Friday, April 24, 2020

Art at Cologne

Filed under: General — Tags: , , — m759 @ 10:53 PM

This post was suggested by a New York Review of Books  article
on Cologne artist Gerhard Richter in the May 14, 2020, issue —

“The Master of Unknowing,” by Susan Tallman.

Some less random art —

Wednesday, July 4, 2018

Raiders of the Lost Spell

Filed under: General — Tags: — m759 @ 2:01 PM

From The New York Review of Books ,
issue dated July 19, 2018 —

"The only useful thing about The Seventh Function of Language 
is the idea that one would need some magical means to persuade
through language, some secret spell. Useful, because perfectly
ridiculous. The spell, we know, exists . . . ."

— "Imagining the Real," by Wyatt Mason

Some nineteenth-century thoughts along these lines:

See also Declarations.

Thursday, May 19, 2016


Filed under: General,Geometry — m759 @ 2:27 AM

From a check tonight of The New York Review of Books

These NYRB  stories from May 15 and May 13 suggest a
review of images on Ratner's Star  and on the Eye of God.

IMAGE- 'Ratner's Star,' by Don DeLillo (1976)

Above image reposted from Jan. 10, 2014

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

Above images reposted from May 5, 2016

Related material:  The previous post, Dueling Formulas.

Tuesday, November 10, 2015

The Hookup

Filed under: General — m759 @ 7:00 PM

"Language is about the world— we use it to communicate
about things. So we must ask what this 'aboutness' is:
what is it and how does it work? That is, how does language
manage to hook up with reality?"

— Colin McGinn in Philosophy of Language :
The Classics Explained
 , MIT Press, Jan. 16, 2015, 
as quoted by Rebecca Newberger Goldstein
in The New York Review of Books , Oct. 8, 2015

See also a Harvard Crimson  review of another book by McGinn.

Saturday, September 19, 2015

Language Game

Filed under: General — m759 @ 6:01 PM

"O God, I could be bounded in a nutshell
and count myself a king of infinite space,
were it not that I have bad dreams." — Hamlet

The New York Review of Books , in a review
of two books on video games today, quotes an author
who says that the Vikings believed the sky to be 
“the blue skull of a giant.”

See as well posts tagged The Nutshell.

Philosophy and Art

Filed under: General — m759 @ 12:00 PM

The current issue (dated Oct. 8, 2015) of
The New York Review of Books  has two
(at least) items related to philosophy —

See also Backstory, a Log24 post of Nov. 22, 2010:


"He said, 'I wrote a piece of code
 that they just can’t seem to do without.'
 He was a symbolic logician.
 That was his career…."

Saturday, September 12, 2015


Filed under: General — Tags: , — m759 @ 4:45 PM

Lorrie Moore, in the current New York Review of Books ,
on a detective in a TV series:

He "takes notes in a large ledger and
speaks as if he were the CEO of
a nihilist fortune cookie company."

— "Sympathy for the Devil," NYRB
      issue dated Sept. 24, 2015

See Harvard president Drew Faust as such a CEO.

The Harvard Crimson

UPDATED: September 12, 2015, at 4:22 pm. 

Luke Z. Tang ’18, a Lowell House sophomore,
has died “suddenly and unexpectedly,”
Lowell House Master Diana L. Eck told
House residents in an email Saturday.

Local authorities are investigating the cause
of the death, Eck wrote, and there is “no reason
to believe that foul play was involved.”

Thursday, July 2, 2015

Deepening the Spielraum

Filed under: General,Geometry — Tags: — m759 @ 2:00 AM

(A sequel to Expanding the Spielraum (Feb. 3, 2015))

"Knowledge, wisdom even, lies in depth, not extension."

Tim Parks in The New York Review of Books ,
     5 PM ET on June 26, 2015

See also Log24 posts on the following figure —

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

Monday, October 6, 2014

Mysterious Correspondences

Filed under: General,Geometry — m759 @ 9:36 AM

(Continued from Beautiful Mathematics, Dec. 14, 2013)

“Seemingly unrelated structures turn out to have
mysterious correspondences.” — Jim Holt, opening
paragraph of 
a book review in the Dec. 5, 2013, issue
The New York Review of Books

One such correspondence:

For bibliographic information and further details, see
the March 9, 2014, update to “Beautiful Mathematics.”

See as well posts from that same March 9 now tagged “Story Creep.”

Tuesday, March 25, 2014

Narrative and Mathematics

Filed under: General — Tags: — m759 @ 1:01 AM


"Richard Hughes’s celebrated short novel is
a masterpiece of concentrated narrative."

New York Review of Books  on
     A High Wind in Jamaica

As perhaps were, in their way, parts of the life
of the late Patrice Wymore Flynn, who reportedly
died at 87 on Saturday.

Deep backstory:  See Colony of Santiago (Jamaica).

For the "mathematics" part of this post's title, see
Saturday's Log24 post on Kummer-surface terms
and a post of September 23, 2012.

Saturday, December 14, 2013

Beautiful Mathematics

Filed under: General,Geometry — Tags: , , — m759 @ 7:59 PM

The title, which I dislike, is taken from a 2011 publication
of the MAA, also sold by Cambridge University Press.

Some material relevant to the title adjective:

"For those who have learned something of higher mathematics, nothing could be more natural than to use the word 'beautiful' in connection with it. Mathematical beauty, like the beauty of, say, a late Beethoven quartet, arises from a combination of strangeness and inevitability. Simply defined abstractions disclose hidden quirks and complexities. Seemingly unrelated structures turn out to have mysterious correspondences. Uncanny patterns emerge, and they remain uncanny even after being underwritten by the rigor of logic."— Jim Holt, opening of a book review in the Dec. 5, 2013, issue of The New York Review of Books

Some relevant links—

The above list was updated on Jan. 31, 2014, to include the
"Strangeness" and "Hidden quirks" links.  See also a post of
​Jan. 31, 2014.

Update of March 9, 2014 —

The link "Simply defined abstractions" is to the construction of the Steiner
system S(5, 8, 24) described by R. T. Curtis in his 1976 paper defining the
Miracle Octad Generator. It should be noted that this construction is due
to Richard J. Turyn, in a 1967 Sylvania research report. (See Emily Jennings's
talk of 1 Nov. 2012.) Compare  the Curtis construction, written in 1974,
with the Turyn construction of 1967 as described in Sphere Packings, Lattices
and Groups , by J. H. Conway and N. J. A. Sloane (first published in 1988).

Saturday, November 16, 2013

Mathematics and Rhetoric

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

Jim Holt in the current (Dec. 5) New York Review of Books

One form of Eros is the sexual desire aroused by the physical beauty of a particular beloved person. That, according to Diotima, is the lowest form. With philosophical refinement, however, Eros can be made to ascend toward loftier and loftier objects. The penultimate of these—just short of the Platonic idea of beauty itself—is the perfect and timeless beauty discovered by the mathematical sciences. Such beauty evokes in those able to grasp it a desire to reproduce—not biologically, but intellectually, by begetting additional “gloriously beautiful ideas and theories.” For Diotima, and presumably for Plato as well, the fitting response to mathematical beauty is the form of Eros we call love.

Consider (for example) the beauty of the rolling donut

            (Animation source: MIQEL.com)

Tuesday, February 5, 2013


Filed under: General — m759 @ 5:10 PM

John Berryman in The New York Review of Books :


"Now he has become, abrupt, an industry.
Professional-Friends-Of-Robert-Frost all over
open their mouths
while the quirky medium of so many truths
is quiet. Let’s all be quiet. Let’s listen:
while he begins to talk with Horace."

Friday, June 22, 2012

Bowling in Diagon Alley

Filed under: General,Geometry — Tags: — m759 @ 8:28 AM

IMAGE- Josefine Lyche bowling, from her Facebook page

Josefine Lyche bowling (Facebook, June 12, 2012)

"Where Does Math Come From?"

A professor of philosophy in 1984 on Socrates's geometric proof in Plato's Meno  dialogue—

"These recondite issues matter because theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling…."

— Ian Hacking in The New York Review of Books , Feb. 16, 1984

The same professor introducing a new edition of Kuhn's Structure of Scientific Revolutions

"Paradigms Regained" (Los Angeles Review of Books , April 18, 2012)—

"That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones."

The Meno  proof involves inscribing diagonals  in squares. It is therefore related, albeit indirectly, to the classic Greek discovery that the diagonals of a square are incommensurable  with its sides. Hence the following discussion of incommensurability seems relevant.

IMAGE- Von Fritz in 1945 on incommensurability and the tetractys (10 as a triangular number)

See also von Fritz and incommensurability in The New York Times  (March 8, 2011).

For mathematical remarks related to the 10-dot triangular array of von Fritz, diagonals, and bowling, see this  journal on Nov. 8, 2011— "Stoned."

Thursday, November 17, 2011


Filed under: General — m759 @ 11:11 AM

From "Elegy to the Void," by Cathleen Schine, New York Review of Books , issue dated Nov. 24, 2011—

“We tell ourselves stories in order to live,” Didion famously wrote in The White Album . Blue Nights  is about what happens when there are no more stories we can tell ourselves, no narrative to guide us and make sense out of the chaos, no order, no meaning, no conclusion to the tale. The book has, instead, an incantatory quality: it is a beautiful, soaring, polyphonic eulogy, a beseeching prayer that is sung even as one knows the answer to one’s plea, and that answer is: No.

Blue Nights  is a sequel of sorts to The Year of Magical Thinking , Didion's story of the year following the death on December 30th, 2003, of her husband, fellow writer John Gregory Dunne.

Related material:




For some context, see

  1. Cosmic Banditos in this journal,
  2. the Fall 1997 newsletter of the Institute for Advanced Study,
  3. and Oppenheimer's Aria.

For a different link to that aria, see a journal entry dated December 28, 2003.
(Click link, scroll down.)

Wednesday, August 24, 2011


Filed under: General — Tags: , — m759 @ 2:02 PM

In the catacomb of my mind
Where the dead endure—a kingdom
I conjure by love to rise

Samuel Menashe, as quoted by
Stephen Spender in a review of four
different poets, "The Last Ditch,"
The New York Review of Books , July 22, 1971

"…the ghost reveals that the beggar
is in fact a sorcerer, a necromancer
who is preparing the mandala in order
to achieve an evil end. The ascetic
intends to bind the ghost to the corpse,
place it in the center of the circle,
and worship it as a deity."

The King and the Corpse  (from synopsis in
"How Many Facets Can a Non-Existent Jewel Have?")

Menashe died on Monday, August 22, 2011.

Related material by and for two other poets
who also died on Monday:

  1. By Jerry Leiber— "Love Potion #9"
  2. For Nick AshfordNicole Kidman in
    Sermon (from Jan. 9) and
    Conjure Wife, a 1943 tale by Fritz  Leiber

See also an excerpt from Kerouac I cached on Monday, and

Men ask the way to Cold Mountain
Cold Mountain: there's no through trail .

Tuesday, June 21, 2011

Requiem for a Publisher

Filed under: General — m759 @ 2:09 AM

In memory of A. Whitney Ellsworth, first publisher of
The New York Review of Books , who died at 75
on Saturday—


The Review  has sometimes been cited in this journal.

See also posts from the date of Ellsworth's death—

Saturday, May 7, 2011

Annals of Mathematics

Filed under: General — m759 @ 10:35 PM

University Diaries praised today the late Robert Nozick's pedagogical showmanship.

His scholarship was less praiseworthy. His 2001 book Invariances: The Structure of the Objective World  failed, quite incredibly, to mention Hermann Weyl's classic summary of  the connection between invariance and objectivity.  See a discussion of Nozick in The New York Review of Books  of December 19, 2002

"… one should mention, first and foremost, the mathematician Hermann Weyl who was almost obsessed by this connection. In his beautiful little book Symmetry  he tersely says, 'Objectivity means invariance with respect to the group of automorphisms….'"

See also this journal on Dec. 3, 2002, and Feb. 20, 2007.

For some context, see a search on the word stem "objectiv-" in this journal.

Tuesday, April 12, 2011

One of a Kind

Filed under: General — m759 @ 1:44 AM

This morning's online New York Times  obituaries—


For the story of the woman at the head of the class,
see Sarah Boxer in The New York Review of Books .

See also Boxer on the Feast of the Assumption, 2009.

Saturday, September 25, 2010

Talking Rot at Harvard

Filed under: General — m759 @ 6:16 AM

"…as Jeremy R. Knowles, Dean of the Faculty of Arts and Sciences, stated in his Fall 2006 address to the Harvard freshman class, being able to tell if a man is 'talking rot' is the ultimate goal of a liberal arts education."

— Yelena S. Mironova ’12 in The Harvard Crimson  yesterday

Is Mironova talking rot? Apparently not, since Knowles did, it seems, use that phrase in such an address. (See an alleged transcript of his remarks by someone at Facebook identifying herself as Van Le, Harvard '10)

Was Knowles talking rot? Perhaps, since the alleged transcript of his remarks indicates he attributed the phrase to a 1914 lecture by one J. A. Smith, a philosopher at Oxford,  but did not give a source for his quotation.

A Google web search for more accurate information yields no exact source. There are two notable hearsay sources—

The weblog Fairing's Parish  on August 16, 2009, gives a version attributed to Smith in More Christmas Crackers  by John Julius Norwich. (The hardcover first edition of this book was published by Viking on Oct. 14, 1991, according to Amazon.co.uk.)

An earlier book in the Christmas Crackers  series was cited as a Smith source by Michael M. Thomas at Forbes.com on Oct. 24, 2008

"I happened upon Professor Smith long years ago, in the 1980 edition of John Julius Norwich's Christmas Cracker  [sic ]…."

The weblog Laudator Temporis Acti  of Michael Gilleland on August 29, 2004, says…

The following quotation comes at second or third hand. John Alexander Smith (1863-1939), Waynflete Professor of Moral and Metaphysical Philosophy at Oxford, gave a lecture sometime before WWI, attended by Harold Macmillan. Macmillan reported Smith's words to Isaiah Berlin, and Isaiah Berlin told them to Ramin Jahanbegloo, who reproduced them in Conversations with Isaiah Berlin  (London: Phoenix Press, 1993), p. 29….

Some further bibliographic notes on the Jahanbegloo book—

Ramin Jahanbegloo, Isaiah Berlin en toutes libertés: entretiens avec Isaiah Berlin  (Paris, 1991: Éditions du Félin); repr. in its original English form as Ramin Jahanbegloo, Conversations with Isaiah Berlin  (London, 1992: Peter Halban; New York, 1992: Scribner’s; London, 1993: Phoenix; 2nd ed., London, 2007: Halban); excerpted in Jewish Quarterly  38 No 3 (Autumn 1991), 15–26, Jewish Chronicle,  7 February 1992, Literary Supplement, ii, Guardian,  7 March 1992, 23, and (as ‘Philosophy and Life: An Interview’) New York Review of Books,  28 May 1992, 46–54; trans. Chinese (both scripts), German, Hebrew, Italian, Japanese, Persian, Polish, Portuguese, Spanish (complete and in part, by different translators)


A Google books  search yields some starting points for a paper chase that might, given library resources like Harvard's, finally nail down the rot quote.

Try smith oxford "talking rot".

The best citation I can find online is not very good. See The Oxford Book of Oxford  (first edition 1978, new edition 2002), edited by Jan (formerly James) Morris, who gives as her source "J. A. Smith, Professor of Moral Philosophy, opening a lecture course in 1914 (quoted by Harold Macmillan in The Times, 1965)." This does not indicate whether Macmillan was quoting Smith from memory or from a written or printed record. Only the latter would clear Macmillan (and all subsequent purveyors of the alleged Smith quote who did not attribute it to Macmillan) from the suspicion of talking rot.

Friday, January 22, 2010

Yesterday’s Man

Filed under: General — m759 @ 12:00 PM

Anne Applebaum in the current New York Review of Books on Arthur Koestler

"At the moment, he still seems like yesterday's man, unfashionable and obsolete."

Rather like God. See this journal yesterday– Darkness at Noon.

See also David Levine's portrait of Koestler (Dec. 30, 2009)–


— and an objective correlative to yesterday's post —

LA mayor says storm front will hit region at noon on June 21, 2010

Click to enlarge.

Wednesday, December 30, 2009

Fearful Symmetry

Filed under: General,Geometry — m759 @ 4:12 PM


Arthur Koestler by David Levine,
New York Review of Books,
December 17, 1964

A Jesuit at the
Gerard Manley Hopkins Archive

‘Bisociation’: The Act of Creation

Koestler’s concept of ‘bisociation’… enters into the very ‘act of creation.’ In every such act, writes Koestler, the creator ‘bisociates,’ that is, combines, two ‘matrices’– two diverse patterns of knowing or perceiving– in a new way. As each matrix carries its own images, concepts, values, and ‘codes,’ the creative person brings together– ‘bisociates’– two diverse matrices not normally connected.

— Joseph J. Feeney, S.J.

See also December 9, 2009:

The theme of the January 2010 issue of the
Notices of the American Mathematical Society
is “Mathematics and the Arts.”

Related material:

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Friday, December 25, 2009

Brightness at Noon

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

New York Times online front page
Christmas morning:

“Arthur Koestler, Man of Darkness”–

NY Times front page, Christmas morning 2009

The photo is of Koestler in 1931 on a zeppelin expedition to the North Pole.

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

From Opus Postumum by Immanuel Kant, Eckart Förster, Cambridge U. Press, 1995, p. 260:

“In January 1697, Leibniz accompanied his New Year Congratulations to Rudolf August with the design of a medal with the duke’s likeness on one side, and the ‘image of Creation’ in terms of the binary number system on the other. Concerning the inscription on this side, Leibniz writes: ‘I have thought for a while about the Motto dell’impresa and finally have found it good to write this line: omnibus ex nihilo ducendis SUFFICIT UNUM [To make all things from nothing, UNITY SUFFICES], because it clearly indicates what is meant by the symbol, and why it is imago creationis’ (G. F. Leibniz, Zwei Briefe über das binäre Zahlensystem und die chinesische Philosophie, ed. Renate Loosen and Franz Vonessen, Chr. Belser Verlag: Stuttgart 1968, p. 21).”

Leibniz, design for medallion showing binary numbers as an 'imago creationis'

Figure from Rudolf  Nolte’s
Gottfried Wilhelms Baron von Leibniz
Mathematischer Beweis der Erschaffung und
Ordnung der Welt in einem Medallion…
(Leipzig: J. C. Langenheim, 1734).

Leibniz, letter of 1697:

“And so that I won’t come entirely empty-handed this time, I enclose a design of that which I had the pleasure of discussing with you recently. It is in the form of a memorial coin or medallion; and though the design is mediocre and can be improved in accordance with your judgment, the thing is such, that it would be worth showing in silver now and unto future generations, if it were struck at your Highness’s command. Because one of the main points of the Christian Faith, and among those points that have penetrated least into the minds of the worldly-wise and that are difficult to make with the heathen is the creation of all things out of nothing through God’s omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing. And it would be difficult to find a better illustration of this secret in nature or philosophy; hence I have set on the medallion design IMAGO CREATIONIS [in the image of creation]. It is no less remarkable that there appears therefrom, not only that God made everything from nothing, but also that everything that He made was good; as we can see here, with our own eyes, in this image of creation. Because instead of there appearing no particular order or pattern, as in the common representation of numbers, there appears here in contrast a wonderful order and harmony which cannot be improved upon….

Such harmonious order and beauty can be seen in the small table on the medallion up to 16 or 17; since for a larger table, say to 32, there is not enough room. One can further see that the disorder, which one imagines in the work of God, is but apparent; that if one looks at the matter with the proper perspective, there appears symmetry, which encourages one more and more to love and praise the wisdom, goodness, and beauty of the highest good, from which all goodness and beauty has flowed.”

See also Parable.

Tuesday, April 3, 2007

Tuesday April 3, 2007

Filed under: General — Tags: , , — m759 @ 1:00 AM

Mathematics Awareness Month

Related material:

“But what is it?”
Calvin demanded.
“We know that it’s evil,
but what is it?”

“Yyouu hhave ssaidd itt!”
Mrs. Which’s voice rang out.
“Itt iss Eevill. Itt iss thee
Ppowers of Ddarrkknesss!”

A Wrinkle in Time

AMS Notices cover, April 2007

“After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called ‘It’ because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil.”

See also
“Darkness Visible”

“When all is said and done,
science is about things and
theology is about words.”

— Freeman Dyson,
New York Review of Books,
issue dated May 28, 1998

Does the word ‘tesseract’
mean anything to you?

Wednesday, March 28, 2007

Wednesday March 28, 2007

Filed under: General — m759 @ 10:10 PM
Plato, God, Stories

Peter Woit’s latest weblog entry links to a discussion of Plato’s cave and the modular group, which in turn suggests a second look at an entry linked to, indirectly, at the end of Saturday’s Log24 entry: Natasha’s Dance.  This leads to the following:

“To me, to worship God means to recognize that mind and intelligence are woven into the fabric of our universe in a way that altogether surpasses our comprehension.”

— Freeman Dyson, “Science & Religion: No Ends in Sight,” The New York Review of Books, issue dated five years ago today– March 28, 2002.

If Dyson’s “recognition” is correct, why should mind and intelligence not be woven into the fabric of the Pennsylvania Lottery?

PA Lottery March 28, 2007: Mid-day 226, Evening 826

The practiced reader of Log24 will have little difficulty in constructing a story based on these numbers.  Briefly, the story is… 2/26 and 8/26.  The way the story was written may “surpass our comprehension,” but the story itself need not.

Those more interested in the writing than the story may consult Edward Rothstein’s piece in the March 26 New York Times, “Texts That Run Rings Around Everyday Linear Logic.”  There they will find a brief discussion of, appropriately, the Bible’s Book of Numbers.

Friday, December 29, 2006

Friday December 29, 2006

Filed under: General — Tags: , — m759 @ 11:01 AM
of Christ Church

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon

Cover of Thomas, by Shelley Mydans: Sword and its shadow, a cross

Click on picture for details.

Today is the feast
of St. Thomas Becket.

In his honor, a meditation
on tools and causation:

"Lewis Wolpert, an eminent developmental biologist at University College London, has just published Six Impossible Things Before Breakfast, a pleasant, though rambling, look at the biological basis of belief. While the book focuses on our ability to form causal beliefs about everyday matters (the wind moved the trees, for example), it spends considerable time on the origins of religious and moral beliefs. Wolpert defends the unusual idea that causal thinking is an adaptation required for tool-making. Religious beliefs can thus be seen as an odd extension of causal thinking about technology to more mysterious matters. Only a species that can reason causally could assert that 'this storm was sent by God because we sinned.' While Wolpert's attitude toward religion is tolerant, he's an atheist who seems to find religion more puzzling than absorbing."

Review by H. Allen Orr in
The New York Review of Books,
Vol. 54, No. 1, January 11, 2007    

"An odd extension"–

Wolpert's title is, of course,
from Lewis Carroll.

Related material:

"It's a poor sort of memory
that only works backwards."
Through the Looking-Glass

An event at the Kennedy Center
broadcast on
December 26, 2006
(St. Steven's Day):

"Conductor John Williams, a 2004 Honoree, says, 'Steven, sharing our 34-year collaboration has been a great privilege for me. It's been an inspiration to watch you dream your dreams, nurture them and make them grow. And, in the process, entertain and edify billions of people around the world. Tonight we'd like to salute you, musically, with a piece that expresses that spirit beautifully … It was written by Leonard Bernstein, a 1980 Kennedy Center Honoree who was, incidentally, the first composer to be performed in this hall.' Backed by The United States Army Chorus and The Choral Arts Society, soprano Harolyn Blackwell and tenor Gregory Turay sing the closing number for Spielberg's tribute and the gala itself. It's the finale to the opera 'Candide,' 'Make Our Garden Grow,' and Williams conducts."

CBS press release

See also the following,
from the conclusion to

"Mathematics and Narrative"

(Log24, Aug. 22, 2005):

Diamond on cover of Narrative Form, by Suzanne Keen

"At times, bullshit can
only be countered
   with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to at least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

"Il faut cultiver notre jardin."
— Voltaire

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

Diamond in a square

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
 Regius Professor of Divinity,
  Christ Church College, Oxford
(the home of Lewis Carroll)

For further details,
click on the
Christ Church diamond.

Sunday, August 6, 2006

Sunday August 6, 2006

Filed under: General — Tags: — m759 @ 7:00 PM
Game Boy
The image “http://www.log24.com/log/pix06A/060806-Einsatz.jpg” cannot be displayed, because it contains errors.
Click on picture for details.
"Nine is a very
powerful Nordic number
— Katherine Neville


to put one's back
into something
bei etwas
Einsatz zeigen
to up the ante
den Einsatz erhöhen
to debrief den Einsatz
nachher besprechen
to be on duty
im Einsatz sein
mil.to be in action im Einsatz sein
to play for
high stakes
mit hohem
Einsatz spielen



"His music had of course come from Russian folk sources and from Rimsky-Korsakov and from other predecessors, in the way that all radical art has roots. But to be a true modernist, a cosmopolitan in the twentieth century, it was necessary to seem to disdain nationalism, to be perpetually, heroically novel– the more aloof, the better. 'Cold and transparent, like an "extra dry" champagne, which gives no sensation of sweetness, and does not enervate, like other varieties of that drink, but burns,' Stravinsky said about his own Octet, Piano Concerto, and Piano Sonata. The description might be applied to works by Picasso or Duchamp."

— Michael Kimmelman in
  The New York Review of Books,
issue dated Aug. 10, 2006

But the description
certainly applies to
Bridget Moynahan:

The image “http://www.log24.com/log/pix06A/060806-Recruit2.jpg” cannot be displayed, because it contains errors.

"… like an 'extra dry' champagne,
which gives no sensation of
sweetness, and does not enervate."

For more on the
"Ice 9" figure, see
Balanchine's Birthday.

Sunday, July 23, 2006

Sunday July 23, 2006

Filed under: General,Geometry — m759 @ 2:56 PM

Dance of the Numbers, continued:


Freeman Dyson on the role of the “crank” in the theory of partitions:

“‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

Erica Klarreich in
    Science News Online, week of
    June 18, 2005, quoted in
   “In Honor of Freeman Dyson’s Birthday:
    Dance of the Numbers
    (Log24, Dec. 15, 2005)

Paraphrase of Freeman Dyson’s remarks in The New York Review of Books, issue dated May 28, 1998:

“Theology is about words; science is about things.

“What is 256 about?”
Reply to Freeman Dyson,
    (May 15, 1998)

A partial answer to that rhetorical question: 256 is the cardinality of the power set of an 8-set.

For the role played by 8-sets and by 23 (today’s date) in partitions of a different sort, see Geometry of the 4×4 Square.

Saturday, June 17, 2006

Saturday June 17, 2006

Filed under: General,Geometry — m759 @ 7:59 AM
In memory of
Barbara Epstein:


“Breaking the spell of religion is a
 game that many people can play.”
— Freeman Dyson in the current
   New York Review of Books

Part I:
The Game

The image “http://www.log24.com/log/pix06A/060617-Boggle.jpg” cannot be displayed, because it contains errors.

Part II:
Many People

The image “http://www.log24.com/log/pix06A/060617-Spellbound.jpg” cannot be displayed, because it contains errors.

For further details,
see Solomon’s Cube
and myspace.com/affine.

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

Sunday, March 12, 2006

Sunday March 12, 2006

Filed under: General,Geometry — m759 @ 1:00 PM

A Circle of Quiet

From the Harvard Math Table page:

“No Math table this week. We will reconvene next week on March 14 for a special Pi Day talk by Paul Bamberg.”

The image “http://www.log24.com/log/pix06/060312-PaulBamberg21.jpg” cannot be displayed, because it contains errors.

Paul Bamberg

Transcript of the movie “Proof”–

Some friends of mine are in this band.
They’re playing in a bar on Diversey,
way down the bill, around…

I said I’d be there.

They’re all in the math department.
They’re good.
They have this song called “i.”
You’d like it. Lowercase i.
They just stand there.
They don’t play anything for three minutes.

Imaginary number?

It’s a math joke.
You see why they’re way down the bill.

From the April 2006 Notices of the American Mathematical Society, a footnote in a review by Juliette Kennedy (pdf) of Rebecca Goldstein’s Incompleteness:

4 There is a growing literature in the area of postmodern commentaries of [sic] Gödel’s theorems. For example, Régis Debray has used Gödel’s theorems to demonstrate the logical inconsistency of self-government. For a critical view of this and related developments, see Bricmont and Sokal’s Fashionable Nonsense [13]. For a more positive view see Michael Harris’s review of the latter, “I know what you mean!” [9]….

[9] MICHAEL HARRIS, “I know what you mean!,” http://www.math.jussieu.fr/~harris/Iknow.pdf.
[13] ALAN SOKAL and JEAN BRICMONT, Fashionable Nonsense, Picador, 1999.

Following the trail marked by Ms. Kennedy, we find the following in Harris’s paper:

“Their [Sokal’s and Bricmont’s] philosophy of mathematics, for instance, is summarized in the sentence ‘A mathematical constant like The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. doesn’t change, even if the idea one has about it may change.’ ( p. 263). This claim, referring to a ‘crescendo of absurdity’ in Sokal’s original hoax in Social Text, is criticized by anthropologist Joan Fujimura, in an article translated for IS*. Most of Fujimura’s article consists of an astonishingly bland account of the history of non-euclidean geometry, in which she points out that the ratio of the circumference to the diameter depends on the metric. Sokal and Bricmont know this, and Fujimura’s remarks are about as helpful as FN’s** referral of Quine’s readers to Hume (p. 70). Anyway, Sokal explicitly referred to “Euclid’s pi”, presumably to avoid trivial objections like Fujimura’s — wasted effort on both sides.32 If one insists on making trivial objections, one might recall that the theorem
that p is transcendental can be stated as follows: the homomorphism Q[X] –> R taking X to The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. is injective.  In other words, The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. can be identified algebraically with X, the variable par excellence.33

The image “http://www.log24.com/log/pix06/060312-X.jpg” cannot be displayed, because it contains errors.

More interestingly, one can ask what kind of object The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. was before the formal definition of real numbers. To assume the real numbers were there all along, waiting to be defined, is to adhere to a form of Platonism.34  Dedekind wouldn’t have agreed.35  In a debate marked by the accusation that postmodern writers deny the reality of the external world, it is a peculiar move, to say the least, to make mathematical Platonism a litmus test for rationality.36 Not that it makes any more sense simply to declare Platonism out of bounds, like Lévy-Leblond, who calls Stephen Weinberg’s gloss on Sokal’s comment ‘une absurdité, tant il est clair que la signification d’un concept quelconque est évidemment affectée par sa mise en oeuvre dans un contexte nouveau!’37 Now I find it hard to defend Platonism with a straight face, and I prefer to regard the formula

The image “http://www.log24.com/log/pix06/060312-pi.jpg” cannot be displayed, because it contains errors.

as a creation rather than a discovery. But Platonism does correspond to the familiar experience that there is something about mathematics, and not just about other mathematicians, that precisely doesn’t let us get away with saying ‘évidemment’!38

32 There are many circles in Euclid, but no pi, so I can’t think of any other reason for Sokal to have written ‘Euclid’s pi,’ unless this anachronism was an intentional part of the hoax.  Sokal’s full quotation was ‘the The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity.’  But there is no need to invoke non-Euclidean geometry to perceive the historicity of the circle, or of pi: see Catherine Goldstein’s ‘L’un est l’autre: pour une histoire du cercle,’ in M. Serres, Elements d’histoire des sciences, Bordas, 1989, pp. 129-149.
33 This is not mere sophistry: the construction of models over number fields actually uses arguments of this kind. A careless construction of the equations defining modular curves may make it appear that pi is included in their field of scalars.
34 Unless you claim, like the present French Minister of Education [at the time of writing, i.e. 1999], that real numbers exist in nature, while imaginary numbers were invented by mathematicians. Thus The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. would be a physical constant, like the mass of the electron, that can be determined experimentally with increasing accuracy, say by measuring physical circles with ever more sensitive rulers. This sort of position has not been welcomed by most French mathematicians.
35 Cf. M. Kline, Mathematics The Loss of Certainty, p. 324.
36 Compare Morris Hirsch’s remarks in BAMS April 94.
37 IS*, p. 38, footnote 26. Weinberg’s remarks are contained in his article “Sokal’s Hoax,” in the New York Review of Books, August 8, 1996.
38 Metaphors from virtual reality may help here.”

* Earlier defined by Harris as “Impostures Scientifiques (IS), a collection of articles compiled or commissioned by Baudouin Jurdant and published simultaneously as an issue of the journal Alliage and as a book by La Découverte press.”
** Earlier defined by Harris as “Fashionable Nonsense (FN), the North American translation of Impostures Intellectuelles.”

What is the moral of all this French noise?

Perhaps that, in spite of the contemptible nonsense at last summer’s Mykonos conference on mathematics and narrative, stories do have an important role to play in mathematics — specifically, in the history of mathematics.

Despite his disdain for Platonism, exemplified in his remarks on the noteworthy connection of pi with the zeta function in the formula given above, Harris has performed a valuable service to mathematics by pointing out the excellent historical work of Catherine Goldstein.   Ms. Goldstein has demonstrated that even a French nominalist can be a first-rate scholar.  Her essay on circles that Harris cites in a French version is also available in English, and will repay the study of those who, like Barry Mazur and other Harvard savants, are much too careless with the facts of history.  They should consult her “Stories of the Circle,” pp. 160-190 in A History of Scientific Thought, edited by Michel Serres, Blackwell Publishers (December 1995).

For the historically-challenged mathematicians of Harvard, this essay would provide a valuable supplement to the upcoming “Pi Day” talk by Bamberg.

For those who insist on limiting their attention to mathematics proper, and ignoring its history, a suitable Pi Day observance might include becoming familiar with various proofs of the formula, pictured above, that connects pi with the zeta function of 2.  For a survey, see Robin Chapman, Evaluating Zeta(2) (pdf).  Zeta functions in a much wider context will be discussed at next May’s politically correct “Women in Mathematics” program at Princeton, “Zeta Functions All the Way” (pdf).

Tuesday, February 14, 2006

Tuesday February 14, 2006

Filed under: General — m759 @ 7:20 AM
Elitist Valentine

“… ‘elite’ is a term of opprobrium on both sides of the Atlantic for both left and right for entirely different reasons–  for the right, an ‘elitist’ is an unpatriotic, degenerate left-wing fan of the avant-garde; for the left, he is an undemocratic enemy of the people.”

— Charles Rosen, review of The Oxford History of Western Music in the Feb. 23, 2006, New York Review of Books

The first person that comes to mind as fitting both left and right descriptions is T. S. Eliot.  Hence the following:

The image “http://www.log24.com/log/pix05/050503-Poets.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
— Marie-Louise von Franz,
   Number and Time (1970)

Saturday, December 10, 2005

Saturday December 10, 2005

Filed under: General — Tags: , — m759 @ 5:24 AM

Roger Shattuck, Scholar, Is Dead at 82

In his honor, some excerpts from previous entries:

Wednesday, January 19, 2005

I just subscribed to The New York Review of Books online for another year,
prompted by my desire to read Roger Shattuck on Rimbaud….

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.

(See Death and the Spirit, Part II.)

The image “http://www.log24.com/log/pix05B/051210-Blue.jpg” cannot be displayed, because it contains errors.

The photo of Nicole Kidman
is from Globe Song
(Log24, Jan. 18, 2005).

The Times says Shattuck died
on Thursday (Dec. 8, 2005).

Here, from 4:00 AM on the
morning of Shattuck's death,
is a brief companion-piece
to Eight is a Gate:

Four is a Door:

From Carole A. Holdsworth,
Dulcinea and Pynchon's V:

Tanner may have stated it best:

“V. is whatever lights you to
 the end of the street:
 she is also the dark annihilation
 waiting at the end of the street.”

(Tony Tanner, page 36,
 "V. and V-2," in
 Pynchon: A Collection
 of Critical Essays.

 Ed. Edward Mendelson.
 Englewood Cliffs, N. J.:
 Prentice-Hall, 1978. 16-55).

She's a mystery
She's everything
   a woman should be
Woman in black
   got a hold on me

Foreigner 4

She's in midnight blue,
 still the words ring true;
woman in blue
got a hold on you.

Friday, July 22, 2005

Friday July 22, 2005

Filed under: General — m759 @ 3:57 PM

For Louise Fletcher
on her birthday

The image “http://www.log24.com/log/pix05A/050722-Fletcher.jpg” cannot be displayed, because it contains errors.

Fletcher in
Exorcist II: The Heretic

From Andrew Delbanco, the author of
The Death of Satan:

How Americans Have Lost the Sense of Evil:

“A couple of years ago, in an article explaining how funds for faculty positions are allocated in American universities, the provost of the University of California at Berkeley offered some frank advice to department chairs, whose job partly consists of lobbying for a share of the budget.  ‘On every campus,’ she wrote, ‘there is one department whose name need only be mentioned to make people laugh; you don’t want that department to be yours.’   The provost, Carol Christ (who retains her faculty position as a literature professor), does not name the offender—but everyone knows that if you want to locate the laughingstock on your local campus these days, your best bet is to stop by the English department.”

Andrew Delbanco in
   The New York Review of Books, Nov. 4, 1999


The image “http://www.log24.com/log/pix05A/050722-Christ.jpg” cannot be displayed, because it contains errors.

Click on picture for details.

For Christ in a different context,
see the 9/11 entry of Log24
in a September 2003 archive.

For exorcism in a different context, see
Exorcism and Multiple Personality Disorder
from a Catholic Perspective
by Fr. J. Mahoney.

“Got to keep the loonies on the path.”
Roger Waters

Thursday, January 20, 2005

Thursday January 20, 2005

Filed under: General — m759 @ 10:00 AM

I mean, seriously…

The Comedians is about three men, Smith, Jones and Brown….

“Again I was aware of the three names, interchangeable like comic masks in a farce.”

— Graham Greene, The Comedians, Penguin paperback, 1991, p. 23

Pico Iyer on Graham Greene in the current New York Review of Books:

“To play out the full logic….”

Brown, Jones, and Smith are suspected of a crime. They testify as follows:

Brown: Jones is guilty and Smith is innocent.

Jones: If Brown is guilty then so is Smith.

Smith: I’m innocent, but at least one of the others is guilty.

Assuming all testimony is true, who is innocent and who is guilty?

Assuming that the innocent told the truth and the guilty told lies, who is innocent and who is guilty?

— Mathematical logic
    homework problem (pdf)

Wednesday, January 19, 2005

Wednesday January 19, 2005

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

But seriously…

A follow-up to the previous "tiger" entry (which was about an old but good dirty joke).

I just subscribed to The New York Review of Books online for another year, prompted by my desire to read Roger Shattuck on Rimbaud, a tiger of another sort:

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.  (See Sunday's Death and the Spirit, Part II.)

Friday, December 10, 2004

Friday December 10, 2004

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

Gray Particular
in Hartford

From Wallace Stevens,

"The Rock, Part III:
Forms of the Rock in a Night-Hymn" —

The rock is
   the gray particular of man's life,
The stone from which
   he rises, up–and–ho,
The step to
   the bleaker depths of his descents…

From this morning's
New York Times obituaries

The image “http://log24.com/log/pix03/nytC.gif” cannot be displayed, because it contains errors.leve Gray, a painter admired for his large-scale, vividly colorful and lyrically gestural abstract compositions, died on Wednesday in Hartford. He was 86.

The cause was a massive subdural hematoma suffered after he fell on ice and hit his head on Tuesday outside his home in Warren, Conn., said his wife, the writer Francine du Plessix Gray.


Jackson Mac Low, a poet, composer and performance artist whose work reveled in what happens when the process of composition is left to carefully calibrated chance, died on Wednesday….

… in 1999 [he] received the Wallace Stevens Award, which carries a $100,000 prize, from the Academy of American Poets.

A Wallace Stevens Award,
in Seven Parts:

  I.  From a page linked to in
      Tuesday's entry White Christmas:

"A bemused Plato reasoned that nonbeing must in some sense be, otherwise what is it that there is not? In our own day Martin Heidegger ventured that das Nichts nichtet — 'the nothing nothings' — evidently still sensing a problem."
— W. V. Quine in Quiddities

 II.  "As if nothingness
             contained a métier…"
      — Wallace Stevens, "The Rock"

III.  "Massive subdural hematoma"
       — Three-word poem
           performed on Tuesday
           in Connecticut

IV.  mé·tier n.


  • An occupation, a trade, or a profession.
  • Work or activity for which a person is particularly suited; one's specialty.

[French, from Old French mestier, from Vulgar Latin misterium, from Latin ministerium. See ministry.]
Source: The American Heritage® Dictionary of the English Language, Fourth Edition


  V.  "ho"
        — Wallace Stevens, "The Rock"

 VI.  Francine du Plessix Gray…
       From the
       Archives of the
       New York Review of Books:

July 16, 1992: Splendor and Miseries, review of

Women for Hire: Prostitution and Sexuality in France after 1850 by Alain Corbin, translated by Alan Sheridan

La Vie quotidienne dans les maisons closes, 1830–1930 by Laure Adler

Figures of Ill Repute: Representing Prostitution in Nineteenth-Century France by Charles Bernheimer

Painted Love: Prostitution in French Art of the Impressionist Era by Hollis Clayson

VII.   From an entry of April 29, 2004:


"… a 'dead shepherd who brought
tremendous chords from hell
And bade the sheep carouse' "


— Wallace Stevens
as quoted by Michael Bryson


(p. 227, The Palm
at the End of the Mind:

Selected Poems and a Play.
Ed. Holly Stevens.

New York: Vintage Books, 1990)


Tuesday, June 22, 2004

Tuesday June 22, 2004

Filed under: General — m759 @ 9:00 AM

Dirty Trick

Some quotations in memory of philosopher Stuart Hampshire, who died on June 13, 2004.

From the Hampshire obituary in The Guardian:


He frequently told the story of how, towards the end of the war, he had to interrogate a French traitor (imprisoned by the Free French), who refused to cooperate unless he was allowed to live. Should Hampshire, knowing the man was condemned to die, promise him a reprieve, which he was in no position to give, or truthfully refuse it, thereby jeopardising the lives of Resistance fighters?

“If you’re in a war,” said Hampshire, “you can’t start thinking, ‘Well I can’t lie to a man who’s going to be shot tomorrow and tell him that he isn’t.’ ”

But what the whole anecdote, and its incessant retelling, revealed was that Hampshire had, in fact, thought precisely what he said was unthinkable, and that whichever of the two decisions he finally took lay heavy on his conscience ever afterwards. Indicatively, too, it was especially loathsome to him because, although he did not say this in so many words, the traitor was almost a mirror image of himself – a cultivated young intellectual, looking like a film star, much influenced by elegant literary stylists – except that, in the traitor’s case, his literary mentors were fascist.


It is hard to know how Hampshire’s academic career was vitiated by the scandal over his affair with Ayer’s wife Renee, whom he married in 1961 after a divorce in which he was named as co-respondent. Even if less a matter of the dons’ moral conviction than their concern over how All Souls would appear, the affair caused a massive furore….

From a log24 entry on the day before Hampshire’s death:


“Hemingway called it a dirty trick.  It might even be an ancient Ordeal laid down on us by an evil Inquisitor in Space…. the dirty Ordeal by Death….”

— Jack Kerouac in Desolation Angels


The New Yorker of June 14  & 21, 2004:

…in ‘The Devil’s Eye,’ Bergman’s little-known comedy of 1960. Pablo seduces the wife of a minister, and then, sorrowful and sated, falling to his knees, he addresses her thus:

‘First, I’ll finish off that half-dug vegetable patch I saw. Then I’ll sit and let the rain fall on me. I shall feel wonderfully cool. And I’ll breakfast on one of those sour apples down by the gate. After that, I shall go back to Hell.’ “

Whether Hampshire is now in Hell, the reader may surmise.  Some evidence in Hampshire’s  favor:

His review of On Beauty and Being Just, by Elaine Scarry, in The New York Review of Books of November 18, 1999.  Note particularly his remarks on Fred Astaire, and the links to Astaire and the Four Last Things in an earlier entry of June 12, which was, as noted above, the day before Hampshire’s death.

As for the day of death itself, consider the  following  remark with which Hampshire concludes his review of Scarry’s  book:

“But one must occasionally fly the flag, and the flag, incorrigibly, is beauty.”

In this connection, see the entry of the Sunday Hampshire died, Spider Web, as well as entries on the harrowing of hell — Holy Saturday, 2004 — and on beauty —  Art Wars for Trotsky’s Birthday and A Mass for Lucero (written, as it happens, on June 13, 2002).

Thursday, June 3, 2004

Thursday June 3, 2004

Filed under: General — Tags: — m759 @ 3:17 PM


Today’s New York Times story on Richard Helms, together with my reminiscences in the entry that follows it below, suggest the following possibility for symbol-mongering:

Compare the 16-point star of the C.I.A.
with the classic 8-point star of Venus:

From today’s New York Times:

The image “http://www.log24.com/log/pix04A/040603-Tenet.jpg” cannot be displayed, because it contains errors.

Not even the most powerful
can alter the alignment
of the stars.

In a related story….

The Good Bad Boy
By Alison Lurie

“Today, many people have the illusion that they know who Pinocchio is. They think that he is a wooden marionette who becomes a human boy; that he was swallowed by a huge fish; and that when he told lies his nose grew longer. These people are right, but often in a very limited way. They know Pinocchio only from the sentimentalized and simplified Disney cartoon, or the condensed versions of his story that are thought more suitable for children. The original novel by Carlo Collodi, which today survives mainly in scholarly editions, is much longer, far more complex and interesting, and also much darker.”

The New York Review of Books, June 24, 2004


Saturday, May 22, 2004

Saturday May 22, 2004

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

A Form

John Leonard in the June 10, 2004, New York Review of Books, on E. L. Doctorow:

"… he's got urgent things to say and seeks some form to say them in, or a form that will tease and torture secret meanings out of what he thinks he already knows, or a form, like a wishing well, down which to dream, scream, or drown."

48. The Well

The Judgment

The Well. The town may be changed,
But the well cannot be changed.
It neither decreases nor increases.
They come and go and draw from the well.
If one gets down almost to the water
And the rope does not go all the way,
Or the jug breaks, it brings misfortune.

From the Book of Ecclesiastes 12:6

or ever the silver cord be loosed, or the golden bowl be broken, or the pitcher be broken at the fountain, or the wheel broken at the cistern

From Chuck Polisher's I Ching Lexicon:

See also the following form, discussed in

Balanchine's Birthday
(1/9/03) and in

Art Theory
for Yom Kippur


Thursday, May 20, 2004

Thursday May 20, 2004

Filed under: General,Geometry — 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.

Thursday, April 22, 2004

Thursday April 22, 2004

Filed under: General — m759 @ 2:14 PM


Picture said to be of
a Japanese Skylark,
Hibari or Alauda japonica.
Photo: 05/2002, Nagano, Japan.

A false definition of “inscape”:

Brad Leithauser, New York Review of Books, April 29, 2004:

“Not surprisingly, most Hopkins criticism is secular at heart, though without always acknowledging just how distorted—how weirdly misguided— Hopkins himself would find all interpretations of a spiritual life that were drawn purely from the outside. For him, a failure to see how divine promptings informed his shaping internal life—his ‘inscape,’ his own term for it—was to miss everything of his life that mattered.”

A truer definition:

“By ‘inscape’ he [Hopkins] means the unified complex of characteristics that give each thing its uniqueness and that differentiate it from other things.”

A false invocation of the Lord:

Brad Leithauser, New York Review of Books, Sept. 26, 2002:

“I’d always thought ‘Skylark’ quite appealing, but it wasn’t until I heard Helen Forrest singing it, in a 1942 recording with Harry James and his Orchestra, that it became for me something far more: one of the greatest popular songs anybody ever wrote. With her modest delivery, a voice coaxing and plaintive, Forrest is a Little Girl Lost who always finds herself coming down on exactly the right note—no easy thing with a song of such unexpected chromatic turns. On paper, the Johnny Mercer lyric looks unpromising—antiquated and clunky:

Have you seen a valley green with Spring
Where my heart can go a-journeying,
Over the shadows and the rain
To a blossom-covered lane?

But in Helen Forrest’s performance, ‘Skylark’ turns out to be a perfect blend of pokiness and urgency, folksiness and ethereality—and all so convincing that it isn’t until the song is finished that you step back and say, ‘Good Lord, she’s singing to a bird!’ “

For Hopkins at midnight in the garden of good and evil, a truer invocation:

Friday, December 27, 2002
12:00 AM

Saint Hoagy’s Day

Today is the feast day of St. Hoagy Carmichael, who was born on the feast day of Cecelia, patron saint of music. This midnight’s site music is “Stardust,” by Carmichael (lyrics by Mitchell Parish). See also “Dead Poets Society” — my entry of Friday, December 13, on the Carmichael song “Skylark” — and the entry “Rhyme Scheme” of later that same day.

Monday, March 22, 2004

Monday March 22, 2004

Filed under: General — m759 @ 10:00 PM

The Hairy Palm Academy

The previous two entries were prompted by a picture in the Washington Post of Spain’s Interior Minister, a member of the secular arm of the Legion of Christ.

Both entries mentioned a school run by the Legion of Christ, the Royal Palm Academy.  As the following excerpt from my March 20 entry indicates, a different sort of palm might also be honored by the Legion — the hairy palm.

“Los Legionarios de Cristo…  es una organización fundada en 1941 en Méjico por el padre Marcel [Marcial] Maciel (rehabilitado por el Vaticano en 1958 tras ser acusado de ayudarse en sus visiones con ampollas de morfina; también fue acusado de pederastia, le gustaba masturbar a jovencitos y que ellos le masturbaran a él).”


Related readings from The New York Review of Books, issue dated April 8, 2004:

God in the Hands of Angry Sinners, by Garry Wills, on the Legion of Christ and on Mel Gibson flogging his God,

and a related article, a review of

Solitary Sex: A Cultural History of Masturbation.

It seems the founder of the Legion of Christ, like many other Catholic priests, may have regarded masturbation as a group sport rather than solitary recreation.

For further details, see an ABC News 20/20 story dated April 26, 2002:

Priestly Sin, Cover-Up

When approached by ABC News’s Brian Ross in Rome with questions of allegations against Father Marcial Maciel, Cardinal Joseph Ratzinger became visibly upset and actually slapped Ross’s hand. — ABCNEWS.com

Thursday, January 8, 2004

Thursday January 8, 2004

Filed under: General — Tags: — m759 @ 4:23 PM

Natasha’s Dance

“… at the still point, there the dance is….”

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint…. “

— T. S. Eliot, Four Quartets

It seems, according to Eliot’s criterion, that the late author John Gregory Dunne may be a saint.

Pursuing further information on the modular group, a topic on which I did a web page Dec. 30, 2003, the date of Dunne’s death, I came across a review of Apostol’s work on that subject (i.e., the modular group, not Dunne’s death, although there is a connection).  The review:

“A clean, elegant,
absolutely lovely text…”

Searching further at Amazon for a newer edition of the Apostol text, I entered the search phrase “Apostol modular functions” and got a list that included the following as number four:

Natasha’s Dance:
A Cultural History of Russia

which, by coincidence, includes all three words of the search.

For a connection — purely subjective and coincidental, of course — with Dunne’s death, see The Dark Lady (Jan. 1, 2004), which concerns another Natasha… the actress Natalie Wood, the subject of an essay (“Star!“) by Dunne in the current issue of the New York Review of Books.

The Review’s archives offer another essay, on science and religion, that includes the following relevant questions:

“Have the gates of death
been opened unto thee?
Or hast thou seen the doors
of the shadow of death?”

From my December 31 entry:

In memory of
John Gregory Dunne,
who died on
Dec. 30, 2003

For further details, click
on the black monolith.

Sunday, January 4, 2004

Sunday January 4, 2004

Filed under: General — m759 @ 10:10 PM

Room 1010

Continuing the hotel theme of the previous entry….

John Gregory Dunne has a letter in the New York Review of Books of December 20 (St. Emil's Day in the previous entry), 1990.  In this letter, he reveals that he and his wife had at one time worked on a Grand Hotel screenplay based in Las Vegas.

For related material in memory of Dunne, see In Lieu of Rosebud, which contains entries for 10/10-10/12, 2002.

Mein Irisch Kind,
Wo weilest du?

Dancing at

Late Night
Grande Hotel

Big Time

Thursday, January 1, 2004

Thursday January 1, 2004

Filed under: General — Tags: — m759 @ 3:36 PM

The Dark Lady

“… though she has been seen by many men, she is known to only a handful of them.  You’ll see her — if you see her at all — just after you’ve taken your last breath.  Then, before you exhale for the final time, she’ll appear, silent and sad-eyed, and beckon to you.

She is the Dark Lady, and this is her story.”

Mike Resnick

“… she played (very effectively) the Deborah Kerr part in a six-hour miniseries of From Here to Eternity….”

John Gregory Dunne on Natalie Wood
in the New York Review of Books
dated Jan. 15, 2004

Very  effectively.

Saturday, December 20, 2003

Saturday December 20, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:00 PM

White, Geometric, and Eternal

This afternoon's surfing:

Prompted by Edward Rothstein's own Fides et Ratio encyclical in today's NY Times, I googled him.

At the New York Review of Books, I came across the following by Rothstein:

"… statements about TNT can be represented within TNT: the formal system can, in a precise way, 'talk' about itself."

This naturally prompted me to check what is on TNT on this, the feast day of St. Emil Artin.  At 5 PM this afternoon, we have Al Pacino in "The Devil's Advocate" — a perfect choice for the festival of an alleged saint.

Preparing for Al, I meditated on the mystical significance of the number 373, as explained in Zen and Language Games: the page number 373 in Robert Stone's theological classic A Flag for Sunrise conveys the metaphysical significance of the phrase "diamonds are forever" — "the eternal in the temporal," according to Stone's Catholic priest.  This suggests a check of another theological classic, Pynchon's Gravity's RainbowPage 373 there begins with the following description of prewar Berlin:

"white and geometric."

This suggests the following illustration of a white and geometric object related to yesterday's entry on Helmut Wielandt:

From antiquark.com

Figure 1

(This object, which illustrates the phrase "makin' the changes," also occurs in this morning's entry on the death of a jazz musician.)

A further search for books containing "white" and "geometric" at Amazon.com yields the following:

Figure 2

From Mosaics, by
Fassett, Bahouth, and Patterson:

"A risco fountain in Mexico city, begun circa 1740 and made up of Mexican pottery and Chinese porcelain, including Ming.

The delicate oriental patterns on so many different-sized plates and saucers [are] underlined by the bold blue and white geometric tiles at the base."

Note that the tiles are those of Diamond Theory; the geometric object in figure 1 above illustrates a group that plays a central role in that theory.

Finally, the word "risco" (from Casa del Risco) associated with figure 2 above leads us to a rather significant theological site associated with the holy city of Santiago de Compostela:

Figure 3

Vicente Risco's
Dedalus in Compostela.

Figure 3 shows James Joyce (alias Dedalus), whose daughter Lucia inspired the recent entry Jazz on St. Lucia's Day — which in turn is related, by last night's 2:45 entry and by Figure 1, to the mathematics of group theory so well expounded by the putative saint Emil Artin.

"His lectures are best described as
polished diamonds."
Fine Hall in its Golden Age,
by Gian-Carlo Rota

If Pynchon plays the role of devil's advocate suggested by his creation, in Gravity's Rainbow, of the character Emil Bummer, we may hope that Rota, no longer in time but now in eternity, can be persuaded to play the important role of saint's advocate for his Emil.

Update of 6:30 PM 12/20/03:


The Absolutist Faith
of The New York Times

White and Geometric, but not Eternal.

Sunday, November 2, 2003

Sunday November 2, 2003

Filed under: General,Geometry — Tags: — m759 @ 11:11 AM

All Souls' Day
at the Still Point

From remarks on Denis Donoghue's Speaking of Beauty in the New York Review of Books, issue dated Nov. 20, 2003, page 48:

"The Russian theorist Bakhtin lends his august authority to what Donoghue's lively conversation has been saying, or implying, all along.  'Beauty does not know itself; it cannot found and validate itself — it simply is.' "

From The Bakhtin Circle:

"Goethe's imagination was fundamentally chronotopic, he visualised time in space:

Time and space merge … into an inseparable unity … a definite and absolutely concrete locality serves at the starting point for the creative imagination… this is a piece of human history, historical time condensed into space….

Dostoevskii… sought to present the voices of his era in a 'pure simultaneity' unrivalled since Dante. In contradistinction to that of Goethe this chronotope was one of visualising relations in terms of space not time and this leads to a philosophical bent that is distinctly messianic:

Only such things as can conceivably be linked at a single point in time are essential and are incorporated into Dostoevskii's world; such things can be carried over into eternity, for in eternity, according to Dostoevskii, all is simultaneous, everything coexists…. "

Bakhtin's notion of a "chronotope" was rather poorly defined.  For a geometric structure that might well be called by this name, see Poetry's Bones and Time Fold.  For a similar, but somewhat simpler, structure, see Balanchine's Birthday.

From Four Quartets:

"At the still point, there the dance is."

From an essay by William H. Gass on Malcolm Lowry's classic novel Under the Volcano:

"There is no o'clock in a cantina."

Friday, October 17, 2003

Friday October 17, 2003

Filed under: General,Geometry — m759 @ 4:15 PM

Happy Birthday, Arthur Miller

Miller, the author of “The Crucible,” is what Russell Baker has called a “tribal storyteller.”

From an essay by Baker in The New York Review of Books, issue dated November 6, 2003 (Fortieth Anniversary Issue):

“Among the privileges enjoyed by rich, fat, superpower America is the power to invent public reality.  Politicians and the mass media do much of the inventing for us by telling us stories which purport to unfold a relatively simple reality.  As our tribal storytellers, they shape our knowledge and ignorance of the world, not only producing ideas and emotions which influence the way we live our lives, but also leaving us dangerously unaware of the difference between stories and reality.”

— Russell Baker, “The Awful Truth,” NYRB 11/6/03, page 8 

Here is a rather similar view of the media:

“Who Rules America?”.

The attentive student of this second essay will have no difficulty finding a single four-letter word to replace both of Baker’s phrases “rich, fat, superpower America” and “politicians and the mass media.”

Baker’s concern for “the difference between stories and reality” is reflected in my own website The Diamond Theory of Truth.  In summary:

“Is it safe?” — Sir Laurence Olivier

Tuesday, October 14, 2003

Tuesday October 14, 2003

Filed under: General — m759 @ 4:07 PM

Saint Leonard’s Day

From a review of Leonard Bernstein’s 1973 Norton lectures at Harvard:

The truly emblematic twentieth-century composer is Mahler, whose attempts to relinquish tonality are reluctant and incomplete, and whose nostalgia for past practice is overt and tragic. Mahler’s Ninth Symphony, his “last will and testament,” shows “that ours is the century of death, and Mahler is its musical prophet.” That is the “real reason” Mahler’s music suffered posthumous neglect–it was, Bernstein says, “telling something too dreadful to hear.” The Ninth Symphony embodies three kinds of death–Mahler’s own, which he knew was imminent; the death of tonality, “which for him meant the death of music itself”; and “the death of society, of our Faustian culture.” And yet this music, like all great art, paradoxically reanimates us.

Joseph Horowitz, New York Review of Books, June 10, 1993

Saturday, October 4, 2003

Saturday October 4, 2003

Filed under: General — m759 @ 5:48 PM

Today’s birthday: ageless Charlton Heston.

Happy Birthday, Moses!

Elaine Pagels,
authority on the Gnostic gospels,
p. 12, New York Review of Books,
issue dated Oct. 23, 2003

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

Thursday, May 22, 2003

Thursday May 22, 2003

Filed under: General — m759 @ 7:29 PM

Seek and Ye Shall Find:

On the Mystical Properties
of the Number 162

On this date in history:

May 22, 1942:  Unabomber Theodore John Kaczynski is born in the Chicago suburb of Evergreen Park, Ill., to Wanda Kaczynski and her husband Theodore R. Kaczynski, a sausage maker. His mother brings him up reading Scientific American.

From the June 2003 Scientific American:

“Seek and ye shall find.” – Michael Shermer

From my note Mark of April 25, 2003:

“Tell me of runes to grave
 That hold the bursting wave,
 Or bastions to design
 For longer date than mine.”

— A. E. Housman, quoted by G. H. Hardy in A Mathematician’s Apology

“Here, as examples, are one rune and one bastion…. (illustrations: the Dagaz rune and the Nike bastion of the Acropolis)…. Neither the rune nor the bastion discussed has any apparent connection with the number 162… But seek and ye shall find.”

Here is a connection to runes:

Mayer, R.M., “Runenstudien,” Beiträge zur Geschichte der deutschen Sprache und Literatur 21 (1896): pp. 162 – 184.

Here is a connection to Athenian bastions from a UN article on Communist educational theorist Dimitri Glinos:

“Educational problems cannot be scientifically solved by theory and reason alone….” (D. Glinos (1882-1943), Dead but not Buried, Athens, Athina, 1925, p. 162)

“Schools are…. not the first but the last bastion to be taken by… reform….”

“…the University of Athens, a bastion of conservatism and counter-reform….”

I offer the above with tongue in cheek as a demonstration that mystical numerology may have a certain heuristic value overlooked by fanatics of the religion of Scientism such as Shermer.

For a more serious discussion of runes at the Acropolis, see the photo on page 16 of the May 15, 2003, New York Review of Books, illustrating the article “Athens in Wartime,” by Brady Kiesling.

Friday, April 11, 2003

Friday April 11, 2003

Filed under: General — m759 @ 2:56 PM

Heaven’s Gate

“Rhetoric is concerned with the state of Babel after the Fall.”

— Kenneth Burke, A Rhetoric of Motives, quoted by Douglas Robinson at the site Linguistics and Language

Mesopotamian mathematics:

“Location: present-day Iraq, between the Tigris and Euphrates

Cities: Babylon, founded 2300 BC, 70 miles south of present Baghdad, on the Euphrates….

Babylon = Bab-ilu, “gate of God,” Hebrew: Babel or Bavel.”

Modern rendition
of “Bab-ilu


Perhaps the real heaven’s gate is at

Pottawatomie College.

Instant karma update:

 At 5:09 PM I read the following in the New York Review of Books, dated May 1, 2003, which arrived today.

From a review of Terror and Liberalism, by Paul Berman:

“As a general analysis of the various enemies of liberalism, and what ties them together, it is superb.  All — Nazis, Islamists, Bolsheviks, Fascists, and so on — are linked by Berman to the ‘ur-myth’ of the fall of Babylon.”

Speaking of Ur, Berman likes to quote a non-Biblical Abraham, named Lincoln.  The first, Biblical, Abraham was a damned homicidal lunatic, and the later American Abraham also delighted in blood sacrifice.  But that’s just my opinion.  For a different view, see the Chautauqua Abrahamic Program.


Wednesday, April 2, 2003

Wednesday April 2, 2003

Filed under: General,Geometry — Tags: — m759 @ 2:30 PM

Symmetries…. May 15, 1998

The following journal note, from the day after Sinatra died, was written before I heard of his death.  Note particularly the quote from Rilke.  Other material was suggested, in part, by Alasdair Gray’s Glasgow novel 1982 Janine.  The “Sein Feld” heading is a reference to the Seinfeld final episode, which aired May 14, 1998.  The first column contains a reference to angels — apparently Hell’s Angels — and the second column provides a somewhat more serious look at this theological topic.

Sein Feld


1984 Janine

“But Angels love their own
And they’re reaching out
    for you
Janine… Oh Janine
— Kim Wilde lyric,
    Teases & Dares album,
    1984, apparently about
    a British biker girl


Logos means above all relation.”
— Simone Weil,
    Gateway to God,
    Glasgow, 1982

Gesang ist Dasein….
 Ein Hauch um nichts.
 Ein Wehn im Gott.
 Ein Wind
— Not Heidegger but Rilke:
Sonnets to Orpheus, I, 3

Geometry and Theology

PA lottery May 14, 1998:
S8  The group of all projectivities and correlations of PG(3,2).

The above isomorphism implies the geometry of the Mathieu group M24.

“The Leech lattice is a blown-up version of
— W. Feit

“We have strong evidence that the creator of the universe loves symmetry.”
— Freeman Dyson

“Mackey presents eight axioms from which he deduces the [quantum] theory.”
— M. Schechter

“Theology is about words; science is about things.
— Freeman Dyson, New York Review of Books, 5/28/98

What is “256” about?

Tape purchased 12/23/97:


      Gypsy Jazz

“In the middle of 1982 Janine there are pages in which Jock McLeish is fighting with drugs and alcohol, attempting to either die or come through and get free of his fantasies. In his delirium, he hears the voice of God, which enters in small print, pushing against the larger type of his ravings.  Something God says is repeated on the first and last pages of Unlikely Stories, Mostly, complete with illustration and the words ‘Scotland 1984’ beside it. God’s statement is ‘Work as if you were in the early days of a better nation.’  It is the inherent optimism in that statement that perhaps best captures the strength of Aladair Gray’s fiction, its straightforwardness and exuberance.”
— Toby Olson, “Eros in Glasgow,” in Book World, The Washington Post, December 16, 1984

 For another look at angels, see “Winging It,” by Christopher R. Miller, The New York Times Book Review Bookend page for Sunday, May 24, 1998. May 24 is the feast day of Sara (also known by the Hindu name Kali), patron saint of Gypsies.

For another, later (July 16, 1998) reply to Dyson, from a source better known than myself, see Why Religion Matters, by Huston Smith, Harper Collins, 2001, page 66.

Tuesday, December 3, 2002

Tuesday December 3, 2002

Filed under: General,Geometry — Tags: — m759 @ 1:45 PM

Symmetry, Invariance, and Objectivity

The book Invariances: The Structure of the Objective World, by Harvard philosopher Robert Nozick, was reviewed in the New York Review of Books issue dated June 27, 2002.

On page 76 of this book, published by Harvard University Press in 2001, Nozick writes:

"An objective fact is invariant under various transformations. It is this invariance that constitutes something as an objective truth…."

Compare this with Hermann Weyl's definition in his classic Symmetry (Princeton University Press, 1952, page 132):

"Objectivity means invariance with respect to the group of automorphisms."

It has finally been pointed out in the Review, by a professor at Göttingen, that Nozick's book should have included Weyl's definition.

I pointed this out on June 10, 2002.

For a survey of material on this topic, see this Google search on "nozick invariances weyl" (without the quotes).

Nozick's omitting Weyl's definition amounts to blatant plagiarism of an idea.

Of course, including Weyl's definition would have required Nozick to discuss seriously the concept of groups of automorphisms. Such a discussion would not have been compatible with the current level of philosophical discussion at Harvard, which apparently seldom rises above the level of cocktail-party chatter.

A similarly low level of discourse is found in the essay "Geometrical Creatures," by Jim Holt, also in the issue of the New York Review of Books dated December 19, 2002. Holt at least writes well, and includes (if only in parentheses) a remark that is highly relevant to the Nozick-vs.-Weyl discussion of invariance elsewhere in the Review:

"All the geometries ever imagined turn out to be variations on a single theme: how certain properties of a space remain unchanged when its points get rearranged."  (p. 69)

This is perhaps suitable for intelligent but ignorant adolescents; even they, however, should be given some historical background. Holt is talking here about the Erlangen program of Felix Christian Klein, and should say so. For a more sophisticated and nuanced discussion, see this web page on Klein's Erlangen Program, apparently by Jean-Pierre Marquis, Département de Philosophie, Université de Montréal. For more by Marquis, see my later entry for today, "From the Erlangen Program to Category Theory."

Sunday, September 15, 2002

Sunday September 15, 2002

Filed under: General,Geometry — m759 @ 11:07 PM

Evariste Galois and 
The Rock That Changed Things

An article in the current New York Review of Books (dated Sept. 26) on Ursula K. Le Guin prompted me to search the Web this evening for information on a short story of hers I remembered liking.  I found the following in the journal of mathematician Peter Berman:

  • A Fisherman of the Inland Sea, Ursula K. Le Guin, 1994:
    A book of short stories. Good, entertaining. I especially liked “The Rock That Changed Things.” This story is set in a highly stratified society, one split between elite and enslaved populations. In this community, the most important art form is a type of mosaic made from rocks, whose patterns are read and interpreted by scholars from the elite group. The main character is a slave woman who discovers new patterns in the mosaics. The story is slightly over-the-top but elegant all the same.

I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:

A table of parallels

between The French Mathematician (a novel about Galois) and Harry Potter and the Sorcerer’s Stone

My own version of the Philosopher’s Stone (the phrase used instead of “Sorcerer’s Stone” in the British editions of Harry Potter) appears in my profile picture at top left; see also the picture of Plato’s diamond figure in my main math website.  The mathematics of finite (or “Galois”) fields plays a role in the underlying theory of this figure’s hidden symmetries.  Since the perception of color plays a large role in the Le Guin story and since my version of Plato’s diamond is obtained by coloring Plato’s version, this particular “rock that changes things” might, I hope, inspire Berman to extend his table to include Le Guin’s tale as well.

Even the mosaic theme is appropriate, this being the holiest of the Mosaic holy days.

Dr. Berman, G’mar Chatimah Tova.

Sunday, July 28, 2002

Sunday July 28, 2002

Filed under: General — 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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