Wednesday, November 29, 2017

The Room

Filed under: General — m759 @ 11:00 AM

The concluding instance of a search for "the room"
in this journal (from Mike Nichols's birthday, 2002) —

"His visitor sat upright, oppressed by the silence,
acutely conscious that the doors to the room were locked."

— Recreation by Sylvia Nasar of a scene starring
mathematicians George Mackey and John Nash.

The reviews are in!

See also today's previous post, Perhaps Not Strange Enough.

Monday, May 23, 2016


Filed under: General — m759 @ 10:00 AM

In memory of the late mathematician John Nash
and of the late actor Alan Young ...

A Talking Horse — 

What the horse says: "First online: 28 August 2013."

See also OverarchingPsychonauts, and Spider Tale in this journal.

Thursday, November 5, 2015

The Monster

Filed under: General,Geometry — m759 @ 9:00 AM

In memory of Princeton mathematician John Nash

"For the past six years all over the world 
experts in the branch of abstract algebra
called group theory have been struggling
to capture a group known as the monster."

—Martin Gardner, Scientific American ,  June 1980

"When the Hawkline Monster moved to get a better view
of what was happening, the shadow, after having checked
all the possibilities of light, had discovered a way that it
could shift itself in front of the monster, so that the monster
at this crucial time would be blinded by darkness for a few
seconds, did so, causing confusion to befall the monster.

This was all that the shadow could do and it hoped that this
would give Greer and Cameron the edge they would need
to destroy the Hawkline Monster using whatever plan they
had come up with, for it seemed that they must have a plan
if they were to have any chance at all with the monster and
they did not seem like fools.

When Cameron yelled at Greer, the shadow interpreted this
as the time to move and did so. It obscured the vision of the
Hawkline Monster for a few seconds, knowing full well that if
the monster were destroyed it would be destroyed, too, but
death was better than going on living like this, being a part of
this evil."

— Richard Brautigan, The Hawkline Monster , 1974

From the post For Scientific Witch Hunters of October 30,
an illustration from The Boston Globe —

From the post Colorful Story (All Souls' Day),  
an Illustration from Google Book Search —

Earlier in Brautigan's tale

" Everybody started to leave the parlor to go downstairs
and pour out the Hawkline Monster but just as
they reached the door and one of the Hawkline women
had her hand on the knob, Cameron said, 'Hold it for a
second. I want to get myself a little whiskey.' "

Saturday, May 30, 2015

Credit Card

Filed under: General — m759 @ 8:42 AM

Detail from the online Fortune  magazine this morning:

                   Dateline of linked article:
                   MAY 30, 2015, 8:12 AM EDT

See yesterday morning's post on G. H. Hardy
and Harvey Cohn as well as a quote from
the 1958 Fortune  article on John Nash:

"The pure mathematician judges his work
largely by aesthetic standards;
the applied mathematician is a pragmatist."

The source of the link to 1958 —

Monday, May 25, 2015

The Secret Life of the Public Mind

Filed under: General — m759 @ 3:37 AM

John Nash in New York Times obituaries

"… an editor (Anne Meara, half of the comedy team of
Stiller and Meara, who are Ben Stiller's parents) asks
Lelaina to define irony. 'I know it when I see it,' says Lelaina…."

Rolling Stone , 1994 film review by Peter Travers

Sunday, May 24, 2015

A Winner at Any Time

Filed under: General — m759 @ 10:54 AM

CNN on the death of John Nash

Friday, July 25, 2014


Filed under: General — m759 @ 10:00 PM

In honor of Ace Greenberg, a major Wall Street player
who reportedly died today at 86:

See also this journal on the date of the above review,
March 9, 2009:  First and Last Things.

Magic for Jews

Filed under: General — Tags: — m759 @ 8:00 PM

(Continued from April 8, 2013.)

See Two Blocks Short of a Design (May 5, 2011).

Thursday, April 17, 2014

Thursday with the Nashes

Filed under: General,Geometry — m759 @ 3:00 PM

“For every kind of vampire, there is a kind of cross.” — Gravity’s Rainbow

“I don’t write exclusively on Jewish themes or about Jewish characters.
My collection of short stories, Strange Attractors , contained nine pieces,
five of which were, to some degree, Jewish, and this ratio has provided me
with a precise mathematical answer (for me, still the best kind of answer)
to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer.”

— Rebecca Goldstein, “Against Logic

Midrashim for Rebecca: 

The Diamond Theory vs.  the Story Theory (of truth)

Story Theory and the Number of the Beast

The Palm Sunday post “Gray Space”

For those who prefer the diamond theory of truth,
a “precise mathematical” view of a Gray code —

IMAGE- Six-bit binary and Gray codes

For those who prefer the story theory of truth,
Thursday with the Nashes —

The actors who portrayed Mr. and Mrs. John Nash in
‘A Beautiful Mind’ now portray Mr. and Mrs. Noah…

IMAGE- At UMC.org, the actors who portrayed Mr. and Mrs. John Nash in 'A Beautiful Mind' now portray Mr. and Mrs. Noah.

Monday, March 9, 2009

Monday March 9, 2009

Filed under: General — m759 @ 5:24 PM
First and Last Things

Next Sunday’s New York Times Book Review arrived in today’s mail. On the inside of the first page is a full-page ad for a course of 24 lectures on DVD’s called “Games People Play: Game Theory in Life, Business, and Beyond.” On the inside of the last page is “Our Steiner Problem– and Mine,” a full-page essay by Lee Siegel on polymath George Steiner.

Related material:

Happy birthday to the late Bobby Fischer.

“For God’s sake, let us sit upon the ground
 And tell sad stories of the death of kings”
Richard II, Act III, Scene ii 
Portrayal of John Nash sitting upon the ground
Russell Crowe as game theorist
John Nash in “A Beautiful Mind”

Sunday, October 5, 2008

Sunday October 5, 2008

Filed under: General — Tags: — m759 @ 4:23 PM
Nash Equilibrium or:
To Make a Short Story Long

Last night's entry presented a
short story summarized by
four lottery numbers.

Today's mid-day lotteries
and associated material:

Pennsylvania, 201– i.e., 2/01:
Kindergarten Theology

Theologian James Edwin Loder:

"In a game of chess, the knight's move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a 'knight's move' in intelligence."

New York, 229– i.e., 2/29:
I Have a Dreamtime

"One must join forces with friends of like mind"

Related material:

Terence McKenna:

"Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey 'haunts time like a ghost.'"

Anonymous author:

"'Knight's move thinking' is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia."

Star Wars:
John Nash, as portrayed by Russell Crowe

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O'Bedlam's Song

For more on the sleep of Apollo,
see the front page of today's
New York Times Book Review.

Garrison Keillor's piece there,
"Dying of the Light," is
about the fear of death felt
by an agnostic British twit.

For relevant remarks by
a British non-twit, see
William Dunbar–

Timor Mortis conturbat me.

Thursday, January 3, 2008

Thursday January 3, 2008

Filed under: General — m759 @ 1:01 PM
Context-Sensitive Theology

The Revelation Game 
New Year’s reading for
the tigers of Princeton

Two reviews from the February 2008 Notices of the American Mathematical Society:

From a review of

A Certain Ambiguity
(A Mathematical Novel)

by Gaurav Suri and Hartosh Singh Bal
Princeton University Press
Hardcover, US$27.95, 281 pages —

“From the Habermas-Lyotard debate (see [1] for an introduction) to the Sokal hoax ([4]), to recent atheist manifestos on the bestseller lists (e.g., [2]) the question of foundations for intellectual thought and especially for intellectual debate has never been more critical or urgent.”

[1] M. Bérubé, What’s Liberal about the Liberal Arts? Classroom Politics and “Bias” in Higher Education, W. W. Norton, 2006.
[2] S. Harris, Letter to a Christian Nation, Knopf, 2006.
[4] A. Sokal and P. Bricmont, Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science, Picador, 1999.

Danny Calegari of Caltech

Also in the February Notices– a review of a book, Superior Beings: If They Exist, How Would We Know?, in which the author

“.. uses elementary ideas from game theory to create situations between a Person (P) and God (Supreme Being, SB) and discusses how each reacts to the other in these model scenarios….

In the ‘Revelation Game,’ for example,
the Person (P) has two options:
1) P can believe in SB’s existence
2) P can not believe in SB’s existence
The Supreme Being also has two options:
1) SB can reveal Himself
2) SB can not reveal Himself….

… [and] goals allow us to rank all the outcomes for each player from best… to worst…. The question we must answer is: what is the Nash equilibrium in this case?”

The answer is what one might expect from the American Mathematical Society:

“… the dominant strategy for both is when SB does not reveal Himself and P does not believe in His existence.”

Other strategies are, of course, possible. See last year’s entries.

See also
the life of John Nash,


for whom the above
equilibrium is named.

Sunday, May 27, 2007

Sunday May 27, 2007

Filed under: General — m759 @ 8:00 AM
Random Number
The previous entry links back to May 18’s “Devil in the Details,” an entry quoting Peter Woit.  Yesterday afternoon Woit, who sometimes writes on pure mathematics as well as physics, posted an entry on a talk said to be related to something called “the ABC-conjecture,” which has been called “the most important unsolved problem in diophantine analysis.” (Dorian Goldfeld,  “Beyond the Last Theorem,” The Sciences, March/April 1996, 34-40)

On the ABC-conjecture in number theory:

“We hope to elucidate the beautiful connections between elliptic curves, modular forms and the ABC–conjecture.” —Dorian Goldfeld (pdf)

An Edinburgh postgraduate student on the conjecture:

“… abc brings us full circle to Fermat’s Last Theorem….” —Graeme Taylor at Everything2.com

I regret I can add nothing to Taylor’s admirable exposition and to Goldfeld’s “beautiful connections” except the following observation of a rather ugly connection.

The previous Log24 entry, from yesterday afternoon, related the May 18 “details” entry to Friday’s PA evening lottery number, 005.  A  followup seems (if only to honor the madcap tradition of John Nash) to be called for.  The PA evening number yesterday evening, Saturday, was 443.  Nash, in his younger days, might have been pleased to note that this number is associated (if only by coincidence) with a topic Woit mentioned earlier yesterday– Fermat’s famed conjecture:

The image “http://www.log24.com/log/pix07/070527-Fermat.jpg” cannot be displayed, because it contains errors.
Page 443

in The Annals of Mathematics,
2nd Ser., Vol. 141, No. 3 (May, 1995)
This is the first page of a rather
 famous paper by Andrew Wiles.

Such coincidences are, of course, anathema to believers in the religion of Scientism.  But one such believer, Natalie Angier (yesterday morning’s entry), at least acknowledges the charm of “the atheist’s favorite Christmas movie, ‘Coincidence on 34th Street.'” (pdf)

Saturday, March 10, 2007

Saturday March 10, 2007

Filed under: General,Geometry — m759 @ 9:00 AM

The Logic of Dreams

From A Beautiful Mind–

“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”


The image “http://www.log24.com/log/pix07/070309-NYlottery.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070309-PAlottery.jpg” cannot be displayed, because it contains errors.

These numbers may, in the mad way so well portrayed by Sylvia Nasar in the above book, be regarded as telling a story… a story that should, of course, not be taken too seriously.

Friday’s New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11.  Clicking on these dates will lead the reader to Log24 entries featuring, among others, T. S. Eliot and Stephen King– two authors not unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:

Chessboard (Detail)

This illustration refers to chess rather than to geometry, and to the mind of an addict rather than to that of a slave, but chess and geometry, like addiction and slavery, are not unrelated.

Friday’s Pennsylvania numbers, midday 429 and evening 038, suggest that the story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“–  “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)

Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).

More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.

Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:

The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Friday, February 2, 2007

Friday February 2, 2007

Filed under: General — m759 @ 7:11 AM

The Night Watch

For Catholic Schools Week
(continued from last year)–

Last night’s Log24 Xanga
footprints from Poland:

Poland 2/2/07 1:29 AM
2/20/06: The Past Revisited
(with link to online text of
Many Dimensions, by Charles Williams)

Poland 2/2/07 2:38 AM
1/15/06 Inscape
(the mathematical concept, with
square and “star” diagrams)

Poland 2/2/07 3:30 AM
2/8/05 The Equation
(Russell Crowe as John Nash
with “star” diagram from a
Princeton lecture by Langlands)

Poland 2/2/07 4:31 AM
8/29/06 Hollywood Birthday
(with link to online text of
Plato on the Human Paradox,
by a Fordham Jesuit)

Poland 2/2/07 4:43 AM
8/30/06 Seven
(Harvard, the etymology of the
word “experience,” and the
Catholic funeral of a professor’s
23-year-old daughter)

Poland 2/2/07 4:56 AM
12/19/05 Quarter to Three (cont.)

(remarks on permutation groups
for the birthday of Helmut Wielandt)

Poland 2/2/07 5:03 AM
5/29/06 For JFK’s Birthday
(The Call Girls revisited)

Poland 2/2/07 5:32 AM
8/24/06 Beginnings
(Nasar in The New Yorker and
T. S. Eliot in Log24, both on the 2006
Beijing String Theory conference)

Poland 2/2/07 5:46 AM
2/22/06 In the Details
(Harvard’s president resigns,
with accompanying “rosebud”)

Sunday, August 7, 2005

Sunday August 7, 2005

Filed under: General — m759 @ 7:20 AM
Presbyterian Justice

News from today’s New York Times:

The Rev. Dr. Theodore Alexander Gill Sr., a Presbyterian theologian, a philosophy teacher, and an influential provost emeritus of John Jay College of Criminal Justice in Manhattan, died at 85 on June 10 in Princeton.  In retirement from John Jay, The Rev. Dr. Gill was theologian in residence at Nassau Presbyterian Church in Princeton.

In memory of The Rev. Dr. Gill:

Religious Symbolism at Princeton
    (on Nassau Presbyterian Church),
    (on number theory at Princeton),
For the Mad Musicians of Princeton,
     (on Schroeder and Bernstein),
Movie Date and its preceding entries
   (on Princeton’s St. John von Neumann),
Why Me?
   (for Princeton theologian Elaine Pagels),
Notes on Literary and Philosophical Puzzles
   (Princeton’s John Nash as Ya Ya Fontana), and
Go Tigers!
   (for the Princeton Evangelical Fellowship).

For a more conventional memorial, see

The image “http://www.log24.com/log/pix05B/050807-SFTS-Logo.gif” cannot be displayed, because it contains errors.

the obituary from

San Francisco Theological Seminary.

Monday, June 13, 2005

Monday June 13, 2005

Filed under: General — m759 @ 9:00 PM


The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

Picture from Feb. 8
(Martin Buber’s birthday)

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Tuesday, June 7, 2005

Tuesday June 7, 2005

Filed under: General — m759 @ 9:39 PM
939, or
Too Clever by Half

On the new
Prime Minister of France:

In Praise of Those Who Stole the Fire, M. de Villepin’s grandest literary effort to date…. will enhance his reputation within a small Paris set, but not in Washington, where he is already regarded as too clever by half.”

— Philip Delves Broughton,
    “De Villepin bares soul
     as France’s politician poet
    The Telegraph, May 23, 2003

From a Study Guide to
Frankenstein, or The Modern Prometheus:

The Titan Prometheus was “‘… chained to Mount Caucasus where an eagle preyed on his liver’ (Bullfinch [sic] 939).”  The study guide does not say whether 939 is a page number or paragraph number, nor does it name which edition of Bulfinch’s Mythology is meant.

The rest of the story:

From the Web-Guide to Thomas Pynchon’s V:

“Prometheus —  One of the Titans of Greek myth, famous as a benefactor of man. Zeus had him make men out of mud and water; however, pitying mankind, he stole fire from heaven and gave it to them. As punishment, Zeus chained him to Mount Caucasus where an eagle preyed on his liver all day, the liver being renewed at night. Hercules eventually released him and killed the eagle. Zeus sent Pandora to Earth with her box of evils to balance the gift of fire.”

Related material:

Pandora’s Box

The image “http://www.log24.com/log/pix05/050310-hex.jpg” cannot be displayed, because it contains errors.


The Barest Vocabulary

The image “http://www.log24.com/log/pix05A/050602-BallotBox.jpg” cannot be displayed, because it contains errors.

Postscript for John Nash:

  Why 939 signifies
“too clever by half” —
see 6:26 and 313.

See also

Joke #939
Date: Thu, 13 Nov 1997
From: Rainybow
Q: Do you know why God created woman second?
A: Because he didn’t want all the advice.

Monday, January 24, 2005

Monday January 24, 2005

Filed under: General,Geometry — 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

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

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.

Sunday, November 23, 2003

Sunday November 23, 2003

Filed under: General — m759 @ 1:06 PM


Yesterday, to give thanks for the winning score in the Harvard-Yale game (Harvard won, 37 to 19), I browsed the Net to find the religious significance, if any, of the number “37.” I encountered the picture at left below, of a burning bush.  (It was frame 37 in a sequence of frames from an episode of The Simpsons.)  The finger of flame did not seem to lead to anything meaningful, so I ignored it.  (Frame 38 in the sequence seems to be a Simpsons version of Edward G. Robinson in “The Ten Commandments.”) Then today, lo and behold, the Commandments themselves appeared before my very eyes, as yet another cartoon… this time, on the editorial page of my local paper (reprinted from McKee in the Augusta Chronicle).  Combining the two cartoons, we see the Flaming Finger of God in action.

The above thought process is, of course, less than mentally healthy, but may be of anecdotal interest to some.  Several other examples of religious insanity seem relevant:

  • Jesus Christ: The Number of His Name, by Bonnie Gaunt, which contains a riff on the number “37” that John Nash at his looniest would be proud of.
  • Mel Gibson on his new film,
    “The Passion” —

    When Gibson was in Rome shooting the film, he told an Italian interviewer that he had felt moved by God’s spirit to undertake the project. I asked him what he’d meant by that. How did he know that God wanted him to make “The Passion”?

    “There are signals,” he said. “You get signals. Signs. ‘Signal graces,’ they’re called. It’s like traffic lights. It’s as clear as a traffic light. Bing! I mean, it just grabs you and you know you have to listen to that and you have to follow it.”

    Peter J. Boyer in The New Yorker

  • Finally, for religious enthusiasts who, like our President, have a Yale background, an article on the mystical properties of Yale’s score yesterday in the big game —

    19th Nervous Breakdown

Saturday, November 15, 2003

Saturday November 15, 2003

Filed under: General — Tags: , — m759 @ 12:00 PM

Aes Triplex

The title, from a Robert Louis Stevenson essay, means “triple brass” (or triple bronze):

From the admirable site of J. Nathan Matias:

Aes Triplex means Triple Bronze, from a line in Horace’s Odes that reads ‘Oak and triple bronze encompassed the breast of him who first entrusted his frail craft to the wild sea.’ ”

From Philip K. Dick’s The Man in the High Castle:

Juliana said, “Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?”

“You have a disconcertingly superstitious way of phrasing your question,” Hawthorne said. But he had squatted down to witness the coin throwing. “Go ahead,” he said; he handed her three Chinese brass coins with holes in the center. “I generally use these.”

This passage, included in my earlier entry of Friday, combined with the opening of yet another major motion picture starring Russell Crowe, suggests three readings for that young man, who is perhaps the true successor to Marlon Brando.

Oracle, for Crowe as John Nash (A Beautiful Mind):

Understanding the I Ching

Mutiny, for Crowe as Jack Aubrey (Master and Commander):

Bartleby, the Scrivener

Storm, for Crowe as Maximus (Gladiator):

Pharsalia, Book V:
The Oracle, the Mutiny, the Storm

As background listening, one possibility is Sinatra’s classic “Three Coins”:

“Three hearts in the fountain,
Each heart longing for its home.
There they lie in the fountain
Somewhere in the heart of Rome.*” 

Personally, though, I prefer, as a tribute to author Joan Didion (who also wrote of coins and the Book of Transformations), the even more classic Sinatra ballad

Angel Eyes.”

 * Horace leads to “Acroceraunian shoals,” which leads to Palaeste, which leads to Pharsalia and to the heart of Rome.  (With a nod to my high school Latin teacher, the late great John Stachowiak.)

Friday, November 7, 2003

Friday November 7, 2003

Filed under: General — m759 @ 7:00 PM

A Beautiful Fantasy:

The Secret life of
 John Nash

“Dr. Blind (pronounced ‘Blend’) was about ninety years old and had taught, for the past fifty years, a course called ‘Invariant Subspaces’ which was noted for its monotony and virtually absolute unintelligibility, as well as for the fact that the final exam, as long as anyone could remember, had consisted of the same single yes-or-no question. The question was three pages long but the answer was always ‘Yes’. That was all you needed to pass Invariant Subspaces.”

The Secret History, by Donna Tartt


“…I put my arms around him yes and drew him down to me so he could feel my breasts all perfume yes and his heart was going like mad and yes I said yes I will Yes.


Ulysses, by James Joyce

Sunday, June 22, 2003

Sunday June 22, 2003

Filed under: General,Geometry — m759 @ 2:28 AM

The Real Hogwarts

is at no single geographical location; it is distributed throughout the planet, and it is perhaps best known (apart from its disguises in the fiction of J. K. Rowling, C. S. Lewis, Charles Williams, and other Inklings) as Christ Church.  Some relevant links:

Christ Church College, Oxford

Christchurch, New Zealand

  • University of Canterbury
    Physical Sciences Library:

    Keeping Current with the Web:
    Maths & Statistics, June 2002

    Diamond Theory:
    Symmetry in Binary Spaces

    The author of this site is Steven Cullinane, who has also written booklets on the subject.  The web site provides detailed discussions of Diamond Theory, and is intended for college math students or mathematicians.  According to Cullinane, Diamond Theory is best classified in the subject of “finite automorphism groups of algebraic, geometric, or combinatorial structures.” The site also includes links to other resources.    From the NSDL Scout Report for Math, Engineering and Technology, Volume 1, No. 9, 7 June 2002, Copyright Internet Scout Project 1994-2002.  http://scout.cs.wisc.edu

Christ Church, Christchurch Road,
Virginia Water, England

Finally, on this Sunday in June, with The New York Review of Books of July 3, 2003, headlining the religion of Scientism (Freeman Dyson reviewing Gleick’s new book on Newton), it seems fitting to provide a link to an oasis of civilisation in the home town of mathematician John Nash — Bluefield, West Virginia.

Christ Church,
Bluefield, West Virginia

Monday, November 25, 2002

Monday November 25, 2002

Filed under: General — m759 @ 11:32 AM

The Artist’s Signature

This title is taken from the final chapter of Carl Sagan’s novel Contact.

“There might be a game in which paper figures were put together to form a story, or at any rate were somehow assembled. The materials might be collected and stored in a scrap-book, full of pictures and anecdotes. The child might then take various bits from the scrap-book to put into the construction; and he might take a considerable picture because it had something in it which he wanted and he might just include the rest because it was there.”

— Ludwig Wittgenstein, Lectures and Conversations on Aesthetics, Psychology and Religious Belief

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

— Stephen Sondheim, in Stephen Schiff, Deconstructing Sondheim,” The New Yorker, March 8, 1993, p. 76

Vesica Piscis

Arch at
Glastonbury Tor

“All goods in this world, all beauties, all truths, are diverse and partial aspects of one unique good. Therefore they are goods which need to be ranged in order. Puzzle games are an image of this operation. Taken all together, viewed from the right point and rightly related, they make an architecture. Through this architecture the unique good, which cannot be grasped, becomes apprehensible. All architecture is a symbol of this, an image of this. The entire universe is nothing but a great metaphor.”

Simone Weil, sister of Princeton mathematician André Weil, First and Last Notebooks, p. 98

This passage from Weil is quoted in
Gateway to God,
p. 42, paperback, fourth impression,
printed in Glasgow in 1982 by
Fontana Books

“He would leave enigmatic messages on blackboards,
signed Ya Ya Fontana.”

Brian Hayes on John Nash,
The Sciences magazine, Sept.-Oct., 1998

“I have a friend who is a Chief of the Aniunkwia (Cherokee) people and I asked him the name of the Creator in which
he replied… Ya Ho Wah. This is also how it is spoken in Hebrew. In my native language it is spoken
Ya Ya*,
which is also what Moses was told
at the ‘Burning Bush’ incident.”

“Tank” (of Taino ancestry), Bronx, NY, Wednesday, April 17, 2002

From a website reviewing books published by

Master and Commander (Patrick O’Brian)”

1/17/02: NEW YORK (Variety) – Russell Crowe is negotiating to star in 20th Century Fox’s “Master and Commander,” the Peter Weir-directed adaptation of the Patrick O’Brian book series.


*For another religious interpretation of this phrase, see my note of October 4, 2002, “The Agony and the Ya-Ya.”

Tuesday, July 30, 2002

Tuesday July 30, 2002

Filed under: General — Tags: — m759 @ 12:12 AM

Aesthetics of Madness

Admirers of the film "A Beautiful Mind" may be interested in the thoughts of psychotherapist Eric Olson on what he calls the "collage method" of therapy.  The fictional protagonist of "A Beautiful Mind," very loosely based on the real-life mathematician John Nash, displays his madness in a visually striking manner (as required by cinematic art).  He makes enormous collages of published matter in which he believes he has found hidden patterns. 

This fictional character is in some ways more like the real-life therapist Olson than like the real-life schizophrenic Nash.  For an excellent introduction to Olson's world, see the New York Times Magazine article of April 1, 2001, on Olson and on the mysterious death of Olson's father Frank, who worked for the CIA.  Here the plot thickens… the title of the article is "What Did the C.I.A. Do to Eric Olson's Father?

For Olson's own website, see The Frank Olson Legacy Project, which has links to Olson's work on collage therapy.   Viewed in the context of this website, the resemblance of Olson's collages to the collages of "A Beautiful Mind" is, to borrow Freud's expression, uncanny.  Olson's own introduction to his collage method is found on the web page "Theory and therapy."

All of the above resulted from a Google search to see if Arlene Croce's 1993 New Yorker article on Balanchine and Stravinsky, "The Spelling of Agon," could be found online.   I did not find Arlene, but I did find the following, from a collage of quotations assembled by Eric Olson —

"There might be a game in which paper figures were put together to form a story, or at any rate were somehow assembled. The materials might be collected and stored in a scrap-book, full of pictures and anecdotes. The child might then take various bits from the scrap-book to put into the construction; and he might take a considerable picture because it had something in it which he wanted and he might just include the rest because it was there.”

— Ludwig Wittgenstein,
Lectures and Conversations on Aesthetics, Psychology and Religious Belief, 1943/1978

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

Stephen Sondheim
in Stephen Schiff, “Deconstructing Sondheim,”
The New Yorker, March 8, 1993, p. 76.

“God creates, I assemble.”

— George Balenchine [sic]
in Arlene Croce, “The Spelling of Agon,”
The New Yorker, July 12, 1993, p. 91

The aesthetics of collage is, of course, not without its relevance to the creation (or assembly) of weblogs.

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