Cut to the Chase.

Leg-Pulling

"… to make the author manifestly unreliable"

Not to mention the reader.

Related material —

But seriously…

From Chomsky's remarks in The New York Times  today —

"It is at once comic and tragic, as Borges might have noted,
that so much money and attention should be concentrated
on so little a thing — something so trivial when contrasted
with the human mind, which by dint of language, in the
words of Wilhelm von Humboldt, can make 'infinite use of
finite means,' creating ideas and theories with universal reach."

A search in this  journal for Humboldt University  yields . . .

"Cum grano salis" — Boris Karloff in "The Black Cat."

The above reading was suggested by a post of
New Year's Day, Jan. 1, 2013 — The Simplest Situation.

See also Ahem (Sunday morning, Dec. 10, 2017).

From Models and Metaphors , by Max Black,
Cornell University Press, 1962 —

I do not recommend the work of Lewin, nor that of a later
science groupie, Keith Devlin. 

In September 2014, Devlin wrote an ignorant column about
a sort of bad mathematical joke based on a divergent infinite series.

He has now returned to the topic, this time writing more about
its proper mathematical background: analytic continuation .

Lewin is to Devlin as Lévi-Strauss is to Chomsky.
None of these four should be taken very seriously.

Max Black, however, should .

A prequel to the 2013 film "The Zero Theorem" —

"Down below, infinitely deep into the blackness,
things were beginning. The blackness had
arranged itself into a whirlpool…."

— Peter Dickinson, A Box of Nothing  (1985),
    "Chapter 19: Star Tree"

— may serve as a sequel to the life of the book's author.

(See Dickinson Sequel in this journal.)

"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.

Review —

From a Jan. 20, 2011, Emory University press release —
"Finite formula found for partition numbers" —

"We found a function, that we call P, that is like
a magical oracle," Ono says. "I can take any number,
plug it into P, and instantly calculate the partitions
of that number. P does not return gruesome numbers
with infinitely many decimal places. It's the finite,
algebraic formula that we have all been looking for."

Some may prefer Chinese  oracles.

(Continued)

Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012—

"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'

The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"

The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."

These same words in a different tongue—  "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)

"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."

— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization , Pantheon
Books, 1946, page 142 

Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.

For those who prefer fiction:

"Many Dimensions  (1931) — An evil antiquarian illegally purchases
the fabled Stone of Suleiman (Williams uses this Muslim form
rather than the more familiar King Solomon) from its Islamic guardian
in Baghdad and returns to England to discover not only that the Stone
can multiply itself infinitely without diminishing the original, but that it
also allows its possessor to transcend the barriers of space and time."

— Wikipedia article on the author Charles Williams

From a film released Friday, April 13th, 2012—

"Time for you to see the field." — Bagger Vance, as quoted here yesterday.

* Title courtesy of David Foster Wallace.

From The Guardian 

On All Hallows' Eve —

The reported last words of
Apple founder Steve Jobs were
"Oh wow. Oh wow. Oh wow."

In the spirit of these words, a
Google search from today—

See also…

1. Lemniscate in this journal as well as
2. Stone Junction  and
3. Infinite Jest .

Review of DeLillo's novel Point Omega—

"One difference between art and entertainment has to do with the speed of perception. Art deliberately slows and complicates reading, hearing, and/or viewing so that you’re challenged to re-think and re-feel form and experience. Entertainment deliberately accelerates and simplifies them so that you don’t have to think about or feel very much of anything at all except, perhaps, the adrenalin rush before dazzling spectacle. Although, of course, there can be myriad gradations between the former and latter, in their starkest articulation we’re talking about the distance between, say, David Foster Wallace’s Infinite Jest  and Dan Brown’s The Lost Symbol…."

— Lance Olsen, March 1, 2010, in The Quarterly Conversation

Robert Hughes on fast and slow art—

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

– Speech of June 1, 2004

Log24 on art speeds—

A Study in Art Education (June 15, 2007)

Twenty-four (March 13, 2011)

Ben Brantley in The New York Times  on May 26—

While you theatergoing butterflies out there keep nattering on about the Tonys— who will win, who should win, and so on— I have been focused on an issue of far greater momentousness and urgency. That’s the shameful squandering on Broadway of what our country would seem to believe is our most valued (and infinitely exploitable) natural resource: our celebrities….

Lindsay Lohan: This undeniably talented (and for all intents and purposes, former) film actress poses a special challenge. Her only recent work appears to have been as a paparazzi model and professional partygoer, and a big, line-laden dramatic part like Blanche DuBois might be too onerous to start with. So why not put her in the Broadway premiere of “Finishing the Picture,” a late-career Arthur Miller play inspired by the travails of making a movie (“The Misfits”) with his wife Marilyn Monroe? Having seen a production of this play in Chicago, I can testify that the Marilyn part requires only that the actress playing her be willing to appear asleep and stupefied and, briefly, to walk across the stage naked. For Ms. Lohan, who credibly impersonated Marilyn for a New York magazine photo shoot, this ought to be a cinch. Should an eight-performance week prove too taxing, I suggest Paris Hilton for matinees.

This midnight post was suggested by Sunday's midday 4-digit NY Lottery number, 7286, and by the following web pages:

7286 Style by Lindsay Lohan and 7286 Prisoner Transport.

Some background from a third 7286 web page—

Starlet Lindsay Lohan is bringing her signature Hollywood style to the masses with her new 7286 line. The starlet's stylish stamp is on every aspect of the line, from the name (7-2-86 is her birthday) to the brand's tag line : "Give a girl the right handbag, and she can conquer the world!"

A Meditation on the NY Lottery of May 29

Yesterday's NY Lottery— Midday 981, Evening 275.

As noted in yesterday  morning's linked-to post,
The Shining of May 29…

"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

One interpretation of the mystic numbers revealed by the Lottery yesterday—

981 as the final page* of David Foster Wallace's famed novel Infinite Jest …

275 as a page in Wallace's non-fiction book about infinity Everything and More …

  Gregory Chaitin points out that this is nonsense …

As noted elsewhere in this journal, I have a different concept of "math's absolute
Prince of Darkness"— and, indeed, of a "quest for Omega." (See posts of May 2010.)

Yesterday's numbers indicate a different struggle between darkness and light—

Light —

Darkness —

* From infinitesummer.org/archives/168 — "A note about editions:
As it turns out, all (physical) editions of Infinite  Jest  have 981 pages:
the one from 1996, the one from 2004, the paperback, the hardcover, etc.
A big thank you to the men and women in the publishing industry who
were kind and/or lazy enough to keep things consistent."

Heisenberg on Heraclitus

From Physics and Philosophy , by Werner Heisenberg, 1958, reprinted by Penguin Classics, 2003—

Page 28—

… In the philosophy of Heraclitus of Ephesus the concept of Becoming occupies the foremost
place. He regarded that which moves, the fire, as the basic element. The difficulty, to reconcile
the idea of one fundamental principle with the infinite variety of phenomena, is solved for him by
recognizing that the strife of the opposites is really a kind of harmony. For Heraclitus the world is
at once one and many, it is just 'the opposite tension' of the opposites that constitutes the unity
of the One. He says: 'We must know that war is common to all and strife is justice, and that all
things come into being and pass away through strife.'

Looking back to the development of Greek philosophy up to this point one realizes that it has
been borne from the beginning to this

Page 29—

stage by the tension between the One and the Many. For our senses the world consists of an
infinite variety of things and events, colors and sounds. But in order to understand it we have to
introduce some kind of order, and order means to recognize what is equal, it means some sort
of unity. From this springs the belief that there is one fundamental principle, and at the same
time the difficulty to derive from it the infinite variety of things. That there should be a material
cause for all things was a natural starting point since the world consists of matter. But when one
carried the idea of fundamental unity to the extreme one came to that infinite and eternal
undifferentiated Being which, whether material or not, cannot in itself explain the infinite variety
of things. This leads to the antithesis of Being and Becoming and finally to the solution of
Heraclitus, that the change itself is the fundamental principle; the 'imperishable change, that
renovates the world,' as the poets have called it. But the change in itself is not a material cause
and therefore is represented in the philosophy of Heraclitus by the fire as the basic element,
which is both matter and a moving force.

We may remark at this point that modern physics is in some way extremely near to the
doctrines of Heraclitus. If we replace the word 'fire' by the word 'energy' we can almost repeat
his statements word for word from our modern point of view. Energy is in fact the substance
from which all elementary particles, all atoms and therefore all things are made, and energy is
that which moves. Energy is a substance, since its total amount does not change, and the
elementary particles can actually be made from this substance as is seen in many experiments on
the creation of elementary particles. Energy can be changed into motion, into heat, into light
and into tension. Energy may be called the fundamental cause for all change in the world. But this
comparison of Greek philosophy with the ideas of modern science will be discussed later.

* See earlier uses of the phrase in this journal. Further background— Hopkins and Heraclitus.

Literary remarks for Maundy Thursday—

      — C. P. Snow, foreword to G. H. Hardy's A Mathematician's Apology

Related material—

Emory University press release of January 20th, 2011:

"In 1937, Hans Rademacher found an exact formula for calculating partition values. While the method was a big improvement over Euler's exact formula, it required adding together infinitely many numbers that have infinitely many decimal places. 'These numbers are gruesome,' Ono says….

… The final eureka moment occurred near another Georgia landmark: Spaghetti Junction. Ono and Jan Bruinier were stuck in traffic near the notorious Atlanta interchange. While chatting in the car, they hit upon a way to overcome the infinite complexity of Rademacher's method. They went on to prove a formula that requires only finitely many simple numbers.

'We found a function, that we call P, that is like a magical oracle,' Ono says. 'I can take any number, plug it into P, and instantly calculate the partitions of that number….'"

See also this journal on April 15 and a Google Groups [sage-devel] thread, Ono-Bruinier partition formula. That thread started on April 15 and was last updated this morning.

Where Entertainment Is God  continues...

New York Lottery today— Midday 710, Evening 563.

This suggeests a scientific note from the date 7/10  (2009) and the page number 563 from Dec. 29—

Bulletin of the American Mathematical Society , October 2002, p. 563:

“To produce decorations for their weaving, pottery, and other objects, early artists experimented with symmetries and repeating patterns.  Later the study of symmetries of patterns led to tilings, group theory, crystallography, finite geometries, and in modern times to security codes and digital picture compactifications.  Early artists also explored various methods of representing existing objects and living things.  These explorations led to… [among other things] computer-generated movies (for example, Toy Story ).”

– David W. Henderson, Cornell University

For a different perspective on Toy Story , see the Dec. 29 post.

Other entertainments — The novel Infinite Jest  and two versions of "Heeere's Johnny !" —

            From Stanley Kubrick and from today's New York Times :

See also All Things Shining  and the lottery theology of Jorge Luis Borges.

Significant Passage:
On the Writing Style of Visual Thinkers

"The words are filled with unstated meaning.
They are (the term is Ricoeur's) 'packed'
and need unpacking." —Gerald Grow

From the date of Ricoeur's death,
May 20, 2005—

“Plato’s most significant passage
    may be found in Phaedrus  265b…."

From Sept. 30, 2004—

Mozart's K 265 is variations on the theme
now known as "Twinkle, Twinkle, Little Star."

For darker variations on the Twinkle theme,
see the film "Joshua" and Martin Gardner's
Annotated Alice  (Norton, 2000, pp. 73-75).

Joshua

For darker variations on the asterisk theme,
see Darkness Visible (May 25)
and Vonnegut's Asterisk.

“Somehow it seems to fill my head with ideas– only I don’t exactly know what they are!…. Let’s have a look at the garden first!”

— A passage from Lewis Carroll’s Through the Looking-Glass. The “garden” part– but not the “ideas” part– was quoted by Jacques Derrida in Dissemination in the epigraph to Chapter 7, “The Time before First.”

“‘For you… he… we aren’t meaning…’ She was almost stammering, as if she were trying to say several things at once…. Suddenly she gave a little tortured scream. ‘O!’ she cried, ‘O! I can’t keep up! it keeps dividing! There’s too many things to think of!'”

— A passage from Charles Williams’s The Place of the Lion, Chapter 12.

“He was thinking faster than he had ever done, and questions rose out of nothing and followed each other– what was to will? Will was determination to choose– what was choice? How could there be choice, unless there was preference, and if there was preference there was no choice, for it was not possible to choose against that preferring nature which was his being; yet being consisted in choice, for only by taking and doing this and not that could being know itself, could it indeed be; to be then consisted in making an inevitable choice, and all that was left was to know the choice, yet even then was the chosen thing the same as the nature that chose, and if not… So swiftly the questions followed each other that he seemed to be standing in flashing coils of subtlety, an infinite ring of vivid intellect and more than intellect, for these questions were not of the mind alone but absorbed into themselves physical passion and twined through all his nature on an unceasing and serpentine journey.”

— A passage from The Place of the Lion, Chapter 10.

“Do you like apples?“

— Good Will Hunting

 Putting the
X
in Xmas

— C. S. Lewis

Apparently they teach them nihilism, empty rhetoric, and despair, as reflected in Borges, Baudrillard, and Benjamin, according to the art review below from today’s New York Times.  Let us hope that the late Peter Boyle, who died on Tuesday, Dec. 12, has moved beyond these now– singing “Heaven, I’m in Heaven,” rather than “Puttin’ on the Ritz.”

Black, White, and Read All Over by Randy Kennedy in The New York Times Friday, Dec. 15, 2006 “In one of Jorge Luis Borges’s best-known short stories, ‘Pierre Menard, Author of the Quixote,’ a 20th-century French writer sets out to compose a verbatim copy of Cervantes’s 17th-century masterpiece simply because he thinks he can, originality perhaps not being all it’s cracked up to be. He manages two chapters word for word, a spontaneous duplicate that Borges’s narrator finds to be ‘infinitely richer’ than the original because it contains all manner of new meanings and inflections, wrenched as it is from its proper time and context….” [An artist’s version of a newspaper is]…. “a drawing of a copy of a version of what happened, holding a mirror up to nature with a refraction or two in between.  In a way that mixes Borges with a dollop of Jean Baudrillard and a heavy helping of Walter Benjamin, the work also upends ideas….”

The Work:

Pennsylvania Lottery
December 2006
Daily Number (Day):

Click on numbers
for commentary.

“There is nothing new under the sun. With the death of the real, or rather with its (re)surrection, hyperreality both emerges and is already always reproducing itself.”  –Jean Baudrillard

Online New York Times today



“With a little effort,

— Opening sentence of
Martha Cooley’s The Archivist

“Frere Jacques, Cuernavaca,
ach du lieber August.”

— John O’Hara, Hope of Heaven, 1938

For Tom Stoppard on his birthday:

“For I remember when I began to read, and to take some pleasure in it, there was wont to lie in my mother’s parlour (I know not by what accident, for she herself never in her life read any book but of devotion), but there was wont to lie Spenser’s works; this I happened to fall upon, and was infinitely delighted with the stories of the knights, and giants, and monsters, and brave houses, which I found everywhere there (though my understanding had little to do with all this); and by degrees with the tinkling of the rhyme and dance of the numbers, so that I think I had read him all over before I was twelve years old, and was thus made a poet.”

— Abraham Cowley, Essays, 1668

Order and Ennui

Meanwhile, back at the Institute for Advanced Study:

May 25, 4:40 PM —
Research Seminar
(Simonyi Hall Seminar Room) —
Pirita Paajanen,
The Hebrew University of Jerusalem:
Zeta functions of
finitely generated infinite groups

Some background cited by Paajanen:

M.P.F. du Sautoy, “Zeta functions of groups: The quest for order versus the flight from ennui,” Groups St Andrews 2001 – in Oxford, Volume 1, CUP 2003.

Those who prefer the showbiz approach to mathematics (the flight from ennui?) may enjoy a website giving further background from du Sautoy.

From James A. Michener‘s The Source:

“Trouble started in a quarter that neither Uriel nor Zadok could have foreseen.  For many generations the wiser men of Zadok’s clan had worshipped El-Shaddai with the understanding that whereas Canaanites and Egyptians could see their gods directly, El-Shaddai was invisible and inhabited no specific place.  Unequivocally the Hebrew patriarchs had preached this concept and the sager men of the clans accepted it, but to the average Hebrew who was not a philosopher the theory of a god who lived nowhere, who did not even exist in corporeal form, was not easy to comprehend.  Such people were willing to agree with Zadok that their god did not live on this mountain– the one directly ahead– but they suspected that he did live on some mountain nearby, and when they said this they pictured an elderly man with a white beard who lived in a proper tent and whom they might one day see and touch.  If questioned, they would have said that they expected El-Shaddai to look much like their father Zadok, but with a longer beard, a stronger voice, and more penetrating eyes.

Now, as these simpler-minded Hebrews settled down outside the walls of Makor, they began to see Canaanite processions leave the main gate and climb the mountain to the north, seeking the high place where Baal lived, and they witnessed the joy which men experienced when visiting their god, and the Hebrews began in subtle ways and easy steps to evolve the idea that Baal, who obviously lived in a mountain, and El-Shaddai, who was reported to do so, must have much in common.  Furtively at first, and then openly, they began to climb the footpath to the place of Baal, where they found a monolith rising from the highest point of rock.  Here was a tangible thing they could comprehend, and after much searching along the face of the mountain, a group of Hebrew men found a straight rock of size equal to the one accorded Baal, and with much effort they dragged it one starless night to the mountain top, where they installed it not far from the home of Baal….”

Rabbi Chitrik died on
Valentine’s Day, 2006,
having had a heart attack
on Feb. 8, 2006–

Grammy Night.

The above monolith is perhaps more
closely related to El-Shaddai than to
Madonna, Grammy Night, and Baal.
It reflects my own interests
(Mathematics and Narrative)
and those of Martin Buber
(Jews on Fiction):
 

“Among Buber’s early philosophical influences were Kant’s Prolegomena, which he read at the age of fourteen, and Nietzsche’s Zarathustra.  Whereas Kant had a calming influence on the young mind troubled by the aporia of infinite versus finite time, Nietzsche’s doctrine of ‘the eternal recurrence of the same’ constituted a powerful negative seduction.  By the time Buber graduated from Gymnasium he felt he had overcome this seduction, but Nietzsche’s prophetic tone and aphoristic style are evident in Buber’s subsequent writings.”

— Plato.stanford.edu

Martin Buber

Rabbi Chitrik

From crankbuster, July 18:

“Do not underestimate Evil Cullinane’s plan for World Domination!  http://www.log24.com now shows that he has crossed over to the dark side, making sacrifices to the Ancient Hindu Goddess ‘Kalli’ to ward off our attacks!  ‘Kalli’-nane will soon appear as the top result on every Google search.

July 20 illustration of
crankbuster’s remarks

Soon, all young mathematicians will be hypnotised by his dark diamonds of falsehood.  At least, that’s his plan.  But wait, who’s that brilliant mathematician who shines the light right through Cullinane’s fraud and exposes him to the whole world?!  Crankbuster saves the day! (applause)”

From Log24, July 18:

“In Hindu mythology, Kali, the Divine Mother, is the symbol for the infinite diversity of experience.  Kali represents the entire physical plane.  She is the drama, tragedy, humor, and sorrow of life.  She is the brother, father, sister, mother, lover, and friend.  She is the fiend, monster, beast, and brute.”

Dance

Yesterday’s AP “Thought for Today”–

“In some sort of crude sense which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose.” – J. Robert Oppenheimer, American physicist (1904-1967).

From Log24 on Dec. 17, 2002:

The Dancing Wu Li Masters,
by Gary Zukav, Harvard ’64:

“The Wu Li Masters know that physicists are doing more than ‘discovering the endless diversity of nature.’ They are dancing with Kali [or Durga], the Divine Mother of Hindu mythology.”

“Eastern religions have nothing to say about physics, but they have a great deal to say about human experience. In Hindu mythology, Kali, the Divine Mother, is the symbol for the infinite diversity of experience. Kali represents the entire physical plane. She is the drama, tragedy, humor, and sorrow of life. She is the brother, father, sister, mother, lover, and friend. She is the fiend, monster, beast, and brute. She is the sun and the ocean. She is the grass and the dew. She is our sense of accomplishment and our sense of doing worthwhile. Our thrill of discovery is a pendant on her bracelet. Our gratification is a spot of color on her cheek. Our sense of importance is the bell on her toe.

This full and seductive, terrible and wonderful earth mother always has something to offer. Hindus know the impossibility of seducing her or conquering her and the futility of loving her or hating her; so they do the only thing that they can do. They simply honor her.”

How could I dance with another….?

— John Lennon and Paul McCartney, 1962-1963