Thursday, June 30, 2011

A Link for Sunrise

Filed under: General — Tags: — m759 @ 5:28 AM

In memory of Robert Morris, former chief scientist
of the National Security Agency's
National Computer Security Center—

Here is a link to a post from last Sunday, the day Morris died.

From a novel mentioned in that post—

IMAGE- Page 163 of 'The End of Mr. Y' by Scarlett Thomas (2007 hardcover)

Wednesday, June 29, 2011

Rome After Dark

Filed under: General — Tags: — m759 @ 9:48 PM


For more about Rome, see two pages from Stevens suggested
by the New York Lottery numbers from today, St. Peter's Day.

The pages mention "Rome after dark" and a "disused ambit
of the soul." Those who prefer a "more severe, more
harassing master" may consult the date 8/6/79 suggested by
the New York Lottery this afternoon and, from that date,
Freeman Dyson's memoir in The New Yorker .

This evening's four-digit number, 0006, may, if one likes,
be regarded as an "artist's signature" of sorts.

The New Yorker  on Dyson—

"He recalls that at age 8 he read 'The Magic City,'
 by Edith Nesbit. It is the story of a crazy universe.
 He now sees that this universe bears a strong
 resemblance to the one we live in."

The Shattered Mind

Filed under: General,Geometry — Tags: , — m759 @ 12:26 AM

For St. Peter's Day

"For Stevens, the poem 'makes meanings of the rock.'
In the mind, 'its barrenness becomes a thousand things/
And so exists no more.' In fact, in a peculiar irony
that only a poet with Stevens's particular notion
of the imagination's function could develop,
the rock becomes the mind itself, shattered
into such diamond-faceted brilliance
that it encompasses all possibilities for human thought…."

—A discussion of Stevens's late poem "The Rock" (1954)
    in Wallace Stevens: A World of Transforming Shapes,
    by Alan D. Perlis, Bucknell University Press, 1976, p. 120

Related material on transforming shapes:

The Diamond 16 Puzzle  and…

IMAGE- The URL for permutationpuzzles.org, with favicon

Tuesday, June 28, 2011

ART WARS continued

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

See the signature link in last night's post for a representation of Madison Avenue.

For a representation by  Madison Avenue, see today's New York Times—

IMAGE- Butter-Cow Lady, NY Math Museum, and World-as-Rubik-Cube ad

"As a movement Pop Art came and went in a flash, but it was the kind of flash that left everything changed. The art public was now a different public— larger, to be sure, but less serious, less introspective, less willing or able to distinguish between achievement and its trashy simulacrum. Moreover, everything connected with the life of art— everything, anyway, that might have been expected to offer some resistance to this wholesale vulgarization and demoralization— was now cheapened and corrupted. The museums began their rapid descent into show biz and the retail trade. Their exhibitions were now mounted like Broadway shows, complete with set designers and lighting consultants, and their directors pressed into service as hucksters, promoting their wares in radio and television spots and selling their facilities for cocktail parties and other entertainments, while their so-called education programs likewise degenerated into sundry forms of entertainment and promotion. The critics were co-opted, the art magazines commercialized, and the academy, which had once taken a certain pride in remaining aloof from the blandishments of the cultural marketplace, now proved eager to join the crowd— for there was no longer any standard in the name of which a sellout could be rejected. When the boundary separating art and fashion was breached, so was the dividing line between high art and popular culture, and upon all those institutions and professions which had been painstakingly created to preserve high art from the corruptions of popular culture. The effect was devastating. Some surrendered their standards with greater alacrity than others, but the drift was unmistakable and all in the same direction— and the momentum has only accelerated with the passage of time."

— Hilton Kramer, The Triumph of Modernism: The Art World, 1985-2005 , publ. by Ivan R. Dee on Oct. 26, 2006, pp. 146-147

Related material— Rubik in this journal, Exorcist in this journal, and For the Class of '11.


Filed under: General — m759 @ 2:45 AM

"He gazed out of the window hoping that somehow everything could make sense to him."

— "Passing in Silence," by Oliver Humpage

"You gotta be true to your code." —Sinatra

Exercise: Trace a path from the June 27 NY Lottery numbers
to the above two quotations.  Hint: See Cuernavaca and
Pilgrim's Progress  in TIME Magazine, May 3, 1948.


For some further background, click on the CBS quote above.
I still prefer, as I did in 1948, less  up-to-the-minute developments.

* The title refers to the phrase "the artist's signature."

Monday, June 27, 2011

Galois Cube Revisited

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

   The 3×3×3 Galois Cube

    See Unity and Multiplicity.

   This cube, unlike Rubik's, is a
    purely mathematical structure.

    Its properties may be compared
    with those of the order-2  Galois
    cube (of eight subcubes, or
    elements ) and the order-4  Galois
    cube (of 64 elements). The
    order-3  cube (of 27 elements)
    lacks, because it is based on
    an odd  prime, the remarkable
    symmetry properties of its smaller
    and larger cube neighbors.

Found: A Handmaid’s Tale

Filed under: General — m759 @ 6:06 AM


404: Not Found

Filed under: General — m759 @ 4:04 AM


Sunday, June 26, 2011

Gloomy Sunday

Filed under: General — m759 @ 9:00 PM

This evening's NY Lottery numbers were 531 and 8372.


From a Google search for "531 Log24"—

Log24  on Sunday, Sept. 21, 2008

531 , Revelation without belief 116. Evening (Belief), Belief without…  The date, 5/24, of the entries linked to in Thursday's noon Log24  entry…

Pynchon on Quaternions – Log24

8. on Page 531 : "… to imps of ingenious discomfort. "Is this a stag affair, or are there likely to be one or two lady Quaternion- ists?…"

The "531" linked to in the Sept. 21, 2008, post above is a mini-drama ending at midnight on 5/31, 2008— the conclusion of Mental Health Month.

And the above 4-digit evening number suggests a search for births on 8/3/72 that yields—

Erika Marozsán, Hungarian actress, 38.

Marozsán starred in "Gloomy Sunday—A Song of Love and Death" (A German/Hungarian film from 1999).

Wikipedia informs us that this "is inaccurately claimed to be the world's longest running film."

Whether Marozsán is a Quaternionist, I do not know.

For love, death, and quaternions, see the post Metaphor from Feb. 22 linked to in this afternoon's Sunday Dinner.

Sunday Dinner

Filed under: General,Geometry — Tags: — m759 @ 2:22 PM

From "Sunday Dinner" in this journal—

"'If Jesus were to visit us, it would have been
the Sunday dinner he would have insisted on
being a part of, not the worship service at the church.'"

Judith Shulevitz at The New York Times
    on Sunday, July 18, 2010

The image “http://www.log24.com/log/pix06/060410-HotelAdlon2.jpg” cannot be displayed, because it contains errors.

Some table topics—

Today's midday New York Lottery numbers were 027 and 7002.

The former suggests a Galois cube, the latter a course syllabus—

CSC 7002
Graduate Computer Security (Spring 2011)
University of Colorado at Denver
Department of Computer Science

An item from that syllabus:

Six 22 February 2011   DES History of DES; Encryption process; Decryption; Expander function; S-boxes and their output; Key; the function f  that takes the modified key and part of the text as input; mulitple Rounds of DES; Present-day lack of Security in DES, which led to the new Encryption Standard, namely AES. Warmup for AES: the mathematics of Fields: Galois Fields, particularly the one of order 256 and its relation to the irreducible polynomial x^8 + x^4 + x^3 + x + 1 with coefficients from the field Z_2.

Related material: A novel, PopCo , was required reading for the course.

Discuss a different novel by the same author—

The End of Mr. Y .

Discuss the author herself, Scarlett Thomas.

Background for the discussion—

Derrida in this journal versus Charles Williams in this journal.

Related topics from the above syllabus date—

Metaphor and Gestell and Quadrat.

Some context— Midsummer Eve's Dream.

Paradigms Lost

Filed under: General,Geometry — m759 @ 7:20 AM

Continued from March 10, 2011 — A post that says

"If Galois geometry is thought of as a paradigm shift
from Euclidean geometry, both… the Kuhn cover
and the nine-point affine plane may be viewed…
as illustrating the shift."

Yesterday's posts The Fano Entity and Theology for Antichristmas,
together with this morning's New York Times  obituaries (below)—


—suggest a Sunday School review from last year's
    Devil's Night (October 30-31, 2010)

Sunday, October 31, 2010


m759 @ 2:00 AM

                                …    There is a Cave
Within the Mount of God, fast by his Throne,
Where light and darkness in perpetual round
Lodge and dislodge by turns, which makes through Heav'n
Grateful vicissitude, like Day and Night….

Paradise Lost , by John Milton


Click on figure for details.


Al Pacino in Devil's Advocate
as attorney John Milton

See also Ash Wednesday Surprise and Geometry for Jews.

Saturday, June 25, 2011

Theology for Antichristmas

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

Hypostasis (philosophy)

“… the formula ‘Three Hypostases  in one Ousia
came to be everywhere accepted as an epitome
of the orthodox doctrine of the Holy Trinity.
This consensus, however, was not achieved
without some confusion….” —Wikipedia



Click for further details:


The Fano Entity

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

The New York Times  at 9 PM ET June 23, 2011

ROBERT FANO: I’m trying to think briefly how to put it.

GINO FANO: "On the Fundamental Postulates"—

"E la prova di questo si ha precisamente nel fatto che si è potuto costruire (o, dirò meglio immaginare) un ente per cui sono verificati tutti i postulati precedenti…."

"The proof of this is precisely the fact that you could build (or, to say it better, imagine) an entity by which are verified all previous assumptions…."

Also from the Times  article quoted above…

"… like working on a cathedral. We laid our bricks and knew that others might later replace them with better bricks. We believed in the cause even if we didn’t completely understand the implications.”

— Tom Van Vleck

Some art that is related, if only by a shared metaphor, to Van Vleck's cathedral—


The art is also related to the mathematics of Gino Fano.

For an explanation of this relationship (implicit in the above note from 1984),
see "The Fano plane revisualized—or: the eIghtfold cube."

Friday, June 24, 2011

Just One More Thing…

Filed under: General — Tags: — m759 @ 11:59 PM


Moonshine and Lion
are left to bury the dead.


Ay, and Wall too.


[Starting up] No assure you;
the wall is down
that parted their fathers.


Click image for details.

The Cube

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

IMAGE- 'The Stars My Destination' (with cover slightly changed)

Click the above image for some background.

Related material:
Skateboard legend Andy Kessler,
this morning's The Gleaming,
and But Sometimes I Hit London.

For Stephen King Fans

Filed under: General,Geometry — Tags: , — m759 @ 6:48 AM

The Gleaming


The column at left is from Galois Geometry.

Midsummer Night Comedy

Filed under: General — m759 @ 12:00 AM

This evening's New York Lottery number was 776.
From this journal's post number 776


Lindsay Lohan was back in court today.

"The judge… ordered Lindsay may have no more than one friend
over at a time for the remainder of her house arrest" —Star Magazine

"Winter, spring, summer or fall
All you have to do is call"

— Eustace Tilley

Thursday, June 23, 2011

Script Magic…

Filed under: General — m759 @ 3:33 AM

In a Jewish Cathedral

From The New York Times Magazine  of Sunday, April 6, 1986—

"David Rayfiel's Script Magic" by Alex Ward

WHEN THE CALL came last year to revise ''The Morning After,'' Rayfiel was working on a screenplay about the 1911 Triangle Shirtwaist Company fire for Barbra Streisand and Jane Fonda. He has now resumed work— as the principal writer, not the reviser— on that script. But chances are good that he will have further interruptions. Pollack will probably call and say, as he usually does, ''David, I need access to your brain.'' And Rayfiel will probably say, as he usually does, ''That's O.K., I'm not using it.'' He will revise another script, and be reluctant about taking credit for it.

''I guess it's like the medieval stonecutters who worked on the cathedrals,'' he says. ''There's all that elaborate work. The saints were carved by one guy, the cherubs by someone else. They didn't care about getting credit, they knew what they'd done. I'm like that. I'm the guy who does the cherubs.''

Related material:

Proginoskes in this journal and Abracadabra from the midnight of June 18-19.

See also Rayfiel's obituary in today"s Times .

For some quite different work, also  from April 1986, see—

Oslo: Points and Hyperplanes.

Wednesday, June 22, 2011

ART WARS continued

Filed under: General,Geometry — Tags: — m759 @ 8:06 PM

This evening's New York Times  obituaries—


A work of art suggested by the first and third items above—


I prefer a work of art that is structurally similar—

IMAGE- The Klein group as art

and is related to a picture, Portrait of O, from October 1, 1983—

IMAGE- A work by Cullinane pirated by artist Steve RIchards in his contribution to London's 'Piracy Project'

For a recent unexpected Web appearance of Portrait of O,
aee Abracadabra from the midnight of June 18-19.

A Flag for Sunrise

Filed under: General — m759 @ 5:48 AM

Thomas N. Armstrong III, a former director of the Whitney Museum of American Art, died at 78 on Monday in Manhattan.

William Grimes in this morning's New York Times

"… Mr. Armstrong set about strengthening the museum’s permanent collection, buying Frank Stella’s 1959 black painting “Die Fahne Hoch!” for $75,000 in 1977…."

See also "Fahne Hoch" in this journal and the following from the date of Armstrong's death—


"Sunrise — Hast thou a Flag for me?" — Emily Dickinson

Related material: Piracy Project and, from Flag Day,
"Dawn's Early Light" and "Expressionistic Depth."

Tuesday, June 21, 2011

The Longest Day Continues

Filed under: General,Geometry — m759 @ 11:32 PM

The AND Publishing weblog page referred to in
a Sunday post has been changed to reflect the
source— my finite-geometry website— of pages
copied and altered by London artist Steve Richards
that are a large part of his contribution to the
AND Publishing Piracy Project.

The new version is as follows—


Note, however, that the cover page is a figure titled
by Richards "metalibrarianship" that has nothing
whatever to do with the concepts in the pages he copied
from my site, finitegeometry.org/sc.


Other pages within Richards's contribution to the
Piracy Project are similarly completely unrelated to
the content of my own site, which deals with geometry.

The image on the cover page also appears, it turns out,
on a website called intertwining.org.

At that site, it occurs in the following resume item:


The links in the resume item do not work,
but some background is available at a page titled
"Circularity, Practicality and Philosophy of Librarianship, or
The Making of 'The Nitecki Trilogy'"
by Joanne Twining.

Other images in Richards's contribution to the Piracy Project also occur
in Twining's webpage "Dimensional Advances for Information Architecture."

I never heard of Twining or Nitecki before I encountered Richards's
Piracy Project contribution, and I do not wish to be associated
again in any way with Twining, with Nitecki, or with Richards.

Truth, Beauty, Bullshit

Filed under: General — Tags: — m759 @ 1:16 PM

This post is for the Stonehenge solstice crowd, who might,
like the London artist Steve Richards, confuse bullshit
with scholarship and inspire the same confusion
in others.

IMAGE- Motto of Forgotten Books, with pirated quotation from Shakespeare that might be appropriate for London's 'Piracy Project'

The image, apparently an epigraph put there
by the author, is from the Forgotten Books edition
of Cassirer's Substance and Function:
And Einstein's Theory of Relativity

This is a scanned copy of the 1923 original.
The egg-figure above, however, is from the publisher's
prefatory notes and not  from the original.

A check of other Forgotten Books publications
shows that the motto and the Bacon
attribution are those of Forgotten Books and
not  of the authors they reprint — in particular,
not  of Ernst Cassirer, who would probably
be dismayed to have this nonsense associated
with his work.

Why nonsense? The attribution to Francis Bacon is
false. The lines are from "The Phoenix and the Turtle"
by William Shakespeare.

Summer in Norway

Filed under: General — m759 @ 11:32 AM



Filed under: General — m759 @ 3:19 AM

This post was suggested by a book advertised
above A. Whitney Ellsworth's obituary in tonight's 
online New York Times .


See also the following illustrations—

From this journal on June 1, 2008:

Click for background

Permutahedron for the symmetric group on four elements

From artist Steve Richards on January 14, 2010:

Click to enlarge

IMAGE- Interview with Steve Richards, who later contributed to London's 'Piracy Project'

Requiem for a Publisher

Filed under: General — m759 @ 2:09 AM

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


The Review  has sometimes been cited in this journal.

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

Piracy Project

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

Recent piracy of my work as part of a London art project suggests the following.


           From http://www.trussel.com/rls/rlsgb1.htm

The 2011 Long John Silver Award for academic piracy
goes to ….

Hermann Weyl, for the remark on objectivity and invariance
in his classic work Symmetry  that skillfully pirated
the much earlier work of philosopher Ernst Cassirer.

And the 2011 Parrot Award for adept academic idea-lifting
goes to …

Richard Evan Schwartz of Brown University, for his
use, without citation, of Cullinane’s work illustrating
Weyl’s “relativity problem” in a finite-geometry context.

For further details, click on the above names.

Monday, June 20, 2011

The Search for Invariants

Filed under: General,Geometry — m759 @ 9:29 AM

The title of a recent contribution to a London art-related "Piracy Project" begins with the phrase "The Search for Invariants."

A search for that phrase  elsewhere yields a notable 1944* paper by Ernst Cassirer, "The Concept of Group and the Theory of Perception."

Page 20: "It is a process of objectification, the characteristic nature
and tendency of which finds expression in the formation of invariants."

Cassirer's concepts seem related to Weyl's famous remark that

“Objectivity means invariance with respect to the group of automorphisms.”
Symmetry  (Princeton University Press, 1952, page 132)

See also this journal on June 23, 2010— "Group Theory and Philosophy"— as well as some Math Forum remarks on Cassirer and Weyl.

Update of 6 to 7:50 PM June 20, 2011—

Weyl's 1952 remark seems to echo remarks in 1910 and 1921 by Cassirer.
See Cassirer in 1910 and 1921 on Objectivity.

Another source on Cassirer, invariance, and objectivity—

The conclusion of Maja Lovrenov's 
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—

"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."

— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241

A search in Weyl's Symmetry  for any reference to Ernst Cassirer yields no results.

* Published in French in 1938.

Sunday, June 19, 2011

The London Piracy Project

Filed under: General,Geometry — m759 @ 6:25 PM

My work has been pirated by an artist in London.

An organization there, AND Publishing, sponsors what it calls
"The Piracy Project." The artist's piracy was a contribution
to the project.

The above material now reflects the following update:

UPDATE of June 21, 2011, 10:00 PM ET:

The organization's weblog (a post for 19th June)
has now been updated, and this  post, which originally
discussed that weblog, has been altered to reflect the
changes that were made at AND Publishing's weblog.

In this  weblog, changes have been made to correct my
earlier incorrect statements that the Piracy Project was
sponsored by the art school where it takes place.
It was not. The organization has informed me that

"AND Publishing is not sponsored by the art school.
We are an independent artist's publishing house,
kindly hosted by the art school. While we are offered
office space on campus, our program and website
are funded, directed and managed by ourselves –
we are an independent entity running an
autonomous program."

As this post originally stated…

The web pages from the site finitegeometry.org/sc that
the artist, Steve Richards, copied as part of his contribution to
the AND Publishing Piracy Project have had the author's name,
Steven H. Cullinane, and the date of composition systematically removed.

See a sample (jpg, 2.1 MB).

Here is some background on Richards.


Filed under: General — m759 @ 7:59 AM

IMAGE- Germany's MathGuide project, an alternative to London's 'Piracy Project'

This screenshot was suggested by the word "metalibrarianship" in a Bloomsday 2011 post by artist Steve Richards.

Note the words in the search field.

The phrase "Dublin Core metadata" refers to a city in Ohio, not in Ireland.

Related material— The highlighted phrase below is in the epigraph to Borges's "The Library of Babel"—

"I would, for these causes, wish him that is melancholy, to use both humane and divine authors, voluntarily to impose some taske upon himself, to divert his melancholy thoughts; to study the art of memory, Cosmus Rosselius, Pet. Ravennas, Scenkelius Detectus, or practise brachygraphy, &c. that will aske a great deal of attention: or let him demonstrate a proposition in Euclide in his five last books, extract a square root, or studie Algebra: than which, as gClavius holds, in all humane disciplines nothing can be more excellent and pleasant, so abstruse and recondite, so bewitching, so miraculous, so ravishing, so easie withal and full of delight, omnem humanum captum superare videtur . By this means you may define ex ungue leonem , as the diverbe is, by his thumb alone the bigness of Hercules, or the true dimensions of the great  hColossus, Solomons temple, and Domitians amphitheater, out of a little part. By this art you may contemplate the variation of the 23 letters…."

g Ad. 2. definit.2. elem.   In disciplinis humanis nihil praestantius reperitur: quippe miracula quaedam numerorum eruit tam abstrusa et recondita, tanta nihilo minus facilitate et voluptate, ut, &c.

h Which contained 1080000 weight of brass.

The Anatomy of Melancholy, Part. 2, Sec. 2, Mem. 4

Abracadabra (continued)

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

Yesterday's post Ad Meld featured Harry Potter (succeeding in business),
a 4×6 array from a video of the song "Abracadabra," and a link to a post
with some background on the 4×6 Miracle Octad Generator  of R.T. Curtis.

A search tonight for related material on the Web yielded…

(Click to enlarge.)

IMAGE- Art by Steven H. Cullinane displayed as his own in Steve Richards's Piracy Project contribution

   Weblog post by Steve Richards titled "The Search for Invariants:
   The Diamond Theory of Truth, the Miracle Octad Generator
   and Metalibrarianship." The artwork is by Steven H. Cullinane.
   Richards has omitted Cullinane's name and retitled the artwork.

The author of the post is an artist who seems to be interested in the occult.

His post continues with photos of pages, some from my own work (as above), some not.

My own work does not  deal with the occult, but some enthusiasts of "sacred geometry" may imagine otherwise.

The artist's post concludes with the following (note also the beginning of the preceding  post)—


"The Struggle of the Magicians" is a 1914 ballet by Gurdjieff. Perhaps it would interest Harry.

Saturday, June 18, 2011

Ad Meld

Filed under: General — m759 @ 2:22 PM

Step One


Step Two

IMAGE- Abracadabra 4x6

Step Three

Image-- 'Then a miracle occurs' cartoon

For further details, click on step two.

Here Be Dragons

Filed under: General — m759 @ 3:33 AM

"… such a long, long time ago" — Harry Chapin

Gate of Ivory

Filed under: General — m759 @ 3:00 AM
"Oh, I've got something inside me
To drive a princess blind.
There's a wild man, wizard, he's hiding in me
Illuminating my mind."

-- Harry Chapin

And she said, "How are you, Harry?"

Plato’s Pheedo

Filed under: General — m759 @ 2:29 AM

(Continued from June 14)



From tonight's midnight post

“Stranger, dreams verily are baffling and unclear of meaning,
and in no wise do they find fulfillment in all things for men.

For two are the gates of shadowy dreams,
and one is fashioned of horn and one of ivory.
Those dreams that pass through the gate of sawn ivory
deceive men, bringing words that find no fulfillment.
But those that come forth through the gate of polished horn
bring true issues to pass, when any mortal sees them."

Homer, Odyssey , Book 19

Midnight in the Garden (continued)–

Filed under: General — m759 @ 12:00 AM

Tracking Shot

IMAGE- Cinema column dated Oct. 1, 2009

Related material—

IMAGE- Quote from Hoyle's 'October the First is Too Late'

See also this journal's September 2009 posts.

This  post was suggested by today's previous post and by today's NY Lottery.
For some background to the ioncinema.com post numbered 4210 above,
see, in conjunction with the page headed "Azazel" linked to here earlier today,
the ioncinema.com post numbered 5601.

“Stranger, dreams verily are baffling and unclear of meaning,
and in no wise do they find fulfillment in all things for men.

For two are the gates of shadowy dreams,
and one is fashioned of horn and one of ivory.
Those dreams that pass through the gate of sawn ivory
deceive men, bringing words that find no fulfillment.
But those that come forth through the gate of polished horn
bring true issues to pass, when any mortal sees them.

But in my case it was not from thence, methinks,
that my strange dream came.”

Homer, Odyssey , Book 19

Translation by A.T. Murray, in two volumes.
Harvard University Press, 1919

Quoted in a press release for the film "Two Gates of Sleep."

From the post numbered 460 in this  journal—

At the still point… from the film "Absolute Power" :

IMAGE- Gene Hackman and Judy Davis dance in 'Absolute Power'
Photo credit – Graham Kuhn

I’ve heard of affairs that are strictly plutonic,
But diamonds are a girl’s best friend!

Marilyn Monroe, modeling a Freudian slip

Friday, June 17, 2011

Royce on Philosophy

Filed under: General — m759 @ 3:33 PM

"Philosophy seeks not absolute first principles,
nor yet purely immediate insights,
but the self-mediation of the system of truth,
and an insight into this self-mediation."

Josiah Royce in his article "Axiom" in Encyclopaedia of Religion and Ethics ,
edited by James Hastings (New York: Charles Scribner's Sons, 1910),
Vol. II, pp. 279-282, on page 282.

Related material: Time and Chance (Dec. 17, 2010).

Bloomsday Lottery

Filed under: General — m759 @ 4:09 AM


This morning's exercise in lottery hermeneutics is unusually difficult.

Yesterday was Bloomsday (the date described in
James Joyce's Ulysses ) and the New York Lottery numbers were…

Midday  numbers:  3-digit 181, 4-digit 9219.

Evening numbers: 3-digit 478, 4-digit 6449.

For 181 and 9219, see the following—

"With respect to every event, we must ask
 which element has been subjected directly to change."
— Ferdinand de Saussure, Course in General Linguistics
   (New York, The Philosophical Library, Inc., 1959), page 181

That Saussure page number was referenced in the following thesis
on James Joyce's other major novel, Finnegans Wake


The thesis is from the University of Vienna (Universität Wien ).


The word Wien , in the derived form denoting an inhabitant of that city,
figured prominently in yesterday's news.

As for the evening numbers—

478 perhaps signifies the year 478 BC,
cited in Lawrence Durrell's Sicilian Carousel  as the year
the ruler Gelon died.

For the evening 6449, note that the poem by Wallace Stevens quoted
here on June 15 in A for Anastasios deals with "the river of rivers"…
perhaps signifying time.

Interpreting 6449 chronologically yields 6/4/49.

The film artist  John Huston, discussed in an essay from that date,
might appreciate the representation of the ancient Sicilian
river god Gelas as a man-headed bull on a coin from
around the year 478 BC.

For some perceptive remarks about Durrell, see the
article by Nigel Dennis in LIFE magazine's Nov. 21, 1960
issue (with cover noting Kennedy's victory in that year's
presidential election).

All of the above may be viewed as an approach to the aesthetic
problem posed by Dennis in yesterday's Bloomsday post

"The problem that arises with this sort of writing is
one of form, i.e. , how to make one strong parcel
out of so many differently shaped commodities,
how to impose method on what would otherwise
be madness."

"The world has gone mad today…." — Cole Porter

For some related remarks, see page 161 of
Joyce's Catholic Comedy of Language
by Beryl Schlossman (U. of Wisconsin Press, 1985)
and James Joyce in the final pages of The Left Hand of God
by Adolf Holl.

* Update of July 6, 2011—
This title is a correction from the previous title
given here, Moral Language  by Mary Gore Forrester.
Google Books had Schlossman's content previewed
under Forrester's title.

Thursday, June 16, 2011

Now Heaven Knows

Filed under: General — m759 @ 2:56 PM

(A note for Bloomsday)


Wednesday, June 15, 2011

A for Anastasios

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

The title was suggested by this evening's 4-digit NY lottery number.

"… the rhetoric might be a bit over the top."


According to Amazon.com, 2198 (i.e., 2/1/98) was the publication
date of Geometry of Vector Sheaves , Volume I, by Anastasios Mallios.

Related material—

The question of S.S. Chern quoted here June 10: —
"What is Geometry?"— and the remark by Stevens that
accompanied the quotation—

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI

The work of Mallios in pure mathematics cited above seems
quite respectable (unlike his later remarks on physics).
His Vector Sheaves  appears to be trying to explore new territory;
hence the relevance of Stevens's "Alpha." See also the phrase
"A-Invariance" in an undated preprint by Mallios*.

For the evening 3-digit number, 533, see a Stevens poem—


This meditation by Stevens is related to the female form of Mallios's Christian name.

As for the afternoon numbers, see "62" in The Beauty Test (May 23, 2007), Geometry and Death, and "9181" as the date 9/1/81.

* Later published in International Journal of Theoretical Physics , Vol. 47, No. 7, cover date 2008-07-01


Filed under: General — m759 @ 11:32 AM

The New York Times  today on a new show by tightrope artist Philippe Petit—

“He comes out of that really wonderful European tradition of street performance— it blends a boundary of what’s art and what’s life,” said Jay Wegman, the director of the Abrons Arts Center, who offered Mr. Petit the three-night run. “He’s also kind of mischievous, not in a threatening or evil way, but in a child’s way of teasing and having fun.”

For a much darker approach to street performance that also involves mischief and blended boundaries, see "Tightrope" (1984)—


Background: Men in Feminism , edited by Alice Jardine and
published by Taylor & Francis in 1987, "Walking the Tightrope
of Feminism and Male Desire," by Judith Mayne, page 64

See also yesterday's Another Opening and Football in this journal.

Tuesday, June 14, 2011

Another Opening

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

NY Lottery this evening: 3-digit 444, 4-digit 0519.


"… of our history … and of our destructive paths.
We are beginning to sense the need to restore
the sacred feminine." She paused. "You
mentioned you are writing a manuscript about
the symbols of the sacred feminine, are you not?"
"I …"

519 (or 5/19):


Related material— "Eightfold Geometry" + Spider in this journal.

For this afternoon's NY numbers— 511 and 9891— see
511 in the "Going Up" post of July 12, 2007, as well as
Ben Brantley's recent suggestion of Paris Hilton as a
matinee attraction and her 9891 photo on the Web.


Filed under: General — m759 @ 2:56 PM

"Turn your head and cough."



Expressionistic Depth

Filed under: General — Tags: — m759 @ 6:20 AM


Update of 7 AM —

Carl Gardner's 1956 hit "Down in Mexico" was featured in the following Hollywood classic:


Click image for video.

Dawn’s Early Light

Filed under: General — m759 @ 5:30 AM


Note that the structure of the central flag above is not unlike that of the skull and crossbones flag.

O say can you see…?

Plato’s Pheedo

Filed under: General — m759 @ 4:30 AM



But seriously—
Degreeless Noon


IMAGE-Sean Penn with Nicole Kidman in 'The Interpreter'
Click to enlarge.
“My card.”

Related material:

"Start the new year off with a new job at Pheedo."

See January 1, 2, 3 of 2010.

Monday, June 13, 2011

Oscar Nightmare

Filed under: General — m759 @ 10:10 PM

Click to enlarge

IMAGE- Oscars producer dies.

Related material: Oscar Day 2007

Thirty Years

Filed under: General — m759 @ 7:59 PM

Yesterday was the anniversary of "Raiders of the Lost Ark."

"And thirty years,
   in the galaxies of birth,

Are time for counting
   and remembering…."

— Wallace Stevens,
   "Of Ideal Time and Choice"

Thirty years and a day after "Raiders" opened…
 a more tranquil religious meditation.

If I Forget Thee…

Filed under: General — m759 @ 10:30 AM

IMAGE- 'Walking Through Walls' speech at Tony Awards 2011 by winner for 'Jerusalem'

IMAGE- Source of Tony Awards 'Walking Through Walls' speech

Click images for further details.

See also Job: A Comedy of Justice  and
the death of Wolf Birger, reportedly on D-Day.

Broadway Cinderella

Filed under: General — m759 @ 12:00 AM

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!"

Sunday, June 12, 2011

Tony Awards Night

Filed under: General — m759 @ 8:00 PM

Magic Time!


           For fans of Douglas Adams and St. Augustine

Update of 2:20 AM June 13:

For the midday "042" as a reference to Adams, see Wikipedia. The "828" may be interpreted as a reference to St. Augustine's feast day, 8/28… or, for the more secularly minded, a reference to the time 8:28 PM (to go with the evening "0845" as a reference to 8:45 PM). For further details, see Times of the Times . The midday "7286" is more difficult. See midnight's Broadway Cinderella.

For Commencement Day at Stanford

Filed under: General — m759 @ 12:30 PM


See also June 2, 2007, and June 19, 2010,
as well as Kernel of Eternity in this journal.

Some background— Square of Opposition
in the Stanford Encyclopedia of Philosophy
and Deep Structures in this journal.

Saturday, June 11, 2011

The Searchers

Filed under: General — m759 @ 2:38 PM


" Try this one."


But Seriously–

Filed under: General — m759 @ 1:30 PM



"Mr. Messina is no ordinary Twitter user. The self-described
'hash godfather,' he officially invented the Twitter hashtag
in August 2007…."

Ashley Parker (page ST1 of tomorrow's
    NY Times  National Edition)

But seriously—
Degreeless Noon


IMAGE-Sean Penn with Nicole Kidman in 'The Interpreter'
Click to enlarge.
“My card.”


Filed under: General — Tags: — m759 @ 12:07 PM

A Comedy of Manners

Today is Stanford's Baccalaureate.

From Stanford Professor Emeritus Donald E. Knuth


From The Blues Brothers


"Inscribe a white diamond…."

Friday, June 10, 2011


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

Some background for yesterday’s posts:

Midrash for Gnostics and related notes,
as well as yesterday’s New York Lottery.

….    “We seek
The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is….”
— Wallace Stevens (1879-1955),
“An Ordinary Evening in New Haven” IX

“Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals.”
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI


“A hierophant is a person who brings religious congregants into the presence of that which is deemed holy . The word comes from Ancient Greece, where it was constructed from the combination of ta hiera , ‘the holy,’ and phainein , ‘to show.’ In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles.”

Weyl as Alpha, Chern as Omega—

(Click to enlarge.)


Postscript for Ellen Page, star of “Smart People
and of “X-Men: The Last Stand“— a different  page 679.

Your assignment, should you choose to accept it—

Interpret today’s  NY lottery numbers— Midday 815, Evening 888.

My own bias is toward 815 as 8/15 and 888 as a trinity,
but there may be less obvious and more interesting approaches.

Thursday, June 9, 2011

Page 679

Filed under: General,Geometry — Tags: — m759 @ 9:00 PM

Click to enlarge.


Good question. See also

Chern died on the evening of Friday, Dec. 3, 2004 (Chinese time).
From the morning of that day (also Chinese time)—
i.e. , the evening of the preceding day heresome poetry.


Filed under: General,Geometry — Tags: — m759 @ 3:01 PM

Suggested by this afternoon’s NY Lottery number, 541—


Click for higher quality.

Related material:  Finite Relativity and The Schwartz Notes.

Proof of Concept

Filed under: General — m759 @ 2:02 PM

Meet Max

Also* in today's New York Times


The Times  piece is about Max Mathews, computer-music pioneer,
who died at 84 on Maundy Thursday, April 21.

* See Historical Fiction, 1 PM ET

Historical Fiction

Filed under: General — m759 @ 1:00 PM

IMAGE- SecDef nominee Panetta ponders X-Men

But perhaps not a supreme  fiction.

"When we left the theater, my son and I knew we had experienced the most thrilling movie of the summer. 'First Class' is narratively lean, beautifully acted and, at all the right moments, visually stunning. But I had experienced something else. My son is 10 and a romantic, as all 10-year-olds surely have the right to be. How then do I speak to him of this world’s masterminds who render you a supporting actor in your own story?"

Wednesday, June 8, 2011

CMT Awards Night

Filed under: General — Tags: — m759 @ 9:00 PM

A meditation, while watching the Country Music Television
CMT Awards, on today's evening NY lottery number 469.

For Reese  Witherspoon* and Dionysus, not Apollo—

A Funny Thing Happened
on the Way to the Edifice


— Page 469 of Wallace Stevens's Collected Poems

See also page 469 of Gravity's Rainbow  (Penguin Classics 1995 paperback)


* Not the Witherspoon Church  of this evening's 6 PM entry.
Reese won Sunday's 2011 MTV Movie Awards' Generation Award .

Both the MTV Movie Awards and the CMT Awards are productions
of MTV Networks, a subsidiary of Viacom Inc. For some background,
see Sumner Redstone (formerly Rothstein).

Songs and Fingerplays

Filed under: General — Tags: — m759 @ 6:00 PM

To Pay Paul


From Princeton Public Library (65 Witherspoon St., on map above)—

Songs and Fingerplays—



Fingerplay— See this morning's 10:30 AM post.

Song— Paul Robeson sings "Summertime."

See also the Harvard version.

… And Rosetta Stone

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

Halle Berry as Rosetta Stone

Halle Berry as Rosetta Stone

For Saint Peter

Filed under: General,Geometry — Tags: — m759 @ 10:30 AM

… and Arthur Koestler

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


Related material:

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


See also two posts from the day Peter Jennings died—

Presbyterian Justice and Religious Symbolism at Harvard.

Hellgate Joke (continued*)

Filed under: General — Tags: — m759 @ 10:00 AM

The New Yorker 's review of The Great Escape  (Simon & Schuster, $27), by Kati Marton—

"Marton, who fled Hungary as a child in 1957, illuminates Budapest's vertiginous Golden Age and the darkness that followed (a darkness that some of her subjects, notably Arthur Koestler, never shook)."

— Issue dated November 6, 2006

See also The Ninth Gate  in this journal and the life of Marton's second husband, Peter Jennings.

* Continued from April 12.

A Look Back

Filed under: General — Tags: — m759 @ 9:00 AM


Apollo (not Orpheus) versus Robert Kaplow,
author of The Cat Who Killed Lilian Jackson Braun


Tuesday, June 7, 2011

… Are Gods

Filed under: General — m759 @ 11:59 PM

Robert A. Heinlein—

    "How about those empty universes?" I demanded.
    "Maybe they are places about which stories will be written
or maybe stories have already been told but aren't favorites
of us four, so we don't emerge close to their scenes.
But those are guesses. So far as my theory is concerned,
such Universes are 'null' — they don't count one way or the other.
We find our  universes."
    "Sharpie, you have just invented pantheistic multiperson solipsism.
I didn't think it was mathematically possible."
    "Zeb, anything  is mathematically possible."
    "Thanks, Jacob. Zebbie, 'solipsism' is a buzz word. I'm saying that
we've stumbled onto 'The Door in the Wall,' the one that leads to
the Land of Heart's Desire. I don't know how and have no use for
fancy rationalizations. I see a pattern; I'm not trying to explain it.
It just is ."

Ernest Hemingway—

"Isn't it pretty to think so?"

Here, Too

Filed under: General — m759 @ 2:19 PM

Today's midday NY lottery number was 176.

An occurrence of that number in this journal

Umberto Eco,
Foucault’s Pendulum, page 176:

Here, too, you entered through a little garden…

Here is a picture of 176.

Cock Tale

Filed under: General — m759 @ 1:44 PM

Continued from D-Day eight years ago

IMAGE- NY Times June 7, 2011, review of Bolano's 'Between Parentheses'

See also Savage Detectives and Two Writers Walk Into a Bar.

Monday, June 6, 2011

Evening Number

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

The NY Lottery's evening number today was 975.

See today's previous remarks and Post  975.

"… What Paris says to me is love story, awash with painters,
shots of the Seine, Champagne. Thank God I have a
can’t-miss notion to sell you. I call it ‘Midnight in Paris.’ ”

“Romantic title,” I had to admit. “Is there a script?”

“Actually, there’s nothing on paper yet, but I can spitball
the main points,” he said, slipping on his tap shoes.

“Maybe some other time,” I said, mindful of Cubbage’s
unbroken string of theatrical Hiroshimas.

— Woody Allen, May 5, 2011

See also "Some Other Time" in Post 552.


Tree of Life — Jewish Version

Filed under: General,Geometry — Tags: — m759 @ 6:48 PM

Today's midday NY Lottery number was 753, the number of a significant page in Gravity's Rainbow .

An excerpt from that page ((Penguin Classics paperback, June 1, 1995)—


"… the Abyss had crept intolerably close, only an accident away…."

Midrash— See Ben Stein in this journal. 

But seriously… See "Geometry and Death" in this journal.

See also PlanetMath.org on the Hesse configuration


A picture of the Hesse configuration—

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors. .

Some context— A Study in Art Education.

The Way of Grace

Filed under: General — Tags: — m759 @ 10:21 AM


"…we're presented with the dream within the dream within the dream…."

— Remark on "Inception" in a review of  Malick's "The Tree of Life"

The Way of Nature

Singer/songwriter/musician Andrew Gold died on Friday, June 3, reportedly in the early morning.

The Way of Grace

"They've heard lonely songs they thought were the livin' end."

— Reviewer's parody of James Taylor's "Fire and Rain"
printed in the Spokane Chronicle  on May 28, 1991—
the Feast of St. Germain


See also First Class, from the day of Gold's death, as well as the later
 Midnight and Paris and Mystery.

Background— The above 1991 story about Taylor mentions his interpretation of
"Getting to Know You," from "The King and I." Gold's mother, Marni Nixon, was
the singing voice of Deborah Kerr in the film of that musical.

It's a very ancient saying, but a true and honest thought…."

Sunday, June 5, 2011

Edifice Complex

Filed under: General,Geometry — Tags: , — m759 @ 7:00 PM

"Total grandeur of a total edifice,
Chosen by an inquisitor of structures
For himself. He stops upon this threshold,
As if the design of all his words takes form
And frame from thinking and is realized."

— Wallace Stevens, "To an Old Philosopher in Rome"

The following edifice may be lacking in grandeur,
and its properties as a configuration  were known long
before I stumbled across a description of it… still…

"What we do may be small, but it has
 a certain character of permanence…."
 — G.H. Hardy, A Mathematician's Apology

The Kummer 166 Configuration
as seen by Kantor in 1969— (pdf, 2.5 MB)

IMAGE-- 16_6 configuration from '2-Transitive Symmetric Designs,' by William M. Kantor (AMS Transactions, 1969)

For some background, see Configurations and Squares.

For some quite different geometry of the 4×4 square that  is
original with me, see a page with that title. (The geometry's
importance depends in part on its connection with the
Miracle Octad Generator (MOG) of R.T. Curtis. I of course
had nothing to do with the MOG's discovery, but I do  claim credit
for discovering some geometric properties of the 4×4 square
that constitutes two-thirds of the MOG as originally defined .)

Related material— The Schwartz Notes of June 1.

Saturday, June 4, 2011


Filed under: General — m759 @ 2:02 PM

"… a little mystery to figure out…." — Bonnie Raitt, 1991

Two writers walk into a bar…
(A phrase from Immoveable Feast on May 28, 2005. See also May 28 this  year.)

Yesterday's post First Class featured a picture of Mystique.

A related passage* from a book pictured here May 28

IMAGE- Alan McGlashan on 'the Hidden Treasure, which is the Center'

See also Wallace Stevens on the Center.

* on participation mystique — "The primitive mind
does not differentiate the supernatural from reality,
but rather uses 'mystical participation'
to manipulate the world."

Midnight and Paris

Filed under: General — m759 @ 12:00 PM

'X-Men: First Class' Does
Good Midnight Business

“Madame, all stories, if continued far enough, end in death,
and he is no true-story teller who would keep that from you.”
– Ernest Hemingway,
   Death in the Afternoon, Ch. 11

“There is never any ending to Paris….”
– Ernest Hemingway, A Moveable Feast

See also Back from the Shadows.

Friday, June 3, 2011

First Class

Filed under: General — m759 @ 6:15 PM

It's a very ancient saying, but a true and honest thought,
that if you become a teacher, by your pupils you'll be taught

Related material—

* Spiritual Exercises  of Ignatius Loyola—

Composition of Place

It should be noted here that for contemplation or meditation about
visible things…  the ‘composition’ will consist in seeing through the
gaze of the imagination the material place where the object I want
to contemplate is situated.

West Side Memories  (an off-off-off-off Broadway production)—


Brightness at Noon (continued)

Filed under: General — m759 @ 12:00 PM



Hexagram 55
Abundance (Fullness)  

"Be not sad.
 Be like the sun at midday."

Waiting for Corky*

Filed under: General — m759 @ 10:00 AM

This morning's previous post suggests the following…



* See May 16.


Filed under: General — m759 @ 7:59 AM

Today is Commencement Day at MIT.

“To measure the changes
     of time and space
the smartest are nothing.”

— Shing-Tung Yau,
 The Emperor of Math
and Harvard philosopher

To measure the changes:

The image “http://www.log24.com/log/pix06A/061017-Yellowbook3.jpg” cannot be displayed, because it contains errors.

The smartest are nothing:

The image “http://www.log24.com/log/pix06A/061017-Gump2A.jpg” cannot be displayed, because it contains errors.

Well, perhaps not quite nothing.

The above pictures were posted here on the day the following book was published—


The lives of the nine Jews in the above book amount to more than Yau's "nothing."

Note, however, that claims by Jews (see Jill Abramson yesterday
that their secular publications constitute a substitute for religion
and contain only "absolute truth" should be viewed with at least one
raised eyebrow.

Abramson's remark yesterday that her promotion to New York Times  executive editor
was like "ascending to Valhalla" had a religious flavor worthy of yesterday's
Feast of the Ascension.

In related news from yesterday's Times

IMAGE- 'Fearless Ascent, as a God or a Jet' -NYT

See also a symbol related to Apollo, to nine, and to "nothing"

A minimalist 3×3 matrix favicon—


This may, if one likes, be viewed as the "nothing"
present at the Creation.  See Jim Holt on physics.

Thursday, June 2, 2011

Exit Keller

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

IMAGE- Jill Abramson is new executive editor at NY Times

See posts on Keller in this journal.

A sample piece by the new editor— “The Lionesses” (2006 book review).

Wednesday, June 1, 2011


Filed under: General — m759 @ 9:00 PM

See today's NY lottery numbers* and Gravity's Rainbow , pp. 656-657.
(Penguin Classics paperback, June 1, 1995.)


"Show me all  the blueprints."
— Howard Hughes, according to Hollywood

* Readers new to lottery hermeneutics may consult
  some remarks by Stuart Moulthrop.

The Schwartz Notes

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

A Google search today for material on the Web that puts the diamond theorem
in context yielded a satisfyingly complete list. (See the first 21 results.)
(Customization based on signed-out search activity was disabled.)

The same search limited to results from only the past month yielded,
in addition, the following—


This turns out to be a document by one Richard Evan Schwartz,
Chancellor’s Professor of Mathematics at Brown University.

Pages 12-14 of the document, which is untitled, undated, and
unsigned, discuss the finite-geometry background of the R.T.
Curtis Miracle Octad Generator (MOG) . As today’s earlier search indicates,
this is closely related to the diamond theorem. The section relating
the geometry to the MOG is titled “The MOG and Projective Space.”
It does not mention my own work.

See Schwartz’s page 12, page 13, and page 14.

Compare to the web pages from today’s earlier search.

There are no references at the end of the Schwartz document,
but there is this at the beginning—

These are some notes on error correcting codes. Two good sources for
this material are
From Error Correcting Codes through Sphere Packings to Simple Groups ,
by Thomas Thompson.
Sphere Packings, Lattices, and Simple Groups  by J. H. Conway and N.
Planet Math (on the internet) also some information.

It seems clear that these inadequate remarks by Schwartz on his sources
can and should be expanded.

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