Wednesday, September 18, 2013


Filed under: General — Tags: , — m759 @ 2:01 AM

An LA obituary online yesterday suggests
a review of Kabbalah in this journal.

See also the final link in last weekend's
Log24 post Sunday Shul.

Tuesday, May 7, 2013

Strange Correspondences

Filed under: General — Tags: — m759 @ 4:00 PM

For Jerusalem Day

Strange Correspondences :

"There are interesting correspondences between
Jewish Kabbala, Torah, and Talmud, and
Chinese Buddhism and Taoism…."

Tony Smith

See also Chinese Checkers in this journal.

Thursday, January 17, 2013

Brazil Revisited

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

Yesterday's post Treasure Hunt, on a Brazilian weblog,
suggests a review of Brazil  in this journal.  The post
most relevant to yesterday's remarks is from
August 15, 2003, with a link, now broken, to the work
of Brazilian artist Nicole Sigaud* that also uses the
four half-square tiles used in 1704 by Sebastien Truchet 
and somewhat later by myself in Diamond Theory 
(see a 1977 version).

A more recent link that works:






© 1997 – 2002 Nicole Sigaud

* Sigaud shares the interests of her fellow Brazilian
   whose weblog was the subject of yesterday's
   Treasure Hunt.—

   "For many years I have dedicated myself to the study
    of medieval magic, demonology, Kabbalah, Astrology,
    Alchemy, Tarot and divination in general."

     — Nicole Sigaud (translated by Google) in a self-profile: 

    I do not share the interest of these authors in such matters,
    except as they are reflected in the works of authors like
    Charles Williams and Umberto Eco.

Wednesday, January 16, 2013

Treasure Hunt

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

The Mathematical Association of America (MAA)
newsmagazine Focus  for December 2012/January 2013: 

The Babylonian tablet on the cover illustrates the
"Mathematical Treasures" article.

A search for related material yields a Babylonian tablet
reproduced in a Brazilian weblog on July 4, 2012:

In that weblog on the same day, July 4, 2012,
another post quotes at length my Diamond Theory page,
starting with the following image from that page—

IMAGE- Plato's Diamond

That Brazilian post recommends use of geometry together
with Tarot and astrology. I do not concur with this 
recommendation, but still appreciate the mention.

Sunday, July 1, 2012


Filed under: General — Tags: — m759 @ 2:48 AM

Death and the Compass  and The Library of Babel .

Related material in this journal—

Wag the Dogma and Widener.

Saturday, October 22, 2011

Lunch at the Y

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

Or: Starting Out in the Evening, continued from noon yesterday

Yesterday evening's New York Lottery numbers were 510 and 5256.

For the former, see post  510, Music for Patricias.

For the latter, see Richard Feynman at the Caltech YMCA Lunch Forum on 5/2/56—

"The Relation of Science and Religion."

Some background….

The Aleph

"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth…."

— Borges, "The Aleph," quoted in Ayn Sof (January 7th, 2011)

The Y

See "Pythagorean Letter" in this journal.


"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses , Proteus chapter

Saturday, October 8, 2011

An Ordinary Evening in Hartford

Filed under: General — Tags: , — m759 @ 7:59 AM

From Rebecca Goldstein's Talks and Appearances page—

• "36 (Bad) Arguments for the Existence of God,"
   Annual Meeting of the Freedom from Religion Foundation,
   Marriot, Hartford, CT, Oct 7 [2011], 7 PM

From Wallace Stevens—

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

For those who prefer greater depth on Yom Kippur, yesterday's cinematic link suggests…

"Yo sé de un laberinto griego que es una línea única, recta."
 —Borges, "La Muerte y la Brújula " ("Death and the Compass")

See also Alpha and Omega (Sept. 18, 2011) and some context from 1931.

Friday, January 7, 2011

Ayn Sof

Filed under: General — Tags: , — m759 @ 7:26 PM

(A continuation of this morning's Coxeter and the Aleph)

"You've got to pick up every stitch… Must be the season of the witch."
Donovan song at the end of Nicole Kidman's "To Die For"

Mathematics and Narrative, Illustrated



"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth, in order to show
that the lower world is the map and mirror of the higher; for Cantor's
Mengenlehre , it is the symbol of transfinite numbers,
of which any part is as great as the whole."

— Borges, "The Aleph"

From WorldLingo.com

Ein Sof

Ein Soph or Ayn Sof (Hebrew  אין סוף, literally "without end", denoting "boundlessness" and/or "nothingness"), is a Kabbalistic term that usually refers to an abstract state of existence preceding God's Creation of the limited universe. This Ein Sof , typically referred to figuratively as the "light of Ein Sof " ("Or Ein Sof "), is the most fundamental emanation manifested by God. The Ein Sof  is the material basis of Creation that, when focused, restricted, and filtered through the sefirot , results in the created, dynamic universe.

Cultural impact

Mathematician Georg Cantor labeled different sizes of infinity using the Aleph. The smallest size of infinity is aleph-null (0), the second size is aleph-one (1), etc. One theory about why Cantor chose to use the aleph is because it is the first letter of Ein-Sof. (See Aleph number)

"Infinite Jest… now stands as the principal contender
for what serious literature can aspire to
in the late twentieth and early twenty-first centuries."

All Things Shining, a work of pop philosophy published January 4th


"You're gonna need a bigger boat." — Roy Scheider in "Jaws"

"We're gonna need more holy water." — "Season of the Witch," a film opening tonight

See also, with respect to David Foster Wallace, infinity, nihilism,
and the above reading of "Ayn Sof" as "nothingness,"
the quotations compiled as "Is Nothing Sacred?"

Sunday, July 11, 2010

Philosophers’ Keystone

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

(Background— Yesterday's Quarter to Three,
A Manifold Showing, Class of 64, and Child's Play.)

Image-- Notes on Lowry's arrival in Mexico on the ship 'Pennsylvania'

Image-- PA Lottery Saturday, July 10, 2010-- Midday 017, Evening 673


Fans of Gregory Chaitin and Harry Potter
may consult Writings for Yom Kippur
for the meaning of yesterday's evening 673.

(See also Lowry and Cabbala.)

Fans of Elizabeth Taylor, Ava Gardner,
and the Dark Lady may consult Prime Suspect
for the meaning of yesterday's midday 17.

For some more serious background, see Dante—

"….mirando il punto 
a cui tutti li tempi son presenti

– Dante, Paradiso, XVII, 17-18

The symbol    is used throughout the entire book
in place of such phrases as ‘Q.E.D.’  or
‘This completes the proof of the theorem’
to signal the end of a proof.”

Measure Theory, by Paul R. Halmos, Van Nostrand, 1950      

Halmos died on the date of Yom Kippur —  
October 2, 2006.            

Thursday, July 1, 2010

Omega at Eight

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

The "compact key to universal wisdom" passage in the previous post seemed
too well written to be the work of an anonymous webforum author.

Here is a slightly expanded version—

Throughout history mystics and philosophers have sought
a compact key to universal wisdom, a finite formula or text
that would provide the answer to every question. The use of
the Bible, the Koran and the I Ching for divination and the
tradition of the secret books of Hermes Trismegistus and the
medieval Jewish Cabala exemplify this belief or hope.  Such
sources of universal wisdom are traditionally protected from
casual use by being difficult to find as well as difficult to un-
derstand and dangerous to use, tending to answer more quest-
ions and deeper ones than the searcher wishes to ask. The
esoteric book is, like God, simple yet undescribable. It is om-
niscient, and it transforms all who know it. The use of clas-
sical texts to foretell mundane events is considered supersti-
tious nowadays, yet in another sense science is in quest of its
own Cabala, a concise set of natural laws that would explain
all phenomena. In mathematics, where no set of axioms can
hope to prove all true statements, the goal might be a concise
axiomatization of all "interesting" true statements.
      Ω is in many senses a Cabalistic number. It can be known
of through human reason, but not known. To know it in detail
one must accept its uncomputable sequence of digits on faith,
like words of a sacred text.   

This is Martin Gardner's* and Charles H. Bennett's
revised version of a passage from Bennett's  paper
"On Random and Hard-to-Describe Numbers," 1979.

The original passage from Bennett's paper—

Throughout history mystics and philosophers have sought a compact key to
universal wisdom, a finite formula or text which, when known and understood,
would provide the answer to every question. The Bible, the Koran, the mythical
secret books of Hermes Trismegistus, and the medieval Jewish Cabala have
been so regarded. Sources of universal wisdom are traditionally protected from
casual use by being hard to find, hard to understand when found, and dangerous
to use, tending to answer more and deeper questions than the user wishes to
ask. Like God the esoteric book is simple yet undescribable, omniscient, and
transforms all who know It. The use of classical texts to fortell [sic] mundane events
is considered superstitious nowadays, yet, in another sense, science is in quest of
its own Cabala, a concise set of natural laws which would explain all phenomena.
In mathematics, where no set of axioms can hope to prove all true statements,
the goal might be a concise axiomatization of all "interesting" true statements.
      Ω is in many senses a Cabalistic number. It can be known of, but not known,
through human reason. To know it in detail, one would have to accept its un-
computable digit sequence on faith, like words of a sacred text.

The Bennett paper deals with Gregory Chaitin's concept of an "Omega Number."

I prefer the Omega of Josefine Lyche—

Image-- Uncertified copy of 1986 figures by Cullinane in a 2009 art exhibit in Oslo

Click for further details.

See also All Hallows' Eve, 2002.

* Martin Gardner's Mathematical Games  column
"The Random Number Omega Bids Fair to Hold the Mysteries of the Universe,"
Scientific American, November 1979, 241(5), pp. 20–34.
The column is reprinted as "Chaitin's Omega," Ch. 21, pp. 307-319 in the
collection of Gardner's columns titled Fractal Music, Hypercards and More,
W.H. Freeman & Co., 1991

Tuesday, August 4, 2009

Tuesday August 4, 2009

Filed under: General,Geometry — Tags: — m759 @ 8:00 AM

Just What We Need

Thomas Pynchon's new novel
Inherent Vice comes out today.

Title of a review in
The New York Times:
Another Doorway to the
Paranoid Pynchon Dimension

More interesting doorways:

Doorway to 'The Aleph Sanctuary,' by Mati Klarwein

An Aleph for Pynchon (July 9)

Click on the doorway for details.

Rabbi Ephraim Oshry

Abstract Aleph

The Aleph (July 8)

Click on the aleph for details.

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 9:00 AM
Wechsler Cubes
“Confusion is nothing new.”
— Song lyric, Cyndi Lauper
Part I:
Magister Ludi

Hermann Hesse’s 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–

“For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar’s Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors.”

Part II:
A Bulky Memorandum

From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–

A description of the work of Bill Wechsler, a fictional artist:

“Bill worked long hours on a series of autonomous pieces about numbers. Like O’s Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has

— End of page 168 —

opened the door to his cell. The hidden rhyme is “free.” Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn’t visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe’s color wheel and in Alfred Jensen’s use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn’t bother with the poet’s meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.

The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page.”

Part III:
Wechsler Cubes(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) —

From 2002:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale “block design” subtest.

Part IV:
A Magic Gallery
Log24, March 4, 2004


Figures from the
Kaleidoscope Puzzle
of Steven H. Cullinane:

Poem by Eugen Jost:
Zahlen und Zeichen,
Wörter und Worte

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
auf weiss
schaffen wir neue Welten
oder gar Universen

 Numbers and Names,
Wording and Words

With numbers and names
we measure heaven and earth
on white
we create new worlds
and universes

English translation
by Catherine Schelbert
A related poem:

by Hermann Hesse

From time to time
we take our pen in hand
and scribble symbols
on a blank white sheet
Their meaning is
at everyone’s command;
it is a game whose rules
are nice and neat.

But if a savage
or a moon-man came
and found a page,
a furrowed runic field,
and curiously studied
lines and frame:
How strange would be
the world that they revealed.
a magic gallery of oddities.
He would see A and B
as man and beast,
as moving tongues or
arms or legs or eyes,
now slow, now rushing,
all constraint released,
like prints of ravens’
feet upon the snow.
He’d hop about with them,
fly to and fro,
and see a thousand worlds
of might-have-been
hidden within the black
and frozen symbols,
beneath the ornate strokes,
the thick and thin.
He’d see the way love burns
and anguish trembles,
He’d wonder, laugh,
shake with fear and weep
because beyond this cipher’s
cross-barred keep
he’d see the world
in all its aimless passion,
diminished, dwarfed, and
spellbound in the symbols,
and rigorously marching
He’d think: each sign
all others so resembles
that love of life and death,
or lust and anguish,
are simply twins whom
no one can distinguish…
until at last the savage
with a sound
of mortal terror
lights and stirs a fire,
chants and beats his brow
against the ground
and consecrates the writing
to his pyre.
Perhaps before his
consciousness is drowned
in slumber there will come
to him some sense
of how this world
of magic fraudulence,
this horror utterly
behind endurance,
has vanished as if
it had never been.
He’ll sigh, and smile,
and feel all right again.

— Hermann Hesse (1943),
Buchstaben,” from
Das Glasperlenspiel,
translated by
Richard and Clara Winston

Wednesday, October 24, 2007

Wednesday October 24, 2007

Filed under: General — Tags: , — m759 @ 9:26 AM
A Story for Dobbs

Internet Movie Database on screenwriter Lem Dobbs:

Son of painter R.B. (Ron) Kitaj.

Took his pseudonym from the character Humphrey Bogart played
in 'The Treasure of the Sierra Madre.'"

Bogart and Robert Blake in The Treasure of the Sierra Madre

Click for details.

NY Lottery Oct. 21, 2007: Mid-day 512, Evening 430

October 21 was the day
that R. B. Kitaj died.
For what Kitaj called
"midrashic glosses"
on the numbers and
the lucky sums, see
4/30, 5/12, and
Eight is a Gate.

Screenwriter Joan Didion:

"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."

David Cohen on R. B. Kitaj:

"He has come to be fascinated… by the kabbalah, finding in it parallels to the world of art and ideas. Every morning, after a long walk, he winds up at a Westwood café surrounded by pretty UCLA students where he studies the writings of Emmanuel Levinas, before working for an hour on his memoirs."

Levinas Adieu:

Levinas, and Derrida, on the Adieu

Click for source.

"There is no teacher
but the enemy.

— Orson Scott Card,  
Ender's Game

Monday, July 23, 2007

Monday July 23, 2007

Daniel Radcliffe
is 18 today.
Daniel Radcliffe as Harry Potter


“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”

Jorge Luis Borges, “Avatars of the Tortoise”

El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”

Jorge Luis Borges, “Los Avatares de la Tortuga

Autonomous Apparition

At Midsummer Noon:

“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.
Related material:
It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure 

Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit,

And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.

– Wallace Stevens, “The Rock”

See also
as well as
Hofstadter on
his magnum opus:
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
Goedel Escher Bach coverHofstadter’s cover.

Here are three patterns,
“shadows” of a sort,
derived from a different
“central object”:
Faces of Solomon's Cube, related to Escher's 'Verbum'

Click on image for details.

Sunday, June 24, 2007

Sunday June 24, 2007

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM
Raiders of
the Lost Stone

(Continued from June 23)

Scott McLaren on
Charles Williams:
"In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew
from a brief description in Waite's
The Holy Kabbalah (1929)
of a supernatural cubic stone
on which was inscribed
'the Divine Name.'"

The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.

Related material:

The image “http://www.log24.com/log/pix07/070624-Cube.gif” cannot be displayed, because it contains errors.

Solomon's Cube,

Geometry of the 4x4x4 Cube,

The Klein Correspondence,
Penrose Space-Time,
and a Finite Model

Saturday, November 12, 2005

Saturday November 12, 2005

Filed under: General,Geometry — Tags: , — m759 @ 1:28 PM
Glory Season

"…his eyes ranged the Consul's books disposed quite neatly… on high shelves around the walls: Dogme et Ritual de la Haute Magie, Serpent and Siva Worship in Central America, there were two long shelves of this, together with the rusty leather bindings and frayed edges of the numerous cabbalistic and alchemical books, though some of them looked fairly new, like the Goetia of the Lemegaton of Solomon the King, probably they were treasures, but the rest were a heterogeneous collection…."

Malcolm Lowry, Under the Volcano, Chapter VI

"… when Saul does reach for a slim leather-bound volume Eliza cannot help but feel that something momentous is about to happen.  There is care in the way he carries the book on the short journey from its shelf, as if it were constructed not of leather and parchment but of flesh and blood….
    "Otzar Eden HaGanuz," Saul says.  "The Hidden Eden.  In this book, Abulafia describes the process of permutation…. Once you have mastered it, you will have mastered words, and once you have mastered words, you will be ready to receive shefa."

Bee Season: A Novel

"In the Inner Game, we call the Game Dhum Welur, the Mind of God."

The Gameplayers of Zan, a novel featuring games based on cellular automata

"Regarding cellular automata, I'm trying to think in what SF books I've seen them mentioned. Off the top of my head, only three come to mind:

The Gameplayers of Zan M.A. Foster
Permutation City Greg Egan
Glory Season David Brin"

— Jonathan L. Cunningham, Usenet

    "If all that 'matters' are fundamentally mathematical relationships, then there ceases to be any important difference between the actual and the possible. (Even if you aren't a mathematical Platonist, you can always find some collection of particles of dust to fit any required pattern. In Permutation City this is called the 'logic of the dust' theory.)….
    … Paul Durham is convinced by the 'logic of the dust' theory mentioned above, and plans to run, just for a few minutes, a complex cellular automaton (Permutation City) started in a 'Garden of Eden' configuration — one which isn't reachable from any other, and which therefore must have been the starting point of a simulation….  I didn't understand the need for this elaborate set-up, but I guess it makes for a better story than 'well, all possible worlds exist, and I'm going to tell you about one of them.'"

— Danny Yee, review of Permutation City

"Y'know, I never imagined the competition version involved so many tricky permutations."

— David Brin, Glory Season, 1994 Spectra paperback, p. 408

Related material:
The image “http://www.log24.com/log/pix05B/051112-EdenFigs.jpg” cannot be displayed, because it contains errors.

Figure 2



"… matter is consciousness expressed in the intermixing of force and form, but so heavily structured and constrained by form that its behaviour becomes describable using the regular and simple laws of  physics. This is shown in Figure 2.
    The glyph in Figure 2 is the basis for a kabbalistic diagram called the Etz Chaiim, or Tree of Life. The first principle of being or consciousness is called Keter, which means Crown. The raw energy of consciousness is called Chokhmah or Wisdom, and the capacity to give form to the energy of consciousness is called Binah, which is sometimes translated as Understanding, and sometimes as Intelligence. The outcome of the interaction of force and form, the physical world, is called Malkhut or Kingdom.  This is shown… in Figure 3."

Figure 3

"This quaternary is a Kabbalistic representation of God-the-Knowable, in the sense that it the most abstract representation of God we are capable of comprehending….
    God-the-Knowable has four aspects, two male and two female: Keter and Chokhmah are both represented as male, and Binah and Malkhut are represented as female. One of the titles of Chokhmah is Abba, which means Father, and one of the titles of Binah is Imma, which means Mother, so you can think of Chokhmah as God-the-Father, and Binah as God-the-Mother. Malkhut is the daughter, the female spirit of God-as-Matter, and it would not be wildly wrong to think of her as Mother Earth. And what of God-the-Son? Is there also a God-the-Son in Kabbalah? There is…."

A Depth of Beginning: Notes on Kabbalah by Colin Low (pdf)

See also
Cognitive Blending and the Two Cultures,
Mathematics and Narrative,
Deep Game,
and the previous entry.

Friday, November 11, 2005

Friday November 11, 2005

Filed under: General,Geometry — Tags: — m759 @ 3:26 PM
720 in the Book

From today's
New York Times:

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

The image “http://www.log24.com/log/pix05B/051111-BeeSeason.jpg” cannot be displayed, because it contains errors.

Phil Bray

Transcendence through spelling:
Richard Gere and Flora Cross
as father and daughter
in "Bee Season."

Words Made Flesh: Code, Culture, Imagination

The earliest known foundation of the Kabbalah is the Sefer Yetzirah (Book of Creation) whose origin and history is unknown….

… letters create things by the virtue of an algorithm…

    "From two letters or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty…."
Sefer Yetzirah    

Foucault's Pendulum

Mystic logic, letters whirling in infinite change, is the world of bliss, it is the music of thought, but see that you proceed slowly, and with caution, because your machine may bring you delirium instead of ecstasy. Many of Abulafia's disciples were unable to walk the fine line between contemplation of the names of God and the practice of magic.

Bee Season

"The exercises we've been doing are Abulafia's. His methods are primarily a kind of Jewish yoga, a way to relax. For most, what Abulafia describes as shefa, the influx of the Divine, is a historical curiosity to be discussed and interpreted. Because, while anyone can follow Abulafia's instructions for permutation and chanting, very few can use them to achieve transcendence….

Spelling is a sign, Elly. When you win the national bee, we'll know that you are ready to follow in Abulafia's footsteps. Once you're able to let the letters guide you through any word you are given, you will be ready to receive shefa."

In the quiet of the room, the sound of Eliza and her father breathing is everything.

"Do you mean," Eliza whispers, "that I'll be able to talk to God?"

Related material:

Log24, Sept. 3, 2002,

Diamond Theory notes
of Feb. 4, 1986,
of April 26, 1986, and
 of May 26, 1986,

  Sacerdotal Jargon
(Log24, Dec. 5, 2002),

and 720 in the Book
(Log24, Epiphany 2004).

Monday, September 20, 2004

Monday September 20, 2004

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

Pi continued:

(see 9/15/04)


Renegade mathematician Max Cohen (Sean Gullette, left) and the leader of the Kabbalah sect, Lenny Meyer (Ben Shenkman) have a chance encounter on a Chinatown street corner.

The Magic Schmuck

"Confucius is said to have received only one inappropriate answer, i.e., hexagram 22, GRACE — a thoroughly aesthetic hexagram. This is reminiscent of the advice given to Socrates by his daemon — 'You ought to make more music' — whereupon Socrates took to playing the flute. Confucius and Socrates compete for first place as far as reasonableness and a pedagogic attitude to life are concerned; but it is unlikely that either of them occupied himself with 'lending grace to the beard on his chin,' as the second line of this hexagram advises. Unfortunately, reason and pedagogy often lack charm and grace, and so the oracle may not have been wrong after all."

— Carl Jung, Foreword to the I Ching 

Yesterday, class, in keeping with our morning German lesson, our evening (5:01:22 PM ET) entry was Hexagram 22, Pi (pronounced "bee"). The Chinese term pi may be translated in various ways… As ornament, as adornment, or as in a German web page:

I-Ching 22 Pi Der Schmuck

The Wilhelm translation of pi is "grace."  This suggests we examine yesterday's evening lottery number in the State of Grace, Pennsylvania:


As kabbalists know, there are many ways of interpreting numbers.  In keeping with the viewpoint of Ecclesiastes — "time and chance happeneth" — let us interpret this instance of chance as an instance of time… namely, 4/08.  Striving for consistency in our meditations, let us examine the lessons for…

4/08 2003 — Death's Dream Kingdom

and 4/08 2004 — Triple Crown

From the former:

"When smashing monuments, save the pedestals; they always come in handy."

Stanislaw J. Lec

From the latter: 

"The tug of an art that unapologetically sees itself as on a par with science and religion is not to be underestimated…. Philosophical ambition and formal modesty still constitute Minimalism's bottom line."

Michael Kimmelman

In keeping with the above, from
this year's Log24.net
Rosh Hashanah service

A Minimalist


For a poetic interpretation
of this symbol, see
Hexagram 20,
Contemplation (View).

Sunday, January 18, 2004

Sunday January 18, 2004

Filed under: General — Tags: — m759 @ 10:12 AM

A Living Church

"Plato has told you a truth; but Plato is dead. Shakespeare has startled you with an image; but Shakespeare will not startle you with any more. But imagine what it would be to live with such men still living. To know that Plato might break out with an original lecture to-morrow, or that at any moment Shakespeare might shatter everything with a single song. The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast. He is always expecting to see some truth that he has never seen before."

— G. K. Chesterton, Orthodoxy

C. P. Snow on G. H. Hardy in the foreword to A Mathematician's Apology:

"… he had another favourite entertainment.  'Mark that man we met last night,' he said, and someone had to be marked out of 100 in each of the categories Hardy had long since invented and defined.  STARK, BLEAK ('a stark man is not necessarily bleak: but all bleak men without exception want to be considered stark')…."

S. H. Cullinane on religion and Hollywood:

"If the incomparable Max Bialystock were to remake 'Up Close and Personal,' he might retitle it 'Distant and Impersonal.'  A Google search on this phrase suggests

a plot outline for Mel Brooks & Co."

In memory of
producer Ray Stark,
an excerpt from that plot outline:

The Oxford University Press summary of

Myths of the Male Divine,
by David Leeming and Jake Page

"They [Leeming and Page] describe the rise of a male sky God as 'the equal to, the true mate, of Goddess, who was still associated with Earth.' In the Iron Age, the sky God became more aggressive, separating from the Goddess and taking his place as the King God, as Zeus, Odin, and Horus. Ultimately he emerged as the creator, a more distant and impersonal force. Here Leeming and Page also illuminate an important trend–a sense that the divine is beyond gender, that it permeates all things (as seen in the Chinese Tao and En Sof of the Kabbalah). They see a movement in the biography of God toward a reunion with the Goddess."

As for the Goddess, see

Art Wars: Just Seventeen

(December 17, 2002). 

Stark, a saint among Hollywood producers, died yesterday, January 17.  If, as Chesterton might surmise, he then met Plato and Shakespeare in Heaven, the former might discuss with him the eternal Platonic form of the number 17, while the latter might offer the following links on Stark's new heavenly laptop:

Cartoon Graveyard and

Art Wars: At the Still Point

This concludes the tribute to Stark.  For a tribute to Bleak, click here.

Sunday, October 5, 2003

Sunday October 5, 2003

Filed under: General — Tags: , — m759 @ 5:09 AM

At Mount Sinai:
Art Theory for Yom Kippur

From the New York Times of Sunday, October 5, 2003 (the day that Yom Kippur begins at sunset):

Rabbi Ephraim Oshry, whose interpretations of religious law helped sustain Lithuanian Jews during Nazi occupation…. died on Sept. 28 at Mount Sinai Hospital in Manhattan. He was 89.”

For a fictional portrait of Lithuanian Jews during Nazi occupation, see the E. L. Doctorow novel City of God.

For meditations on the spiritual in art, see the Rosalind Krauss essay “Grids.”   As a memorial to Rabbi Oshry, here is a grid-based version of the Hebrew letter aleph:

Rabbi Oshry


Click on the aleph for details.

“In the garden of Adding,
Live Even and Odd….”
— The Midrash Jazz Quartet in
       City of God, by E. L. Doctorow

Here are two meditations
on Even and Odd for Yom Kippur:

Meditation I

From Rosalind Krauss, “Grids”:

“If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World, for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example, we could think about Ad Reinhardt who, despite his repeated insistence that ‘Art is art,’ ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek cross.  There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora’s box of spiritual reference that is opened once one uses it.”

Meditation II

Here, for reference, is a Greek cross
within a nine-square grid:

 Related religious meditation for
Doctorow’s “Garden of Adding”…

 4 + 5 = 9.

Saturday, November 30, 2002

Saturday November 30, 2002

Filed under: General — Tags: — m759 @ 2:13 PM

Archetypal Criticism

My previous note includes the following:

"For a… literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill."

This week's
Time Magazine cover
suggests a followup to
the Gill reference
in defense of Jung and
his theory of archetypes.

Carl Gustav Jung, from a strongly Protestant background, has been vilified as an "Aryan Christ" by Catholics and Jews

To counteract this vilification, here are two links:

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