Tuesday, August 30, 2016

Shema, Faust

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

"The quotes create the illusion
that the dead are still speaking
to the reader. Faust writes about
the efforts of spiritualists to believe
in an afterlife for their slain kin, but
she’s the one summoning spirits."

April Yee, Harvard Crimson
     staff writer, February 7, 2008

"0! = 1" 

Quine's Shema

See also yesterday's Into the Woods 
and posts now tagged Willow and Mandorla.

Saturday, July 16, 2016

Binary Shema: The “O” and the “I”

Filed under: General,Geometry — Tags: — m759 @ 4:35 AM

The "I" of "I Am that I Am" has been described as a creation of
an "ur-unity" (see the Anderson passage below) and this ur-unity,
denoted by "O," has been described elsewhere as "a primary reality"
(see the Sullivan passage below). These descriptions are of course 
much less clear than those usually given for the similar purely
mathematical *  notations "0" and "1."

See also Quine's Shema  in "Is Nothing Sacred?" —

0! = 1.

Quoted here on July 30, 2015

Kabbalah and Finnegans Wake

Linked to here on June 29, 2016

Bion and the 'O'

*  Note for mathematicians: Here characteristic 0 is assumed .
    Quine's Shema does not apply to Galois.

Monday, June 20, 2016

Shema, Salinger

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

"I've got a brand-new pair of roller skates "

Melanie, 1971

Related material —  Salinger in the Park and
                                 Philosophy in a New Key.

Tuesday, July 7, 2015

Shema Israelite*

Filed under: General — m759 @ 1:00 PM

"Throughout the years, weapons and targeting systems
were added to the aircraft without diminishing the F-16’s
agility, making it a true multirole aircraft."

— WCSC Television 
    Charleston, SC 

* See yesterday's War Haiku.

Thursday, July 2, 2015

Shema Cartier*

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

Woody as Figaro

* For the title, see a search for Inside Man .

Related material: The co-editor of The Architecture of Modern Mathematics

"I love those Bavarians."

Monday, January 19, 2015


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

In memory of a mathematician who
reportedly died on Dec. 16, 2014:

"Four dimensions is where things change a lot."

Backstory:  Or Only Die.

Thursday, August 11, 2016

The O and the I

Filed under: General — m759 @ 1:00 PM

See Binary Shema.

Tuesday, August 2, 2016

Notes Towards a Dark Tower*

Filed under: General — m759 @ 1:00 PM

Or:  Shema, SXSW

The doors open slowly. I step into a hangar. From the rafters high above, lights blaze down, illuminating a twelve-foot cube the color of gunmetal. My pulse rate kicks up. I can’t believe what I’m looking at. Leighton must sense my awe, because he says, “Beautiful, isn’t it?” It is exquisitely beautiful. At first, I think the hum inside the hangar is coming from the lights, but it can’t be. It’s so deep I can feel it at the base of my spine, like the ultralow-frequency vibration of a massive engine. I drift toward the box, mesmerized.

— Crouch, Blake. Dark Matter: A Novel
(Kindle Locations 2004-2010).
Crown/Archetype. Kindle Edition.

Related reading —

“Do you know there is a deliberate sinister conspiracy at work?”

“No, but hum a few bars and I’ll fake it.”

A few bars —

* Not the Dark Tower of Stephen King, but that of the
University of Texas at Austin, back in time 50 years and a day.

Sunday, March 13, 2016

Space-Time Sermon

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


      "… and the clocks were striking thirteen."

Monday, August 31, 2015


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

Or:  A Shema for Sacks.

"We’ve already seen the hexagon painted over a
propaganda poster. It’s obviously a mark of defiance,
or maybe a geometry lesson. It’s still not clear.

Hey, it’s that clown dictator again. Who’s his stylist?"

Perhaps Orwell, perhaps Waugh.

Thursday, August 20, 2015

Language Game

Filed under: General — m759 @ 1:00 AM

See Nine-Headed Dragon in this journal.

Shema, JC.

Wednesday, January 21, 2015

High Concept:

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

The Dark Fields  Meet  The Big Seal .

Recall the punchline of Tuesday afternoon's post
on the 2012 film "Travelling Salesman" —

"What am I, the farmer's daughter?"

For background from the dark fields of the republic,
see a speech last night by Iowa Senator Joni Ernst.

Related material:

At the end of the 2012 film "Travelling Salesman,"
the main character holds up to the light a letter that has
at the top the presidential seal of the United States:

The camera pans down, and the character then
sees a watermark that echoes another famous seal,
from the U.S. one-dollar bill:

For related paranoia, see the novels of Dan Brown

as well as

See also Shema and Clocks Striking 13.

Tuesday, December 16, 2014

Say Hello to My Little Friend

Filed under: General — Tags: — m759 @ 7:11 PM

For some backstory, see
Feast of the Holy Innocents, 2012.

Sunday, October 14, 2007

Sunday October 14, 2007

Filed under: General — m759 @ 11:00 AM
The Dipolar God

Steven H. Cullinane, 'The Line'

“Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word….”

— Wallace Stevens,
   “Notes Toward a Supreme Fiction

Yesterday’s meditation (“Simon’s Shema“) on the interpenetration of opposites continues:

Part I: The Jewel in the Lotus

“The fundamental conception of Tantric Buddhist metaphysics, namely, yuganaddha, signifies the coincidence of opposites.  It is symbolized by the conjugal embrace (maithuna or kama-kala) of a god and goddess or a Buddha and his consort (signifying karuna and sunyata or upaya and prajna, respectively), also commonly depicted in Tantric Buddhist iconography as the union of vajra (diamond sceptre) and padme (lotus flower).  Thus, yuganaddha essentially means the interpenetration of opposites or dipolar fusion, and is a fundamental restatement of Hua-yen theoretic structures.”

— p. 148 in “Part II: A Whiteheadian Process Critique of Hua-yen Buddhism,” in Process Metaphysics and Hua-Yen Buddhism: A Critical Study of Cumulative Penetration vs. Interpenetration (SUNY Series in Systematic Philosophy), by Steve Odin, State University of New York Press, 1982

Part II: The Dipolar God

And on p. 163 of Odin, op. cit., in “Part III: Theology of the Deep Unconscious: A Reconstruction of Process Theology,” in the section titled “Whitehead’s Dipolar God as the Collective Unconscious”–

“An effort is made to transpose Whitehead’s theory of the dipolar God into the terms of the collective unconscious, so that now the dipolar God is to be comprehended not as a transcendent deity, but the deepest dimension and highest potentiality of one’s own psyche.”

Part III: Piled High and Deep

Odin obtained his Ph.D. degree from the Department of Philosophy at the State University of New York (SUNY) at Stony Brook in 1980. (See curriculum vitae (pdf).)

For an academic review of Odin’s book, see David Applebaum, Philosophy East and West, Vol. 34 (1984), pp. 107-108.

It is perhaps worth noting, in light of the final footnote of Mark D. Brimblecombe’s Ph.D. thesis “Dipolarity and Godquoted yesterday, that “tantra” is said to mean “loom.” For some less-academic background on the Tantric iconography Odin describes, see the webpage “Love and Passion in Tantric Buddhist Art.” For a fiction combining love and passion with the word “loom” in a religious context, see Clive Barker’s Weaveworld.  This fiction– which is, if not “supreme” in the Wallace Stevens sense, at least entertaining– may correspond to some aspects of the deep Jungian psychological reality discussed by Odin.

Happy Birthday,
Hannah Arendt

(Oct. 14, 1906-
Dec. 4, 1975)


Hannah (Arendt) and Martin (Heidegger) as portrayed in a play of that name

Actors portraying
Arendt and Heidegger

Click on image for details.

Saturday, October 13, 2007

Saturday October 13, 2007

Filed under: General — Tags: — m759 @ 9:22 AM

Simon’s Shema

“When times are mysterious
Serious numbers will always be heard
And after all is said and done
And the numbers all come home
The four rolls into three
The three turns into two
And the two becomes a

Paul Simon, 1983

Related material:

Simon’s theology here, though radically reductive, is at least consistent with traditional Jewish thought. It may help counteract the thoughtless drift to the left of academic writing in recent decades. Another weapon against leftist nonsense appears, surprisingly, on the op-ed page of today’s New York Times:

“There is a Communist jargon recognizable after a single sentence. Few people in Europe have not joked in their time about ‘concrete steps,’ ‘contradictions,’ ‘the interpenetration of opposites,’ and the rest.”

— Doris Lessing, winner of this year’s Nobel Prize in Literature

The Times offers Lessing’s essay to counter Harold Bloom’s remark that this year’s award of a Nobel Prize to Lessing is “pure political correctness.” The following may serve as a further antidote to Bloom.

The Communist use of “interpenetration,” a term long used to describe the Holy Trinity, suggests– along with Simon’s hymn to the Unity, and the rhetorical advice of Norman Mailer quoted here yesterday—  a search for the full phrase “interpenetration of opposites” in the context* of theology.  Such a search yields a rhetorical gem from New Zealand:

“Dipolarity and God”
by Mark D. Brimblecombe,
Ph.D. thesis,
University of Auckland, 1999

* See the final footnote on the final page (249) of Brimblecombe’s thesis:

3 The Latin word contexo means to interweave, join, or braid together.

A check of the Online Eymology Dictionary supports this assertion:

context 1432, from L. contextus “a joining together,” orig. pp. of contexere “to weave together,” from com “together” + textere “to weave” (see texture).

See also Wittgenstein on “theology as grammar” and “context-sensitive” grammars as (unlike Simon’s reductive process) “noncontracting”– Log24, April 16, 2007: Happy Birthday, Benedict XVI.

Tuesday, June 19, 2007

Tuesday June 19, 2007

Filed under: General — m759 @ 1:00 PM
Quine’s Shema:

0! = 1.

Hickory Dickory Dock…

Scene from A Good Year

A Good Year

Saturday, May 12, 2007

Saturday May 12, 2007

Filed under: General — Tags: — m759 @ 11:07 AM
Artistic Vision

Last night's entry "A Midrash for Hollywood" discussed a possible interpretation of yesterday's Pennsylvania Lottery numbers– mid-day 384, evening 952.

In memory of a blacklisted Hollywood screenwriter who died yesterday, here is another interpretation of those numbers.

First, though, it seems appropriate to quote again the anonymous source from "Heaven, Hell, and Hollywood" on screenwriters– "You can be replaced by some Ping Pong balls and a dictionary."  An example was given illustrating this saying.  Here is another example:

Yesterday's PA lottery numbers in the dictionary–

Webster's New World Dictionary,
College Edition, 1960–

Page 384: "Defender of the Faith"
Related Log24 entries:
"To Announce a Faith," Halloween 2006,
and earlier Log24 entries from
that year's Halloween season

Page 952: "monolith"
Related Log24 entries:
"Shema, Israel," and "Punch Line"
(with the four entries that preceded it).

It may not be entirely irrelevant that a headline in last night's entry– "Lonesome No More!"– was linked to a discussion of Kurt Vonnegut's Slapstick, that a film version of that novel starred Jerry Lewis, and that yesterday afternoon's entry quoted a vision of "an Ingmar Bergman script as directed by Jerry Lewis."


See also April 7, 2003:


April is Math Awareness Month.
This year's theme is "mathematics and art."

"Art isn't easy."
— Stephen Sondheim    

Friday, May 12, 2006

Friday May 12, 2006

Filed under: General — m759 @ 3:00 PM
The Carlin Code

The image “http://www.log24.com/log/pix06A/060512-Carlin1.jpg” cannot be displayed, because it contains errors.
Happy birthday, George:

The image “http://www.log24.com/log/pix06A/060512-Harvard.gif” cannot be displayed, because it contains errors.


Tom Hanks’s birthday, 2005

Salute to Anthony Hopkins,
May 3, May 4, May 5

Today’s Wizard of Id

Judeo-Christian Heritage:
The Wiener Kreis

André Weil As I Knew Him,
by Goro Shimura (pdf)

Simone Weil
on George Herbert

Related material:

The Prime Cut Gospel

Harvard Symbology

God Is Red

Quine’s Shema

The Big Red One

Friday, December 30, 2005

Friday December 30, 2005

Filed under: General — m759 @ 1:00 AM


Expression is an impossible word.
If you want to use it
I think you have to
explain it further…
— Ad Reinhardt,
Art as Art

“… an equation is a very
abstract expression
of knowledge
about something.”
The Hidden Side
of Visualization

Well, yes.
For example:

The image “http://www.log24.com/log/pix05B/051230-Shema.jpg” cannot be displayed, because it contains errors.
Abstract Expression
pixels on screen, 12/30/05

The Scope and Limits
of Quotation
(pdf), in
The Philosophy of
Donald Davidson,
ed. L. E. Hahn,
Open Court Publishers,
1999, pp. 691-714,
by Dr. Ernest Lepore,
Rutgers University:

“… an assumption I wish to reject, namely, that in quotation an abstract expression (shape) is denoted….

Since Davidson, however, only says ‘we may  take [an expression] to be an abstract shape’ [1979, p.85, my emphasis], his theory is compatible with expressions being something else. We need only find something that can be instantiated by radically differently shaped objects. Whatever it is must be such that written tokens, spoken tokens, signed tokens, Braille tokens, Semaphore tokens, finger language tokens, and any other way in which words can be produced, can be instantiated by it….

Such entities might  exist; if they do, they might ultimately play some role in the metaphysics of language.”

My emphasis.


Davidson, D., 1979, “Quotation,” in Inquiries into Truth and Interpretation , Oxford, Oxford University Press, 1984, pp.79-92.

For more on zero and other entities,
see Is Nothing Sacred?

For more on Davidson,
see Shema .

Tuesday, December 7, 2004

Tuesday December 7, 2004

Filed under: General — m759 @ 1:00 PM

White Christmas

Starring W. V. Quine as
the Ghost of Christmas Past

“Birthday, death-day —
   what day is not both?”
   — John Updike

“We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas’ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”

Joan Didion, The White Album

The image “http://www.log24.com/log/pix04B/041207-Quine.gif” cannot be displayed, because it contains errors.

0! = 1

Quine’s Shema

Saturday, May 15, 2004

Saturday May 15, 2004

Filed under: General — m759 @ 4:23 AM

Language Game

In memory of
Samuel Iwry, Hebrew scholar,
who died on May 8, 2004:

From a log24 entry of May 8, 2004,
on Wittgenstein’s “language games” —

    “Let us imagine a language …”

— Ludwig Wittgenstein,
    Philosophical Investigations


Moral of the story:
If you must have a
religious language,
Elvish may,
in some situations,
do as well as Hebrew.

See also

The Unity of Mathematics,
or Shema, Israel

Monday, September 1, 2003

Monday September 1, 2003

Filed under: General — m759 @ 3:33 PM

The Unity of Mathematics,

or “Shema, Israel”

A conference to honor the 90th birthday (Sept. 2) of Israel Gelfand is currently underway in Cambridge, Massachusetts.

The following note from 2001 gives one view of the conference’s title topic, “The Unity of Mathematics.”

Reciprocity in 2001

by Steven H. Cullinane
(May 30, 2001)

From 2001: A Space Odyssey, by Arthur C. Clarke, New American Library, 1968:

The glimmering rectangular shape that had once seemed no more than a slab of crystal still floated before him….  It encapsulated yet unfathomed secrets of space and time, but some at least he now understood and was able to command.

How obvious — how necessary — was that mathematical ratio of its sides, the quadratic sequence 1: 4: 9!  And how naive to have imagined that the series ended at this point, in only three dimensions!

— Chapter 46, “Transformation”

From a review of Himmelfarb, by Michael Krüger, New York, George Braziller, 1994:

As a diffident, unsure young man, an inexperienced ethnologist, Richard was unable to travel through the Amazonian jungles unaided. His professor at Leipzig, a Nazi Party member (a bigot and a fool), suggested he recruit an experienced guide and companion, but warned him against collaborating with any Communists or Jews, since the objectivity of research would inevitably be tainted by such contact. Unfortunately, the only potential associate Richard can find in Sao Paulo is a man called Leo Himmelfarb, both a Communist (who fought in the Spanish Civil War) and a self-exiled Jew from Galicia, but someone who knows the forests intimately and can speak several of the native dialects.

“… Leo followed the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity, which I could not even imitate.”

… E. M. Forster famously advised his readers, “Only connect.” “Reciprocity” would be Michael Kruger’s succinct philosophy, with all that the word implies.

— William Boyd, New York Times Book Review, October 30, 1994

Reciprocity and Euler

Applying the above philosophy of reciprocity to the Arthur C. Clarke sequence

1, 4, 9, ….

we obtain the rather more interesting sequence
1/1, 1/4, 1/9, …..

This leads to the following problem (adapted from the St. Andrews biography of Euler):

Perhaps the result that brought Euler the most fame in his young days was his solution of what had become known as the Basel problem. This was to find a closed form for the sum of the infinite series

1/1 + 1/4 + 1/9 + 1/16 + 1/25 + …

— a problem which had defeated many of the top mathematicians including Jacob Bernoulli, Johann Bernoulli and Daniel Bernoulli. The problem had also been studied unsuccessfully by Leibniz, Stirling, de Moivre and others. Euler showed in 1735 that the series sums to (pi squared)/6. He generalized this series, now called zeta(2), to zeta functions of even numbers larger than two.

Related Reading

For four different proofs of Euler’s result, see the inexpensive paperback classic by Konrad Knopp, Theory and Application of Infinite Series (Dover Publications).

Related Websites

Evaluating Zeta(2), by Robin Chapman (PDF article) Fourteen proofs!

Zeta Functions for Undergraduates

The Riemann Zeta Function

Reciprocity Laws
Reciprocity Laws II

The Langlands Program

Recent Progress on the Langlands Conjectures

For more on
the theme of unity,

Monolithic Form

Wednesday, July 30, 2003

Wednesday July 30, 2003

Filed under: General — m759 @ 2:45 AM

Transcendental Meditation

This week’s
 New Yorker

Transcendental Man
New books on
Ralph Waldo Emerson
for his bicentennial.
by John Updike

This week’s
 Time cover

The bicentennial of Ralph Waldo Emerson was on May 25, 2003.  For a commemoration of Emerson on that date, click on the picture below of Harvard University’s Room 305, Emerson Hall.


This will lead you to a discussion of the properties of a 5×5 array, or matrix, with a symbol of mystical unity at its center.  Although this symbol of mystical unity, the number “1,” is not, pace the Shema, a transcendental number, the matrix is, as perhaps a sort of Emersonian compensation, what postmodernists would call phallologocentric.  It is possible that Emerson is a saint; if so, his feast day (i.e., date of death), April 27, might reveal to us the sort of miraculous fact hoped for by Fritz Leiber in my previous entry.  A check of my April 27 notes shows us, lo and behold, another phallologocentric 5×5 array, this one starring Warren Beatty.  This rather peculiar coincidence is, perhaps, the sort of miracle appropriate to a saint who is, as this week’s politically correct New Yorker calls him, a Big Dead White Male.

 Leiber’s fiction furnishes “a behind-the-scenes view of the time change wars.”

“It’s quarter to three…” — St. Frank Sinatra

Powered by WordPress