De Loop,' Diamond Records, 1962

* Funny peculiar, not funny ha-ha.

Analogical Extension at Cornell

Filed under: Uncategorized — m759 @ 1:30 PM

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*

Filed under: Uncategorized — Tags: — m759 @ 2:17 PM

From "The Man Who Tried to Redeem the World with Logic" —

"To store the programs as data, the computer would need
something newa 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

Quick Now, Here, Now, Always

Filed under: Uncategorized — Tags: — m759 @ 11:25 AM

'Only a peculiar can enter a time loop' — Nov. 21, 2016

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Tuesday, December 27, 2016

The Dark Side

Filed under: Uncategorized — m759 @ 10:04 PM

"The record, released on the Diamond label,
became a big hit, rising to no. 4 on the
Billboard  Hot 100 in early 1963." — Wikipedia

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Saturday, December 3, 2016

SIAM Publication

Filed under: Uncategorized — m759 @ 10:01 AM

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

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM


"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

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM

A search for "Max Black" in this journal yields some images
from a post of August 30, 2006 . . .

A circular I Ching

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified the seventh symbol."
— Stargate

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,'
to borrow I. A. Richards' happy title. They, too, bring about a wedding
of disparate subjects, by a distinctive operation of transfer of the
implications  of relatively well-organized cognitive fields. And as with
other weddings, their outcomes are unpredictable."

Max Black in Models and Metaphors , Cornell U. Press, 1962

A Motive for Metaphor

Filed under: Uncategorized — m759 @ 12:00 PM

From 'Models and Metaphors' by Max Black, Cornell U. Press 1962

Saturday, March 26, 2016

Story Idea

Filed under: Uncategorized — m759 @ 3:24 AM

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

Filed under: Uncategorized — m759 @ 10:26 PM

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.

The image “http://www.log24.com/log/pix06B/061122-Flywheel.gif” cannot be displayed, because it contains errors.

Sunday, November 22, 2015

Overlook Video

Filed under: Uncategorized — m759 @ 7:26 AM

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

Filed under: Uncategorized — m759 @ 9:00 AM

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

Filed under: Uncategorized — m759 @ 10:07 AM

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

Filed under: Uncategorized — m759 @ 6:00 PM

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

Filed under: Uncategorized — m759 @ 9:00 AM

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

Filed under: Uncategorized — Tags: — m759 @ 5:55 PM

Continued from Nobel Note (Jan. 29, 2014).

IMAGE- 'Launched from Cuber' scene in 'X-Men: First Class'

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

Say Bingo to my little friend

    … and on Bruce Springsteen's birthday this year —

Tuesday, September 23, 2014


Filed under: Uncategorized — m759 @ 11:00 AM 

From AP’s Today in History:

Happy birthday.

“It all adds up.” — Saul Bellow

The Matrix:





Thursday, September 11, 2014

A Class by Itself

Filed under: Uncategorized — Tags: — m759 @ 9:48 AM

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.")

From Google Books:

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

Filed under: Uncategorized — m759 @ 3:00 PM

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

Filed under: Uncategorized — Tags: — m759 @ 11:06 AM

(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.


“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

Filed under: Uncategorized — m759 @ 2:01 PM


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


Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

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

Filed under: Uncategorized — m759 @ 9:45 AM

"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

Filed under: Uncategorized — m759 @ 9:29 PM

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

Filed under: Uncategorized — Tags: — m759 @ 4:00 PM


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

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

Filed under: Uncategorized — m759 @ 1:04 PM

"Rep-tiles Revisited," by Viorel Nitica, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics ,  American Mathematical Society, 2003—

"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"—



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

Filed under: Uncategorized — m759 @ 2:01 AM

IMAGE- Rudolf Koch's version of the 'double cross' symbol

  Source: Rudolf KochThe Book of Signs

The American Mathematical Society
(AMS) yesterday:

Lars Hörmander (1931-2012)
Friday November 30th 2012

Hörmander, who received a Fields Medal in 1962,
died November 25 at the age of 81. …

more »

Some related material:

See also posts on Damnation Morning and, from the
date of Hörmander's death,

Sunday, November 18, 2012


Filed under: Uncategorized — Tags: — m759 @ 11:00 AM

Happy birthday to

IMAGE- Margaret Atwood, Kim Wilde, Peta Wilson

Today's sermon, by Marie-Louise von Franz

Number and Time, 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

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

The circle above is marked with a version
of the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

For the square, see the diamond theorem.

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

— Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
  Canto IV of "It Must Change"

Wednesday, July 18, 2012


Filed under: Uncategorized — m759 @ 9:48 AM

(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." 

The Enneagram as Mandala

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)

Filed under: Uncategorized — m759 @ 11:59 PM

Background— August 30, 2006—

The Seventh Symbol:

The image “http://www.log24.com/log/pix06A/060830-Algebra.jpg” cannot be displayed, because it contains errors.

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—

"Time for you to see the field."
Bagger Vance

Thursday, April 26, 2012

Rainbow People

Filed under: Uncategorized — m759 @ 6:29 PM

(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."

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

Filed under: Uncategorized — m759 @ 9:48 AM

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

IMAGE- Theologian William Hamilton at the University of St. Andrews, Scotland, February 10, 1950

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

History Highlights

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
Oct. 8, 2006



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.


At Last, a
Guiding Philosophy

The General Education report is a strong cornerstone, though further scrutiny is required.

After four long years, the Curricular Review has finally found its heart.

The Trouble
With the Germans

The College is a little under-educated these days.

Harvard College– in the best formulation I’ve heard– promulgates a Japanese-style education, where the professoriate pretend to teach, the students pretend to learn, and everyone is happy.

Sunday, December 4, 2011

Code Wars

Filed under: Uncategorized — m759 @ 2:00 PM

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"



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*)

Filed under: Uncategorized — m759 @ 12:00 PM

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

Filed under: Uncategorized — m759 @ 12:00 AM

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

Filed under: Uncategorized — m759 @ 1:31 AM

Continued from Good Friday

Emmylou Harris and Rivka Galchen in the May 2, 2011 New Yorker

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

Hard Bargain

m759 @ 11:01 PM

In memory of Hazel Dickens, two links —
Unique Figure and Hello Stranger .

Weepin' like a willow, mournin' like a dove
Weepin' like a willow, mournin' like a dove
There's a girl of the country
That I really love

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

Filed under: Uncategorized — Tags: — m759 @ 4:04 AM

(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

Filed under: Uncategorized — m759 @ 5:01 AM

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

Filed under: Uncategorized — m759 @ 7:26 PM

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

  1. 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.
  2. 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.
  3. The Carpenter Center exhibition will have an opening reception on February 4.
  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

Filed under: Uncategorized — m759 @ 11:00 AM

Dies Natalis of
Emil Artin

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

Filed under: Uncategorized — m759 @ 2:56 PM

“There are two silences.
One when no word is spoken.
The other when perhaps a torrent
of language is being employed.”

Harold Pinter, 1962

Stille Nacht…

Pinter died on December 24, 2008:

Top center front page, online NY Times, Christmas 2008-- Pinter dead at 78

Heilige Nacht…

Also on Christmas Eve, 2008

(“24/12/08  3:23 pm”):


Click to enlarge.


Wednesday, March 4, 2009

Wednesday March 4, 2009

Filed under: Uncategorized — m759 @ 9:00 AM
Markoff Process

“So fearsome was Dr. Schwartz’s early reputation as a mathematician that when John Forbes Nash Jr., the Nobel Prize winning mathematician and economist, learned that he was attempting to solve an extremely challenging mathematical problem…. he became agitated, apparently fearing Dr. Schwartz might beat him to a solution, said Sylvia Nasar, author of ‘A Beautiful Mind,’ a biography of Nash.”

New York Times obituary of Jacob T. Schwartz dated Tuesday, March 3, 2009

 Author of the obituary:
John Markoff.

New York Lottery
March 3, 2009:

NY Lottery March 3, 2009-- Midday 491, Evening 116

“His background in mathematical algorithms led Dr. Schwartz to develop an early programming language…. The language would later influence the designer of the Python programming language, widely used by programmers today.” —NY Times

“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.”*

Monty Python - Bright Side of Life

Dr. Schwartz died on Monday,
birthday of Tom Wolfe —
who wrote
The Painted Word.

1/16: “It’s all there, hiding behind the realistic side.” –Andrew Wyeth

Related material: The previous five entries.

* 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

Filed under: Uncategorized — m759 @ 9:00 AM
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…”

Paul Simon, Graceland album 

NY Times obituaries, Tuesday, June 17, 2008-- Tony Schwartz, Walter Netsch, Tim Russert

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….”

Center of Town, Cuernavaca, from Paul Goodman's Communitas
Log24, Feb. 24, 2008:

Candela's 'Capilla Abierta' chapel, Cuernavaca, Mexico

Chapel, Cuernavaca, Mexico

“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:

No se puede vivir sin amar.”

— Malcolm Lowry,
Under the Volcano

Photo by Gerry Gantt

(March 3, 2004)

Saturday, July 14, 2007

Saturday July 14, 2007

Filed under: Uncategorized — m759 @ 4:07 AM
A Note from the
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, 2006April 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

Father Robert Sokolowski

Father Robert Sokolowski

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.

Thomas Aquinas College newsletter

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

Filed under: Uncategorized — Tags: — m759 @ 3:09 AM

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

Filed under: Uncategorized — Tags: — m759 @ 8:35 AM
Footprints for

The image “http://www.log24.com/log/pix07/070307-Baudrillard.jpg” cannot be displayed, because it contains errors.

"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"

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
Beijing String
12:04 PM
District of Columbia
12:03 PM
District of Columbia
About God, Life, Death
12:03 PM
District of Columbia
A Library of Congress Reading
12:03 PM
District of Columbia
Binary Geometry
12:03 PM
District of Columbia
Prequel on St. Cecelia's Day
12:03 PM

Thursday, March 1, 2007

Thursday March 1, 2007

Filed under: Uncategorized — Tags: — m759 @ 6:29 AM

Senior Honors

Notes in Memory of
a Father, a Son, and a Holy Ghost

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.'"

Douglas Martin

From The Catholic Encyclopedia:

"It is sufficient for true knowledge that it affirm as real that which is truly real."

Article on Ontologism

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

Filed under: Uncategorized — m759 @ 3:09 PM

“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

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.'”

— 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.

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Sunday, November 12, 2006

Sunday November 12, 2006

Filed under: Uncategorized — m759 @ 12:25 AM


Log24, Feb. 25, 2004:

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

Filed under: Uncategorized — m759 @ 4:04 AM
A Game of Chess

for Isak Dinesen,
who died in 1962
on this date

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Click on pictures for details.

Thursday, August 31, 2006

Thursday August 31, 2006

Filed under: Uncategorized — Tags: — m759 @ 11:09 PM
Wag the Dogma
(continued from 2001)
Ingrid Thulin and
Glenn Ford in
“The 4 Horsemen
of the Apocalypse”:

The 4 Horsemen, Ingrid Thulin, Glenn Ford

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:

The image “http://www.log24.com/log/pix06A/060831-ScotsmanLogo3.gif” cannot be displayed, because it contains errors.

Screen icon Glenn Ford
dies at 90


GLENN 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:

The image “http://www.log24.com/log/pix06A/060831-4Horsemen.jpg” cannot be displayed, because it contains errors.

 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:

Mathematics and The Seventh Seal

Wednesday, August 30, 2006

Wednesday August 30, 2006

Filed under: Uncategorized — m759 @ 10:07 AM
The Seventh Symbol:

A Multicultural Farewell

to a winner of the
Nobel Prize for Literature,
the Egyptian author of
The Seventh Heaven:
Supernatural Stories

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The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified
the seventh symbol."

Other versions of
the seventh symbol —

Chinese version:

The image “http://www.log24.com/log/pix06A/060830-hexagram20.gif” cannot be displayed, because it contains errors.

pictorial version:

The image “http://www.log24.com/log/pix06A/060830-Box.jpg” cannot be displayed, because it contains errors.

algebraic version:

The image “http://www.log24.com/log/pix06A/060830-Algebra.jpg” cannot be displayed, because it contains errors.

"… 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

Filed under: Uncategorized — m759 @ 4:00 PM
Today’s Saint:

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

Filed under: Uncategorized — m759 @ 2:02 PM
Two-Bar Hook
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:

The image “http://www.log24.com/log/pix06A/060809-Bottle.jpg” cannot be displayed, because it contains errors.
Photo by Lars Klove for
The New York Times

— Essay by Eric Asimov,
  “Spirits of the Times

“Remember that we deal with
Herb Alpert–

The image “http://www.log24.com/log/pix06A/060809-Alpert.jpg” cannot be displayed, because it contains errors.
First album, 1962

cunning, baffling, and powerful.”

(Adapted from Chapter 5
of Alcoholics Anonymous)

Related Material:

by The Champs

The Spirituality of
Addiction and Recovery

Kylie on Tequila:

“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 ):

The image “http://www.log24.com/log/pix06A/Closer.jpg” cannot be displayed, because it contains errors.

“Just listen to how he attacks the two-bar hook of  ‘Tequila.’ After planting it firmly in our brains, he finds new ending notes for each measure; then he drops half a bar by an octave; then he substitutes a new melodic detour for the first bar, retaining the second; then he inverts that approach. He keeps twisting the phrase into new melodic shapes, but he never obscures the original motif and he never loses the beat.”

Review of Sanborn’s album “Timeagain
    by Geoffrey Himes in Jazz Times,
    June 2003

Update of 3:57 PM:
Robin Williams in Rehab

“It may be that Kylie is,
in her own way, an artist…
with a 357.”

Symmetry and Change

Friday, May 19, 2006

Friday May 19, 2006

Filed under: Uncategorized — m759 @ 2:02 AM
Peter Viereck

August 5, 1916 – May 13, 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.

Related material:

Five Log24 entries
ending May 13,
 the date of Viereck’s death.

Friday, May 12, 2006

Friday May 12, 2006

Filed under: Uncategorized — Tags: — m759 @ 3:00 AM

"Does the word 'tesseract'
mean anything to you?"
— Robert A. Heinlein in
The Number of the Beast

My reply–

Part I:

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A Wrinkle in Time, by
Madeleine L'Engle
(first published in 1962)

Part II:

Diamond Theory in 1937
Geometry of the 4×4 Square

Part III:

Catholic Schools Sermon


"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

Related material:

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

Filed under: Uncategorized — Tags: — m759 @ 3:24 PM

To Serve Man

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Sir Anthony Hopkins
as Smithers
(See previous entry.)

In memory of Lloyd Bochner,
who died on Oct. 29, 2005:

"In his most memorable television role, Mr. Bochner starred as Michael Chambers in the famous 1962 'Twilight Zone' episode 'To Serve Man.' Chambers and his assistant are decoding experts in charge of translating a book given to Earth by visiting extraterrestrials. The assistant learns that it is a cookbook, but is too late to save Mr. Bochner's character from boarding a spaceship and heading toward becoming an alien meal."

Monica Potts in today's New York Times

Sunday, July 17, 2005

Sunday July 17, 2005

Filed under: Uncategorized — m759 @ 7:59 PM


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  

See also yesterday‘s entry.

Saturday, June 4, 2005

Saturday June 4, 2005

Filed under: Uncategorized — m759 @ 7:00 PM
  Drama of the Diagonal
   The 4×4 Square:
  French Perspectives

The image “http://www.log24.com/log/pix05A/050604-Fuite1.jpg” cannot be displayed, because it contains errors.
   Les Anamorphoses:
   The image “http://www.log24.com/log/pix05A/050604-DesertSquare.jpg” cannot be displayed, because it contains errors.
  “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.”
  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

The image “http://www.log24.com/log/pix05/050124-galois12s.jpg” cannot be displayed, because it contains errors.

Evariste Galois

 Weyl also says that the profound branch
of mathematics known as Galois theory

   “… is nothing else but the
   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.” 

   — attributed, in varying forms, 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
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

  A New Slant…  

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

Filed under: Uncategorized — Tags: — m759 @ 2:45 PM

Old School Tie

From a review of A Beautiful Mind:

"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.' "

The image “http://www.log24.com/log/pix05/050124-Tie.gif” cannot be displayed, because it contains errors.

"Three readings of diamond and box
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…."

— "Modal Kleene Algebra
and Applications: A Survey"
(pdf), by Jules Desharnais,
Bernhard Möller, and
Georg Struth, March 2004
See also
Galois Correspondence

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Evariste Galois

and Log24.net, May 20, 2004:

"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

Filed under: Uncategorized — m759 @ 7:11 AM

Death and the Spirit

A meditation for Twelfth Night
on “the whirligig of time

Today’s New York Times obituaries feature two notable graphic artists: 

  • 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

The image “http://log24.com/log/pix05/050105-Mate.jpg” cannot be displayed, because it contains errors.

A diamond and its dual “whirl” figure—
or a “jewel-box and its mate”

For details, see the five Log24 entries
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

Filed under: Uncategorized — m759 @ 12:12 PM
Dead On:
A Triple Play


From today’s New York Times, in reverse order:

Vaughn Meader, Star as Kennedy Mimicker, Dies at 68
Vaughn Meader was a comic who attained instant celebrity in 1962 with his record “The First Family,” a dead-on spoof of President John F. Kennedy and his entourage.

James Rousmaniere, 86, Skilled Yachtsman, Dies
James A. Rousmaniere was a socially prominent yachtsman and professional fund-raiser.

Sister Nancy Salisbury, 74, Headmistress, Dies
Sister Nancy Salisbury was the longtime headmistress of New York’s oldest independent school for girls, the Convent of the Sacred Heart..

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

Filed under: Uncategorized — m759 @ 3:33 PM

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

Filed under: Uncategorized — m759 @ 7:00 AM


“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.”


“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

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

Filed under: Uncategorized — m759 @ 1:09 AM

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


Friday, November 7, 2003

Friday November 7, 2003

Filed under: Uncategorized — m759 @ 1:28 PM

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

Filed under: Uncategorized — Tags: , — m759 @ 6:25 PM


Walter J. Ong


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 —

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

Filed under: Uncategorized — Tags: — m759 @ 5:37 PM

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,
on the set of
“It’s a Mad, Mad,
Mad, Mad
in 1962.

Whatever.  We may imagine he has now walked, leading a parade of many other stand-up saints, into a bar.

Hepburn at Chaillot

for Buddy Hackett

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:

On Linguistic Creation

Picasso’s Birthday

1991 Yearbook
Rolling Stone


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”

Sunday, June 22, 2003

Sunday June 22, 2003

Filed under: Uncategorized — m759 @ 9:00 PM

Trance of the Red Queen

In memory of playwright George Axelrod, who died Saturday, June 21, 2003.

From the Chicago Sun-Times:

“In 1987, Mr. Axelrod was saluted at the New York Film Festival. He told the admiring crowd: ‘I always wanted to get into the major leagues, and I knew my secret: luck and timing. I had a small and narrow but very, very sharp talent, and inside it, I’m as good as it gets.’

The Manchurian Candidate,’ in 1962, based on Richard Condon’s novel about wartime brainwashing and subversive politics, may have been Mr. Axelrod’s best achievement. He declared in 1995 that the script ‘broke every rule. It’s got dream sequences, flashbacks, narration out of nowhere . . . Everything in the world you’re told not to do.’

He considered ‘The Manchurian Candidate’ a comedy….”

“Don’t you draw the queen of diamonds,
     boy, she’ll beat you if she’s able.
You know the queen of hearts
     is always your best bet.”

— The Eagles, “Desperado”

Another quotation that seems relevant:

“The hypnosis was performed by
the good and pious nuns….”

For the Diocese of Phoenix 

See entries of June 4 and June 15.

See also two items from Tuesday, June 17, 2003:

A 6/17 Arizona Daily Star article on Phoenix bishop Thomas O’Brien, and the 6/17 cartoon below.


Tony Auth, Philadelphia Inquirer,
June 17, 2003

For background, see Frank Keating in the New York Times, 6/17/03.

My entry of 5 PM EDT Saturday, June 14, 2003, which preceded the death involving Bishop O’Brien, may also be of interest.

Friday, May 9, 2003

Friday May 9, 2003

Filed under: Uncategorized — m759 @ 6:30 PM


The Rhetoric of Power:
A meditation for Mental Health Month

From “Secondary Structures,” by Tom Moody, Sculpture Magazine, June 2000:

“By the early ’90s, the perception of Minimalism as a ‘pure’ art untouched by history lay in tatters. The coup de grâce against the movement came not from an artwork, however, but from a text. Shortly after the removal of Richard Serra’s Tilted Arc from New York City’s Federal Plaza, Harvard art historian Anna Chave published ‘Minimalism and the Rhetoric of Power’ (Arts Magazine, January 1990), a rousing attack on the boys’ club that stops just short of a full-blown ad hominem rant. Analyzing artworks (Walter de Maria’s aluminum swastika, Morris’s ‘carceral images,’ Flavin’s phallic ‘hot rods’), critical vocabulary (Morris’s use of ‘intimacy’ as a negative, Judd’s incantatory use of the word ‘powerful’), even titles (Frank Stella’s National Socialist-tinged Arbeit Macht Frei and Reichstag), Chave highlights the disturbing undercurrents of hypermasculinity and social control beneath Minimalism’s bland exterior.  Seeing it through the eyes of the ordinary viewer, she concludes that ‘what [most] disturbs [the public at large] about Minimalist art may be what disturbs them about their own lives and times, as the face it projects is society’s blankest, steeliest face; the impersonal face of technology, industry and commerce; the unyielding face of the father: a face that is usually far more attractively masked.’ ”

From Maureen Dowd’s New York Times column of June 9, 2002: 

“The shape of the government is not as important as the policy of the government. If he makes the policy aggressive and pre-emptive, the president can conduct the war on terror from the National Gallery of Art.”

From the New York Times
Friday, May 2, 2003:

The National Gallery of Art in Washington has just acquired Tony Smith’s first steel sculpture: “Die,” created in 1962 and fabricated in 1968.

“It’s a seminal icon of postwar American art,” said Earl A. Powell III, director of the National Gallery.

Die (Tony Smith)

Bishop Moore

From a New York Times obituary,
Friday, May 2, 2003:

Bishop Dies

by Ari L. Goldman

Paul Moore Jr., the retired Episcopal bishop of New York who for more than a decade was the most formidable liberal Christian voice in the city, died yesterday at home in Greenwich Village. He was 83….

Bishop Moore argued for his agenda in the most Christian of terms, refusing to cede Biblical language to the Christian right. Although he retired as bishop in 1989, he continued to speak out, taking to the pulpit of his former church as recently as March 24, even as illness overtook him, to protest the war in Iraq.

“It appears we have two types of religion here,” the bishop said, aiming his sharpest barbs at President Bush. “One is a solitary Texas politician who says, `I talk to Jesus, and I am right.’ The other involves millions of people of all faiths who disagree.”

He added: “I think it is terrifying. I believe it will lead to a terrible crack in the whole culture as we have come to know it.”….

[In reference to another question] Bishop Moore later acknowledged that his rhetoric was strong, but added, “In this city you have to speak strongly to be heard.”

Paul Moore’s early life does not immediately suggest an affinity for the kinds of social issues that he would later champion…. His grandfather was one of the founders of Bankers Trust. His father was a good friend of Senator Prescott Bush, whose son, George H. W. Bush, and grandson, George W. Bush, would become United States presidents.

Related material (update of May 12, 2003):

  1. Pilate, Truth, and Friday the Thirteenth
  2. The Diamond Theory of Truth
  3. Understanding


Which of the two theories of truth in reading (2) above is exemplified by Moore’s March 24 remarks?

Monday, March 24, 2003

Monday March 24, 2003

Filed under: Uncategorized — m759 @ 12:52 PM

Orwell’s question, according to
an admirer of leftist Noam Chomsky:

“When so much of the BS is right out in the open,
why is it that we know so little about it?
Why don’t we see what’s right in front of our eyes?”

Deep Chomsky:
Lying, Truth-Telling,
and the Social Order

“First of all, I’d like to thank the Academy….”
— Quotation attributed to Plato

The New Yorker of March 31, 2003, discusses leftist academic Noam Chomsky.  The online edition provides a web page listing pro-Chomsky links.

Chomsky’s influence is based in part on the popularity of his half-baked theories on linguistics, starting in the 1950’s with “deep structure” and “transformational,” or “generative,” grammar.

Chomsky has abandoned many of his previous ideas and currently touts what he calls The Minimalist Program.

For some background on Chomsky’s recent linguistic notions, see the expository essay “Syntactic Theory,” by Elly van Gelderen of the Arizona State University English Department.  Van Gelderen lists her leftist political agenda on her “Other Interests” page.  Her department may serve as an example of how leftists have converted many English departments in American universities to propaganda factories.

Some attacks on Chomsky’s scholarship:

The Emperor’s New Linguistics

The New Grammarians’ Funeral

Beyond Chomsky

Could Chomsky Be Wrong? 

Forty-four Reasons Why the Chomskians Are Mistaken

Call for Papers, Chomsky 2003

Chomsky’s (Mis)Understanding of Human Thinking

Anatomy of a Revolution… Chomsky in 1962

…Linguistic Theory: The Rationality of Noam Chomsky

A Bibliography

Some attacks on Chomsky’s propaganda:

LeftWatch.com Chomsky page

Destructive Generation excerpt

The Sick Mind of Noam Chomsky

Partners in Hate: Noam Chomsky and the Holocaust Deniers

Chomsky and Plato’s Diamond

Like another purveyor of leftist nonsense, Jacques Derrida, Chomsky is fond of citing Plato as a precedent.  In particular, what Chomsky calls “Plato’s problem” is discussed in Plato’s Meno.  For a look at the diamond figure that plays a central role in that dialogue, see Diamond Theory.  For an excellent overview of related material in Plato, see Theory of Forms.

Thursday, March 6, 2003

Thursday March 6, 2003

Filed under: Uncategorized — Tags: , — m759 @ 2:35 AM


Geometry for Jews

Today is Michelangelo's birthday.

Those who prefer the Sistine Chapel to the Rothko Chapel may invite their Jewish friends to answer the following essay question:

Discuss the geometry underlying the above picture.  How is this geometry related to the work of Jewish artist Sol LeWitt? How is it related to the work of Aryan artist Ernst Witt?  How is it related to the Griess "Monster" sporadic simple group whose elements number 

808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000?

Some background:

Monday, January 20, 2003

Monday January 20, 2003

Filed under: Uncategorized — Tags: — m759 @ 5:00 PM

Shine On, Robinson Jeffers

"…be in nothing so moderate as in love of man, 
      a clever servant, insufferable master.
There is the trap that catches noblest spirits,
     that caught — they say — God, when he walked on earth."
Shine, Perishing Republic, by Robinson Jeffers

Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.

"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence.   His verse also flashes with a diamond's hardness when he portrays human pain and folly."
Gary Suttle  

"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov, 
   Grace To Be Said at the Supermarket 

"Across my foundering deck shone 
A beacon, an eternal beam. | Flesh fade, and mortal trash 
Fáll to the resíduary worm; | world's wildfire, leave but ash: 
In a flash, at a trumpet crash, 
I am all at once what Christ is |, since he was what I am, and 
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
    immortal diamond, 
Is immortal diamond."
— Gerard Manley Hopkins,
    That Nature is a Heraclitean Fire and of the Comfort of the Resurrection

"In the last two weeks, I've been returning to Hopkins.  Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
    in Vanity Fair, May 2002, page 162

"There's none but truth can stead you.  Christ is truth."
— Gerard Manley Hopkins

"The rock cannot be broken.  It is the truth."
— Wallace Stevens 

"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House

On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.

"…today, the Rock cries out to us, clearly, forcefully…."
Maya Angelou, January 20, 1993

"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX

Top view of

Top view of
Hearts On Fire

Advertising Copy:

What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond.


"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."

"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame."
Song of Solomon

"The last words from the people in the towers and on the planes, over and over again, were 'I love you.'  Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock:  we are learning just how powerful love really is, even in the face of death."
The Rev. Kenneth E. Kovacs

"Then I'll get on my knees and pray
We don't get fooled again."
The Who 

See also my note, "Bright Star," of October 23, 2002.


Saturday, January 4, 2003

Saturday January 4, 2003

Filed under: Uncategorized — m759 @ 3:33 PM

Opening of the Graves

Revelation 20:12 
I saw the dead,
the great and the small,
standing before the throne,
and they opened books.

The Dead —

The Great: 

On January 4, 1965,
T. S. Eliot

The Small:

On January 4, 1991,
T. S. Matthews,
author of
Great Tom:
Notes Towards the Definition
of T. S. Eliot

From the website of the Redwood Library and Athenæum, Newport, Rhode Island:

The Library of a 20th-Century
Man of Letters

Redwood is the delighted recipient of part of the personal library of Thomas Stanley Matthews ([Jan. 16] 1901- [Jan. 4] 1991), a shareholder from 1947 until his death and a generous benefactor. Matthews, who summered in Middletown for over 50 years, began his journalism career with The New Republic, where he served as assistant editor between 1925 and 1927 and as an associate editor between 1927 and 1929. He was then hired as books editor at Time, where over the next 20 years he held the positions of assistant managing editor, executive editor, and managing editor. In 1949 he succeeded the magazine’s founder, Henry Luce, as editor. Upon retiring in 1953, he moved to England.

Matthews edited The Selected Letters of Charles Lamb (1956), for which he wrote the introduction. He published two volumes of memoirs, Name and Address: An Autobiography (1960) and Jacks or Better (1977; published in England as Under the Influence); two volumes of poetry; The Sugar Pill: An Essay on Newspapers (1957); O My America! Notes on a Trip (1962); Great Tom: Notes Towards the Definition of T. S. Eliot (1974); a volume of character sketches, Angels Unawares: Twentieth-Century Portraits (1985); and eight volumes of aphorisms, witticisms, and verse.

Shortly before his death, Matthews expressed the desire that all his books be left to Redwood Library…. [including] books by Seamus Heaney, Louis MacNeice, Ezra Pound, Laura Riding, Edward Arlington Robinson, W. H. Auden, e e cummings, and Robert Graves.

Of particular interest are the 16 volumes by Graves, most of them autographed by the author….

“Like the beat, beat, beat
of the tom-tom….”
— Cole Porter, 1932 


n. itinerant seller or giver of books,
especially religious literature.

Now you has jazz.

— Cole Porter, lyric for “High Society,”
set in Newport, Rhode Island, 1956

Tuesday, December 17, 2002

Tuesday December 17, 2002

Filed under: Uncategorized — m759 @ 12:00 AM


Just Seventeen


Today's site music*
is in honor of
a memorable date.

Northern Songs.
Quiet may be restored by using
the midi control box at the top right
of this page.  Please let me know
if your browser is not showing
this control box.



From a June/July 1997
Hadassah Magazine article:

"Plato is obviously Jewish."

— Rebecca Goldstein

Readings on the Dark Lady  

From a July 27, 1997
New York Times article
by Holland Cotter:

"The single most important and sustained model for Khmer culture was India, from which Cambodia inherited two religions, Buddhism and Hinduism, and an immensely sophisticated art. This influence announces itself early in this exhibition in a spectacular seventh-century figure of the Hindu goddess Durga, whose hip-slung pose and voluptuous torso, as plush and taut as ripe fruit, combine the naturalism and idealism of the very finest Indian work."

From 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  

Friday, November 8, 2002

Friday November 8, 2002

Filed under: Uncategorized — m759 @ 3:33 AM

Religious Symbolism
at Princeton

In memory of Steve McQueen (“The Great Escape” and “The Thomas Crown Affair”… see preceding entry) and of Rudolf Augstein (publisher of Der Spiegel), both of whom died on November 7 (in 1980 and 2002, respectively), in memory of the following residents of

The Princeton Cemetery
of the Nassau Presbyterian Church
Established 1757

SYLVIA BEACH (1887-1962), whose father was pastor of the First Presbyterian Church, founded Shakespeare & Company, a Paris bookshop which became a focus for struggling expatriate writers. In 1922 she published James Joyce’s Ulysses when others considered it obscene, and she defiantly closed her shop in 1941 in protest against the Nazi occupation.

KURT GÖDEL (1906-1978), a world-class mathematician famous for a vast array of major contributions to logic, was a longtime professor at the Institute for Advanced Study, founded in 1930. He was a corecipient of the Einstein Award in 1951.

JOHN (HENRY) O’HARA (1905-1970) was a voluminous and much-honored writer. His novels, Appointment in Samarra (1934) and Ten North Frederick (1955), and his collection of short stories, Pal Joey (1940), are among his best-known works.

and of the long and powerful association of Princeton University with the Presbyterian Church, as well as the theological perspective of Carl Jung in Man and His Symbols, I offer the following “windmill,” taken from the Presbyterian Creedal Standards website, as a memorial:

The background music Les Moulins de Mon Coeur, selected yesterday morning in memory of Steve McQueen, continues to be appropriate.

“A is for Anna.”
— James Joyce

Tuesday, November 5, 2002

Tuesday November 5, 2002

Filed under: Uncategorized — m759 @ 2:56 AM

Back to You, Kylie

From the 440 International Archives:

1988 – And speaking of music trivia (thanks to http://www.rockdate.co.uk Rockdate Diary): “The Loco-Motion”, by Kylie Minogue hit #4 on the “Billboard Hot 100” this day, the song became the first to reach the top-5 in the U.S. for three different artists (Little Eva in 1962, Grand Funk in 1974).

Click here for a nicely done vibraphone-midi version of “Locomotion.”  To honor Kylie’s unforgettable video of that classic, this site’s music is now one of my childhood favorites.

Kylie, 1988

Down by the Station

Down by the station early in the morning,
See the little puffer bellies all in a row.
See the engine driver pull the little throttle:
Puff, puff, Toot! Toot! Off we go!

As Sinatra said,
“Whatever gets you through the night, baby.”

Wednesday, October 23, 2002

Wednesday October 23, 2002

Filed under: Uncategorized — m759 @ 6:35 AM

Eleven Years Ago Today…

On October 23, 1991, I placed in my (paper) journal various entries that would remind me of the past… of Cuernavaca, Mexico, and a girl I knew there in 1962. One of the entries dealt with a book by Arthur Koestler, The Challenge of Chance. A search for links related to that book led to the following site, which I find very interesting:


This is a commonplace-book site, apparently a collection of readings for the end of the century and millennium. No site title or owner is indicated, but the readings are excellent. Accepting the challenge of chance, I reproduce one of the readings… The author was not writing about Cuernavaca, but may as well have been.

From Winter’s Tale, Harcourt Brace (1983):

Four Gates to the City


Every city has its gates, which need not be of stone. Nor need soldiers be upon them or watchers before them. At first, when cities were jewels in a dark and mysterious world, they tended to be round and they had protective walls. To enter, one had to pass through gates, the reward for which was shelter from the overwhelming forests and seas, the merciless and taxing expanse of greens, whites, and blues–wild and free–that stopped at the city walls.

In time the ramparts became higher and the gates more massive, until they simply disappeared and were replaced by barriers, subtler than stone, that girded every city like a crown and held in its spirit. Some claim that the barriers do not exist, and disparage them. Although they themselves can penetrate the new walls with no effort, their spirits (which, also, they claim do not exist) cannot, and are left like orphans around the periphery.

To enter a city intact it is necessary to pass through one of the new gates. They are far more difficult to find than their solid predecessors, for they are tests, mechanisms, devices, and implementations of justice. There once was a map, now long gone, one of the ancient charts upon which colorful animals sleep or rage. Those who saw it said that in its illuminations were figures and symbols of the gates. The east gate was that of acceptance of responsibility, the south gate that of the desire to explore, the west gate that of devotion to beauty, and the north gate that of selfless love. But they were not believed. It was said that a city with entryways like these could not exist, because it would be too wonderful. Those who decide such things decided that whoever had seen the map had only imagined it, and the entire matter was forgotten, treated as if it were a dream, and ignored. This, of course, freed it to live forever.

Sunday, October 13, 2002

Sunday October 13, 2002

Filed under: Uncategorized — Tags: — m759 @ 10:55 PM

Two Literary Classics
(and a visit from a saint)

On this date in 1962, Edward Albee's classic play, "Who's Afraid of Virginia Woolf?" opened on Broadway.

George and Martha by
Edward Albee

Click to enlarge.
George and Martha by
 St. James Marshall

As I was preparing this entry, based on the October 13 date of the Albee play's opening, after I looked for a picture of Marshall's book I thought I'd better check dates related to Marshall, too.   This is what I was surprised to find:  Marshall (b. Oct. 10, 1942) died in 1992 on today's date, October 13.  This may be verified at

The James Edward Marshall memorial page,

A James Edward Marshall biography, and

Author Anniversaries for October 13.

The titles of the three acts of Albee's play suffice to indicate its dark spiritual undercurrents:

"Fun and Games" (Act One),
"Walpurgisnacht" (Act Two) and
"The Exorcism" (Act Three).

A theological writer pondered Albee in 1963:

"If, as Tillich has said of Picasso's Guernica, a 'Protestant' picture means not covering up anything but looking at 'the human situation in its depths of estrangement and despair,' then we could call Edward Albee's Who's Afraid of Virginia Woolf? a 'Protestant' play. On any other definition it might be difficult to justify its religious significance except as sheer nihilism."
— Hugh T. Kerr, Theological Table-Talk, July 1963

It is a great relief to have another George and Martha (who first appeared in 1972) to turn to on this dark anniversary, and a doubly great relief to know that Albee's darkness is balanced by the light of Saint James Edward Marshall, whose feast day is today.

For more on the carousel theme of the Marshall book's cover, click the link for "Spinning Wheel" in the entry below.

Tuesday, September 24, 2002

Tuesday September 24, 2002

Filed under: Uncategorized — m759 @ 11:33 PM

The Shining of Lucero

From my journal note, “Shining Forth“:

The Spanish for “Bright Star” is “Lucero.”

The Eye of the Beholder:

When you stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been travelling for a hundred years toward your eyes, but also advanced waves from your eyes have reached a hundred years into the past to encourage the star to shine in your direction.

— John Cramer, “The Quantum Handshake

From Broken Symmetries, by Paul Preuss, 1983:

He’d toyed with “psi” himself…. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand — for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox….   

Peter [Slater] had never thirsted after “hidden variables” to explain what could not be pictured.  Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once.  It was a thin nectar, but he was convinced it was the nectar of the gods.


Those so-called crazy psychics were too sane, that was their problem — they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry. (Ch. 16)

From Secret Passages, by Paul Preuss, 1997:

Minakis caught up and walked beside him in silence, moving with easy strides over the bare ground, listening as Peter [Slater] spoke. “Delos One was ten years ago — quantum theory seemed as natural as water to me then; I could play in it without a care. If I’d had any sense of history, I would have recognized that I’d swallowed the Copenhagen interpretation whole.”

“Back then, you insisted that the quantum world is not a world at all,” Minakis prompted him. “No microworld, only mathematical descriptions.”

“Yes, I was adamant. Those who protested were naive — one has to be willing to tolerate ambiguity, even to be crazy.”

“Bohr’s words?”

“The party line. Of course Bohr did say, ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’ Meaning that when we start to talk what sounds like philosophy, our colleagues should rip us to pieces.” Peter smiled. “They smell my blood already.”

Peter glanced at Minakis. “Let’s say there are indications — I have personal indications — not convincing, perhaps, but suggestive, that the quantum world penetrates the classical world deeply.” He was silent for a moment, then waved his hand at the ruins. “The world of classical physics, I mean. I suppose I’ve come to realize that the world is more than a laboratory.”

“We are standing where Apollo was born,” Minakis said. “Leto squatted just there, holding fast to a palm tree, and after nine days of labor gave birth to the god of light and music….”

From my journal note, “A Mass for Lucero“:

To Lucero, in memory of
1962 in Cuernavaca

From On Beauty, by Elaine Scarry,
Princeton University Press, 1999 —

“Homer sings of the beauty of particular things. Odysseus, washed up on shore, covered with brine, having nearly drowned, comes upon a human community and one person in particular, Nausicaa, whose beauty simply astonishes him. He has never anywhere seen a face so lovely; he has never anywhere seen any thing so lovely….

I have never laid eyes on anyone like you,
neither man nor woman…
I look at you and a sense of wonder takes me.

Wait, once I saw the like —
in Delos, beside Apollo’s altar —
the young slip of a palm-tree
springing into the light.”

From Secret Passages, by Paul Preuss, 1997:

“When we try to look inside atoms,” Peter said, “not only can we not see what’s going on, we cannot even construct a coherent picture of what’s going on.”

“If you will forgive me, Peter,” Minakis said, turning to the others. “He means that we can construct several pictures — that light and matter are waves, for example, or that light and matter are particles — but that all these pictures are inadequate. What’s left to us is the bare mathematics of quantum theory.”

…. “Whatever the really real world is like, my friend, it is not what you might imagine.”


Talking physics, Peter tended to bluntness. “Tell me more about this real world you imagine but can’t describe.”

Minakis turned away from the view of the sunset. “Are you familiar with John Cramer’s transactional interpretation of quantum mechanics?”

“No I’m not.”


“Read Cramer. I’ll give you his papers. Then we can talk.” 

 From John Cramer, “The Quantum Handshake“:

Advanced waves could perhaps, under the right circumstances, lead to “ansible-type” FTL communication favored by Le Guin and Card…. 

For more on Le Guin and Card, see my journal notes below.

For more on the meaning of “lucero,” see the Wallace Stevens poem “Martial Cadenza.”

Thursday, September 12, 2002

Thursday September 12, 2002

Filed under: Uncategorized — m759 @ 2:56 PM

In memory of Kim Hunter,
who died on 9/11, 2002:

A transcription of a journal note from 1996…

National Dance Week

Thursday, May 2, 1996

National Day of Prayer will be observed at noon today, Thursday, May 2, at City Hall.

“Bush once joked that he picked Sununu because his surname rhymed with “deep doo-doo.”
— Dan Goodgame, Time magazine, May 21, 1990
For a time, Sununu wrote stories and poems for children. Concord lawyer Ned Helms recalls that when his wife fell ill, Sununu gave her a book of poems that he said he enjoyed, by Sylvia Plath.

Do do that voodoo that you do so well.

One summer when I played in a small stock company, after the last curtain had come down we would clear the stage and then put on records of Viennese waltzes. We’d dance wildly, joyfully…
— Madeleine L’Engle, Victoria Magazine, November 1995

We’re arranging to have the children baptized on Sunday afternoon, March 25, by the way. Although I honestly dislike, or rather, scorn the rector. I told you about his ghastly H-bomb sermon, didn’t I, where he said this was the happy prospect of the Second Coming and how lucky we Christians were compared to the stupid pacifists and humanists and “educated pagans” who feared being incinerated, etc., etc. I have not been to church since. I felt it was a sin to support such insanity even by my presence.
— Sylvia Plath, March 12, 1962. Amen.
[The bathroom door opens and Stella comes out. Blanche continues talking to Mitch.]
Oh! Have you finished? Wait — I’ll turn on the radio.
[She turns the knobs on the radio and it begins to play “Wien, Wien, nur du allein.” Blanche waltzes to the music with romantic gestures. Mitch is delighted and moves in awkward imitation like a dancing bear. Stanley stalks fiercely through the portieres into the bedroom. He crosses to the small white radio and snatches it off the table. With a shouted oath, he tosses the instrument out the window.]

Colby’s nickname among some of his subordinates at CIA is said to be “The Bookkeeper.”

Alabama plans
female chain gangs

Friday, April 26, 1996, story:

MONTGOMERY, Ala. (AP) — The Montgomery prison system is preparing to snap shackles around the ankles of women prisoners, creating female chain gangs in the state that revived male leg-iron crews last year.

I will try to finish my novel and a second book of poems by Christmas. I think I’ll be a pretty good novelist, very funny — my stuff makes me laugh and laugh, and if I can laugh now it must be hellishly funny stuff.
— Sylvia Plath, October 12, 1962
An engine, an engine
Chuffing me off like a Jew,
A Jew to Dachau, Auschwitz, Belsen.
There’s a stake in your fat black heart
And the villagers never liked you.
They are dancing and stamping on you.


Everybody’s doin’ a brand new dance now;
I know you’re gonna like it if you give it a chance now…
So come on, c’mon, and do the locomotion with me!

Sunday, July 28, 2002

Sunday July 28, 2002

Filed under: Uncategorized — m759 @ 2:16 PM

Memories, Dreams, Reflections

Saul Steinberg in The New York Review of Books issue dated August 15, 2002, page 32:

“The idea of reflections came to me in reading an observation by Pascal, cited in a book by W. H. Auden, who wrote an unusual kind of autobiography by collecting all the quotations he had annotated in the course of his life, which is a good way of displaying oneself, as a reflection of these quotations.  Among them this observation by Pascal, which could have been made only by a mathematician….”

Pascal’s observation is that humans, animals, and plants have bilateral symmetry, but in nature at large there is only symmetry about a horizontal axis… reflections in water, nature’s mirror.

This seems related to the puzzling question of why a mirror reverses left and right, but not up and down.

The Steinberg quote is from the book Reflections and Shadows, reviewed here.

Bibliographic data on Auden’s commonplace book:

AUTHOR      Auden, W. H. (Wystan Hugh),              1907-1973. TITLE       A Certain World; a Commonplace Book   
            [selected by] W. H. Auden.
PUBLISHER   New York, Viking Press [1970]
SUBJECT     Commonplace-books.

A couple of websites on commonplace books:

Quotation Collections and

Weblets as Commonplace Books.

A classic:

The Practical Cogitator – The Thinker’s Anthology
by Charles P. Curtis, Jr., and Ferris Greenslet,
Houghton Mifflin Company Boston, Massachusetts
c 1962 Third Edition – Revised and Enlarged

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