Log24

Mathematics and Religion, continued–

Calvin Jongsma, review of an anthology titled Mathematics and the Divine–

"Believers of many faiths have found significant points of contact between their religious outlooks and mathematics. Not all of these claims were made in the distant past or by certified crackpots…."

Edward Nelson in "Warning Signs of a Possible Collapse of Contemporary Mathematics"–

"The most impressive feature of Cantor’s theory is that he showed that there are different sizes of infinity, by his famous diagonal argument. But Russell applied this argument to establish his paradox: the set of all sets that are not elements of themselves both is and is not an element of itself."

Jongsma's assertion appears to be true. Nelson's appears to be false. Discuss.

Remarks:

Saying that someone applied some argument– any argument will do here– to establish a paradox– any paradox will do here– casts into doubt the validity of either the argument, the application of the argument, or both. In the Cantor-Russell case, such doubt is unnecessary, since the paradox is clearly independent of the diagonal argument. There is certainly an historical connection between Cantor's argument and Russell's paradox– see, for instance, Wikipedia on the latter. The historical connection is, however, not a logical connection.

For Russell discovering his paradox without the use of Cantor's diagonal argument, see Logicomix–

Click for some context.

Argument for the Existence of Rebecca

Adapted from YouTube's "Mathematics and Religion," starring Rebecca Newberger Goldstein, author of the recent novel 36 Arguments for the Existence of God–

The added Quaternion  picture is from
Groundhog Day, 2009.

The Plane of Time

From tomorrow's NY Times Book Review, Geoff Dyer's review of DeLillo's new novel Point Omega is now online–

"The book begins and ends with Douglas Gordon’s film project '24 Hour Psycho' (installed at the Museum of Modern Art in Manhattan in 2006), in which the 109-­minute Hitchcock original is slowed so that it takes a full day and night to twitch by. DeLillo conveys with haunting lucidity the uncanny beauty of 'the actor’s eyes in slow transit across his bony sockets,' 'Janet Leigh in the detailed process of not knowing what is about to happen to her.' Of course, DeLillo being DeLillo, it’s the deeper implications of the piece— what it reveals about the nature of film, perception and time— that detain him. As an unidentified spectator, DeLillo is mesmerized by the 'radically altered plane of time': 'The less there was to see, the harder he looked, the more he saw.'

This prologue and epilogue make up a phenomenological essay on one of the rare artworks of recent times to merit the prefix 'conceptual.'"

Related material:

Steering a Space-Plane
(February 2, 2003)

Holly Day
(February 3, 2010)

Attitude Adjustment
(February 3, 2010)

Cover illustration by Stephen Savage,
NY Times Book Review,
Feb. 2 (Candlemas), 2003

“We live the time that a match flickers.”

– Robert Louis Stevenson, Aes Triplex

Today's New York Times on a current theatrical presentation of The Great Gatsby–

"Throughout the show, the relationship between what is read and its context keeps shifting, with the real world finally giving way entirely to the fictive one."

Owl Eyes in The Great Gatsby–

"This fella's a regular Belasco."

David Brown, producer. Brown died on Monday.

From The Diamond as Big as the Monster in this journal on Dec. 21, 2005–

"At the still point, there the dance is.” –T. S. Eliot, Four Quartets

Eliot was quoted in the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron, published when Cameron was at Merton College, Oxford.

“As Gatsby closed the door of ‘the Merton College Library’ I could have sworn I heard the owl-eyed man break into ghostly laughter.” –F. Scott Fitzgerald

Related material: Yesterday's posts and the jewel in Venn's lotus.

Where Three Worlds Meet

From an obituary for David Brown, who died at 93 on Monday–

"David Brown was a force in the entertainment, literary and journalism worlds," Frank A. Bennack, Jr., vice chairman and chief executive officer of Hearst Corporation, said in a statement Tuesday. –Polly Anderson of the Associated Press

Mark Kramer, "Breakable Rules for Literary Journalists," Section 8–

"Readers are likely to care about how a situation came about and what happens next when they are experiencing it with the characters. Successful literary journalists never forget to be entertaining. The graver the writer's intentions, and the more earnest and crucial the message or analysis behind the story, the more readers ought to be kept engaged. Style and structure knit story and idea alluringly.

If the author does all this storytelling and digressing and industrious structure-building adroitly, readers come to feel they are heading somewhere with purpose, that the job of reading has a worthy destination. The sorts of somewheres that literary journalists reach tend to marry eternal meanings and everyday scenes. Richard Preston's 'The Mountains of Pi,' for instance, links the awkward daily lives of two shy Russian emigre mathematicians to their obscure intergalactic search for hints of underlying order in a chaotic universe."

Hints:

“Logic is all about the entertaining of possibilities.”

– Colin McGinn, Mindsight: Image, Dream, Meaning, Harvard U. Press, 2004

"According to the Buddha, scholars speak in sixteen ways of the state of the soul after death…. While I hesitate to disagree with the Compassionate One, I think there are more than sixteen possibilities described here…."

– Peter J. Cameron today

"That's entertainment!"

– Jack Haley Jr.

From Peter J. Cameron's weblog today–

According to the Buddha,

Scholars speak in sixteen ways of the state of the soul after death. They say that it has form or is formless; has and has not form, or neither has nor has not form; it is finite or infinite; or both or neither; it has one mode of consciousness or several; has limited consciousness or infinite; is happy or miserable; or both or neither.

He does go on to say that such speculation is unprofitable; but bear with me for a moment.

With logical constructs such as “has and has not form, or neither has nor has not form”, it is perhaps a little difficult to see what is going on. But, while I hesitate to disagree with the Compassionate One, I think there are more than sixteen possibilities described here: how many?

Cameron's own answer (from problem solutions for his book Combinatorics)–

One could argue here that the numbers of choices should be multiplied, not added; there are 4 choices for form, 4 for finiteness, 2 for modes of consciousness, 2 for finiteness of consciousness, and 4 for happiness, total 2⁸ = 256. (You may wish to consider whether all 256 are really possible.)

Related material– "What is 256 about?"

Some partial answers–

April 2, 2003 — The Question (lottery number)

May 2, 2003 — Zen and Language Games (page number)

August 4, 2003 — Venn's Trinity (power of two)

September 28, 2005 — Mathematical Narrative (page number)

October 26, 2005 — Human Conflict Number Five (chronomancy)

June 23, 2006 — Binary Geometry (power of two)

July 23, 2006 — Partitions (power of two)

October 3, 2006 — Hard Lessons (number of pages,
                                 as counted in one review)

October 10, 2006 — Mate (lottery number)

October 8, 2008 — Serious Numbers (page number)

Quoted here Nov. 10, 2009–

Epigraphs at
Peter Cameron’s home page:

Happy birthday, Russell Hoban.

"A generation lost in space"
– American Pie

Sperry F3 attitude gyroscope

Click image for details.

See also the concepts of inner-direction
and other-direction in The Lonely Crowd
by David Riesman et al.  Riesman was,
according to Harvard Square Library,
a contract termination lawyer for
Sperry Gyroscope before turning
to sociology.

EXERCISE — Discuss inner- and
other-direction in education and
in journalism, using the material
in Monday's entry on the
New York Times dunce cap –

  — contrasted with the webpage
excerpted below –

Today's word:

fermata

"February made me shiver…."
– American Pie

Godmother and Cinderella

Meryl Streep and Amy Adams in "Julie & Julia"

The image is from gossipsauce.com on August 2, 2009.

For a darker Godmother/Cinderella pair,
see the film discussed in this journal
on that same date (Lughnasa 2009).

A thought from Pynchon's Against the Day quoted here on Groundhog Day a year ago today–

“We thus enter the whirlwind. It becomes the very essence of a refashioned life, providing the axes to which everything will be referred. Time no long ‘passes,’ with a linear velocity, but ‘returns,’ with an angular one…. We are returned to ourselves eternally, or, if you like, timelessly.”

“Born again!” exclaimed a Christer in the gathering, as if suddenly enlightened.

From "Time's Breakdown," September 17, 2003–

This flashback was suggested by

1. A review in next Sunday's New York Times Book Review of a new novel, Point Omega, by Don DeLillo. The review's title (for which the reviewer, Geoff Dyer, should not be blamed) is "A Wrinkle in Time." The review and the book are indeed concerned with time, but the only apparent connection to the 1962 novel of Madeleine L'Engle also titled A Wrinkle in Time is rather indirect– via the Walsh functions mentioned above.
2. A phrase in the Times's review, "frame by frame," also appeared in this jounal on Saturday. It formed part of the title of a current exhibition at Harvard's Carpenter Center for the Visual Arts.
3. The Carpenter Center exhibition will have an opening reception on February 4.
4. February 4 is also the birthday of the above Russell Hoban, who will turn 85. See a British web page devoted to that event.

DeLillo is a major novelist, but the work of Hoban seems more relevant to the phrase "frame by frame."

"But wait, there's more!"
– Stanley Fish, NY Times Jan. 28

From the editors at The New York Times who, left to their own devices, would produce yet another generation of leftist morons who don't know the difference between education and entertainment–

A new Times column starts today–

The quality of the column's logo speaks for itself. It pictures a cone with dashed lines indicating height and base radius, but unlabeled except for a large italic x to the right of the cone. This enigmatic variable may indicate the cone's height or slant height– or, possibly, its surface area or volume.

Instead of the column's opening load of crap about numbers and Sesame Street, a discussion of its logo might be helpful.

The cone plays a major role in the historical development of mathematics.

Some background from an online edition of Euclid–

"Euclid proved in proposition XII.10 that the cone with the same base and height as a cylinder was one third of the cylinder, but he could not find the ratio of a sphere to the circumscribed cylinder. In the century after Euclid, Archimedes solved this problem as well as the much more difficult problem of the surface area of a sphere."

For Archimedes and the surface area of a sphere, see (for instance) a discussion by Kevin Brown. For more material on Archimedes, see "Archimedes: Volume of a Sphere," by Doug Faires (2001)– Archimedes' heuristic argument from mechanics that involves the volume of a cone– and Archimedes' more rigorous approach in The Works of Archimedes, edited by T. L. Heath (1897).

The work of Euclid and Archimedes on volumes was, of course, long before the discovery of calculus.  For a helpful discussion of cone volumes involving high-school-level calculus, see, for instance,  the following–

The Times editors apparently feel that
few of their readers are capable of
such high-school-level sophistication.

For some other geometric illustrations
perhaps more appealing than the Times's

dunce cap, see the symbol of
  today's saint– a Bridget Cross–
and a web page on
visualized quaternions.

From The New York Times –

4^TH NIGHT FREE

From this journal –

Sunday, November 5, 2006

Sybil on the Beach

"I was waiting for you," said the young man. "What's new?"

"What?" said Sybil.

"What's new? What's on the program?"

"Animation tends to be a condensed art form, using metamorphosis and metaphor to collide and expand meaning. In this way it resembles poetry."

– Harvard's Carpenter Center for the Visual Arts,
   description of an exhibition–

FRAME BY FRAME: ANIMATED AT HARVARD

January 28–Feb 14, 2010

For example–

Animation – The Animated Diamond Theorem,
                      now shown frame by frame for selected frames

Poetry–

Part I –  "That Nature is a Heraclitean Fire…."

Part II – Metaphor on the covers of a Salinger book–

Click image for details.

For other thoughts on
metamorphosis and metaphor,
see Endgame.

Part I:

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.' She shows deftly and delicately that the void inside Keats’s urn, Heidegger’s jug, or Wallace Stevens’s jar forms the center around which we tend to organize our worlds."

– Harvard University Press on Persons and Things (April 30, 2008), by Barbara Johnson

Part II:

"Did you see more glass?"

Part III:

From the date of Barbara Johnson's death:

"Mathematical relationships were
enough to satisfy him, mere formal
relationships which existed at
all times, everywhere, at once."

– Broken Symmetries, 1983

The X's refer to the pattern on the
cover of a paperback edition
  of Nine Stories, by J. D. Salinger.
Salinger died on Wednesday.

"You remember that book he sent me
from Germany? You know–
those German poems."

In Germany, Wednesday was
Holocaust Memorial Day, 2010.

Home Delivery

"But wait, there's more!"
– Stanley Fish, NY Times today

For a larger image, click on The Catcher.

"Anyway, I keep picturing all these little kids playing some game in this big field of rye and all.  Thousands of little kids, and nobody's around– nobody big, I mean– except me.  And I'm standing on the edge of some crazy cliff.  What I have to do, I have to catch everybody if they start to go over the cliff– I mean if they're running and they don't look where they're going I have to come out from somewhere and catch them.  That's all I'd do all day.  I'd just be the catcher in the rye and all.  I know it's crazy, but that's the only thing I'd really like to be."

– J.D. Salinger, The Catcher in the Rye, Chapter 22

This journal on Aug. 17, 2008:

That post linked to an earlier post illustrating
the triangle formed by Harvard, by the
Mystic River at Somerville, and
by Bunker Hill Community College–

That post also linked to the Wikipedia article
Triangulation, which now states that
"Some members of the U.S. Democratic
Party, in particular the left, insist that
triangulation is 'dead.'"

Perhaps. Click the image below
for some background.

For a view of Somerville from Harvard for Zinn,
see May 31, 2006. For a view of Summertime
for Auchincloss, see the NY Times obituary
of a political figure who died on Sunday.

On that day, this journal pictured a different
 metaphor from Robert Stone's Father Egan–
the jewel in the lotus–

Euclid's classic construction
of the equilateral triangle
offers a different view of
the jewel in Venn's lotus–

For a more poetic approach to
this metaphor, see Log24 on
another Sunday– July 1, 2007.

Happy birthday, Rick Warren.

Yesterday's post may, if one likes, be regarded
  as a nod to Dionysus, god of tragedy.

Here is a complementary passage:

Related material:
Jung and the Imago Dei

From this journal:

Transition to the
Garden of Forking Paths–

(See For Baron Samedi)–

The Found Symbol

and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–

Pages 354-355
On the mirror-play of the fourfold

Pages 356-357
Shaking up a whole culture

Pages 358-359
Cornerstone and crossroads

Pages 360-361
A deep impression embedded in stone

Pages 362-363
A certain Y, a certain V

Pages 364-365
The world is Zeus's play

Page 366
It was necessary to begin again

Recent Log24 entries on Hamlet suggest a look at Giorgio de Santillana's Hamlet's Mill on the Web.

There is a useful transcription by Clifford Stetner. See also an excellent review of Hamlet's Mill by Cecilia Payne-Gaposchkin.

The work of Giorgio de Santillana (like that of Stetner) suggests in turn the following recently quoted advice–

"…you should read Middlemarch every five years or so. Every time… it's a different book, and an even more powerful one."

– Robert Weisbuch, quoted at Critical Mass on Jan. 23.

Related material: Mr. Casaubon and the Key to All Mythologies.

For a simpler key, see On Linguistic Creation.

Sting as Hamlet

Detail, cover of Synchronicity album, 1983

Further details of the text on the album cover–

More Than Matter

"In one or other of G. F. H. Shadbold's two published notebooks, Beyond Narcissus and Reticences of Thersites, a short entry appears as to the likelihood of Ophelia's enigmatic cry: 'Oh, how the wheel becomes it!' referring to the chorus or burden 'a-down, a-down' in the ballad quoted by her a moment before, the aptness she sees in the refrain."

– First words of Anthony Powell's novel "O, How the Wheel Becomes It!" (See Library Thing.)

Related material:

Photo uploaded on January 14, 2009
with caption "This nothing's more than matter"

and the following nothings from this journal
on the same date– Jan. 14, 2009–

Continued from yesterday
and from March 28, 2008–

Being and Nothingness

Jean Simmons and Laurence Olivier, 1948

"Ophelia’s story becomes the Story of O…."
– Elaine Showalter, "Representing Ophelia:
Women, Madness, and the
Responsibilities of Feminist Criticism."
Pp. 220-238 in
Hamlet. Ed. Susanne L. Wofford.
Boston: Bedford Books, 1994.

Yesterday's Times –

Today's Times –

   Annals of Deconstruction –

Click on image for background.

Related material
   for Baron Samedi –

The Found Symbol

"…something is rotten in Denmark. And nothing I have read in the news headlines is going to solve it.

Rant over.

Back to our regular programming."

– A Circle of Quiet today

Our regular programming:

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 –

Click to enlarge.

Church Emblem

Related material:

Faust in Copenhagen,
Meta Physics,
and yesterday's entry.

A NY Times review dated Jan. 20 has the headline

Trying to Paint the Deity by Numbers
Against a Backdrop of Jewish Culture

By JANET MASLIN

"…this novel’s bracing intellectual energy never flags. Though it is finally more a work of showmanship than scholarship, it affirms Ms. Goldstein’s position as a satirist…."

The title of the book under review is
36 Arguments for the
Existence of God: A Work of Fiction.

Related "by the numbers" material–

From the I Ching, commentaries on the lines of Hexagram 36–

"Here the Lord of Light is in a subordinate place and is wounded by the Lord of Darkness…."

"The dark power at first held so high a place that it could wound all who were on the side of good and of the light. But in the end it perishes of its own darkness, for evil must itself fall at the very moment when it has wholly overcome the good, and thus consumed the energy to which it owed its duration."

The Times review of 36 Arguments notes that the book's chapters of fiction number 36, as do the 36 philosophical arguments in the book's title and appendix.

The reviewer– "So much for structure. It is not Ms. Goldstein’s strong suit…."

Some structure related to the above occurrence of 36 in the I Ching–

Another example of eightfold symmetry:

The Large Hadron Collider

See also Angels & Demons in
Hollywood and in this journal.

"I need a man who knows
how the story goes."
– Shania Twain

"The causal story is that a crippled epistemology leads to fanaticism, which then leads to the urge for governmental control…

It is only through gaining control of a state in the modern era that a fanatical group could expect to exclude contrary views and thereby maintain the crippled epistemology of their followers. With the power of a state behind them, they can coerce."

– P. 18 in Russell Hardin, "The Crippled Epistemology of Extremism" (Pp. 3-22 in Political Rationality and Extremism, Albert Breton et al., eds., Cambridge University Press, 2002).

This is the source of more recent uses of the phrase "crippled epistemology."

Cognitive Infiltration

"Conspiracy theorists are not likely to be persuaded by an attempt to dispel their theories; they may even characterize that very attempt as further proof of the conspiracy. Because those who hold conspiracy theories typically suffer from a crippled epistemology, in accordance with which it is rational to hold such theories, the best response consists in cognitive infiltration of extremist groups."

– Cass R. Sunstein, Harvard Law professor,
abstract of "Conspiracy Theories," Jan. 15, 2008

Critical Mass Monday, Jan. 18, 2010, 7:06  AM–

Here you've got three high-powered academics… all engaged in highly pernicious and mutually enabling forms of professional dishonesty. Sunstein comes up [with] what Timothy Burke calls a "consensus-politics liberal-leaning version of COINTELPRO," — Erin O'Connor

Critical Mass? Campaigns Work to Get Voters to Polls

– Washington Wire:
Political Insight and Analysis from
The Wall Street Journal Capital Bureau
January 19, 2010, 11:17 AM ET

David Weigel, "Attacks on Sunstein Frustrate Conservative Fans,"
The Washington Independent, 9/9/09–

"The campaign against Sunstein has largely written itself."

Two classics of politics–

1956– The Ninth Wave, by Eugene Burdick

2010– "Scott Brown" in Google's new "As It Happens" format

NY Times obituary of Knox Burger,
book editor and agent, who died at 87 on January 4–

"As a magazine editor in the 1950s, Knox Burger published Kurt Vonnegut’s first short story….

During Mr. Burger’s tenure at Collier’s, a short story by Vonnegut, whom he had known slightly when both were at Cornell and who was then working in public relations for General Electric, crossed his desk. He asked for changes, which Vonnegut made, and the story, 'Report on the Barnhouse Effect,' appeared in the magazine in February 1950. It was the first published work of fiction for Vonnegut, who recounted the episode decades later….

At least half a dozen authors… honored Mr. Burger by dedicating books to him. Vonnegut, who died in 2007, did, too. His dedication of Welcome to the Monkey House, a 1968 collection of short stories that included 'Report on the Barnhouse Effect,' read:

'To Knox Burger. Ten days older than I am. He has been a very good father to me.'"

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.

Robert Stone in A Flag for Sunrise
(Knopf hardcover, 1981)–

"The eye you see him with is the same eye with which he sees you."

– Father Egan on page 333

Pablo on page 425–

"'…You know, he told me– that old man told me– the eye you look at it with, well, that's the eye it sees you with. That's what he told me.'

Holliwell was moved to recall an experiment he had once read about; he had clipped the report of it for his class. An experimenter endeavoring to observe chimpanzee behavior had fashioned a spy hole in the door of the animals' chamber through which he might watch them unobserved. Putting his eye to it, he had seen nothing more than what he finally identified as the eye of a chimpanzee on the other side of the door. Ape stuff."

More ape stuff from a Jesuit–

"This Jack, joke, poor potsherd, patch, matchwood, immortal diamond,
                Is immortal diamond."

– Gerard Manley Hopkins,
"That Nature is a Heraclitean Fire
and of the comfort of the Resurrection"

More ape stuff from myself–

Problem: Perform this transformation
by combining the sorts of permutations allowed
in the diamond puzzle. A solution: click here.

American Literary Historical Society

Robert Redford and Brad Pitt
in "Spy Game" (2001)

James Dean in LIFE, 1955.

Photo by Dennis Stock,
who died on Monday.

"The eye you see him with
is the same eye
with which he sees you."

– Father Egan on page 333
of the classic novel
A Flag for Sunrise
(Knopf hardcover, 1981)

In Julie Taymor's film version of "The Tempest" (now in post-production), Helen Mirren, in a gender switch, plays "Prospera."

See a recent interview, "Helen Mirren Talks About Playing Prospera in The Tempest" (ScreenCrave.com, Friday, January 8, 2010, 4:50 PM, By Mali Elfman)—

"With Prospero you can change it into a woman without changing much of the text, very little of the text has changed, only at the very beginning— the backstory. In fact, one of the most famous of Prospero’s speeches, it’s an invocation— brilliant, fabulous speech— is actually from 'Medea,' almost lifted lock, stock, and barrel from the play 'Medea' and it’s Medea’s speech and Shakespeare just took it. It’s incredible. Like three words have changed. So it’s actually a woman’s speech."

It's actually not from "Medea" (the play by Euripides), but rather from the version of Medea in Ovid's Metamorphoses, Book 7.

Related material: Blurring the Lines and Mutatis Mutandis.

See also Tuesday's entry on Taymor and theatre.

Death and the Apple Tree
continued from January 4

– "Araby," by James Joyce.
 Joyce died on this date in 1941.

New York Times, January 12, 2010, 12:26 PM–

"Spider-Man" Musical Will Refund Tickets

"With… direction by Julie Taymor ['Frida'], 'Spider-Man' has been marred by delays….

The musical’s troubles have unfolded at the same time that the next “Spider-Man” movie has been descending into disarray…."

Related material:

"No Great Magic," by Fritz Leiber–

"The white cosmetic came away, showing sallow skin and on it a faint tattoo in the form of an 'S' styled like a yin-yang symbol left a little open.

'Snake!' he hissed. 'Destroyer! The arch-enemy, the eternal opponent!'"

“Ay que bonito es volar  
    A las dos de la mañana….”
— “La Bruja“

Robert Redford in "Spy Game."
This 2001 film premiered
on AMC TV last night.

Motto of the British
information technology (IT)
journal The Register –

"Biting the hand that feeds IT."

An illustration:

Click for further details.

Related material:

Christ in the Aberdeen Bestiary

For those who prefer
the Harvard Psychedelic Club to
the Harvard Alcoholic Club
(see The Nexus) –

Nicolas Cage leaving the 
church of The Rock –

Related material:

A sermon for the father of Kal-El.
See also related material in this journal
on Vegas and on Maniacs.

Rock's top 40 on Jan. 9, 1982

"The positional meaning of a symbol derives from its relationship to other symbols in a totality, a Gestalt, whose elements acquire their significance from the system as a whole."

– Victor Turner, The Forest of Symbols, Ithaca, NY, Cornell University Press, 1967, p. 51, quoted by Beth Barrie in "Victor Turner."

To everything, turn, turn, turn…
– Peter Seeger

The Galois Quaternion:

Click for context.

Part I:

Last night's post for the birthday of
Nicolas Cage, which linked to a
description of his upcoming film–

Nicolas Cage as Balthazar Blake

Part II:

From this morning's comics:

Balthasar Meets Blake

Happy birthday, Nicolas Cage.

The Difference

There is a small but important difference
between "No One" and "No. One."

Images from a website in this journal
on June 10, 2009:
 

That website's author died this afternoon.

For related symbols, see the five Log24 entries
ending on June 10, 2009.

Note the resemblance of the following work
pictured here on that date

to the 1958 painting "No. One,"
by the late Kenneth Noland–

The Galois Quaternion

Related material:
The Galois Quaternion

Click for context.
(See also Nativity and the end
of this morning's post.)

Nativity

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

– Rubén Darío

See also diadema and an obituary
for Noland, who died today.

A Medal

In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–

See also a rather different medal discussed
here in the context of an Orwellian headline from
The New York Times on Christmas morning,
the day before Sevcenko died.
That headline, at the top of the online front page,
was "Arthur Koestler, Man of Darkness."

The medal, offered as an example of brightness
to counteract the darkness of the Times, was designed
by Leibniz in honor of his discovery of binary arithmetic.
See Brightness at Noon and Brightness continued.

"By groping toward the light we are made to realize
how deep the darkness is around us."
– Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118

"There must be…
50 ways to leave Las Vegas."

– This journal on Dec. 19, 2009

The 10 —

A Fresh Start

Happy birthday,
Mel Gibson

AVATAR:
The Legend of Bhagavan

LIFE magazine photo, Jan. 1, 1947

Powell died on New Year's Eve– the day before yesterday. Yesterday's post was dedicated to Will Smith in his role as golf caddy Bagger Vance. In the novel from which the Smith film was taken, "Bagger Vance" is an anglicized form of the term "Bhagavan" from the Bhagavad Gita. In the Gita, "Bhagavan" refers to Krishna– an incarnation, or avatar, of the god Vishnu.

Let us hope that when, on the last day of the old year, Powell met the Reaper, he appeared as neither fearsome Krishna nor grim Oppenheimer, but rather as the kinder, gentler Bagger Vance.

See also "Bhagavad Gita" in this journal.

For Will Smith–

"How much for a dream?"

"Five dollars, guaranteed."

Genesis 3:24–
So he drove out the man; and he placed
at the east of the garden of Eden Cherubims,
and a flaming sword which turned every way,
to keep the way of the tree of life.

Carlene Hatcher Polite–
"Shall I help you?" asked a bass voice.
"If you can," answered a contralto.
"Trace down this tree. Let me show you
men in its stead. Leaf through this bush,
extinguish the burning fire…"
– The Flagellants, page 8

"How much story do you want?"
– George Balanchine

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

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:

See also the page linked to on
Becket’s Day last year,
as well as…

This journal’s Christmas Day entry, Brightness at Noon, was in response to the Orwellian headline “Arthur Koestler, Man of Darkness,” at the top of the online New York Times front page on Christmas morning.

The entry offered, as an example of brightness, some thoughts of Leibniz on his discovery of binary arithmetic.

Related material:

From Mikhail Krawtchouk: Short Biography–

Anyone knowing even a little Soviet history of the thirties can conclude that Krawtchouk could not avoid the Great Terror. During the Orwellian “hours of hatred” in 1937 he was denounced as a “Polish spy,” “bourgeois nationalist,” etc. In 1938, he was arrested and sentenced to 20 years of confinement and 5 years of exile.

Academician Krawtchouk, the author of results which became part of the world’s mathematical knowledge, outstanding lecturer, member of the French, German, and other mathematical societies, died on March 9, 1942, in Kolyma branch of the GULAG (North-Eastern Siberia) more than 6 months short of his 50th birthday.

Incidentally, happy birthday
to John von Neumann.

Towards a Philosophy of Real Mathematics, by David Corfield, Cambridge U. Press, 2003, p. 206:

“Now, it is no easy business defining what one means by the term conceptual…. I think we can say that the conceptual is usually expressible in terms of broad principles. A nice example of this comes in the form of harmonic analysis, which is based on the idea, whose scope has been shown by George Mackey (1992) to be immense, that many kinds of entity become easier to handle by decomposing them into components belonging to spaces invariant under specified symmetries.”

For a simpler example of this idea, see the entities in The Diamond Theorem, the decomposition in A Four-Color Theorem, and the space in Geometry of the 4×4 Square.  The decomposition differs from that of harmonic analysis, although the subspaces involved in the diamond theorem are isomorphic to Walsh functions– well-known as discrete analogues of the trigonometric functions of traditional harmonic analysis.