Monday, March 31, 2014

Art Wars for Coxeter

Filed under: General,Geometry — m759 @ 10:30 PM

Geometer H. S. M. Coxeter died on this date in 2003.

This evening’s daily number from the Keystone state:   822.

IMAGE- Review of 'Geometry of the I Ching'

The Story of Noam

Filed under: General — m759 @ 1:00 PM

On The Blazing World , a new novel —

“Hustvedt uses fragment-stories, frame narratives, and unreliable
narrators to talk about the ways in which brilliant women across
history have been silenced, forgotten, and appropriated by men.
This is a narrative suspicious of narratives, a story that
demonstrates how damaging stories can be.”

— Review by Amal El-Mohtar

The protagonist of Hustvedt’s novel is named Harriet Burden.

A midrash for Darren Aronofsky, director of The Fountain*  and Noah

Part I: The Burden of Proof —

Part II: The Story of Noam

* See The Fountain  in “The Story Theory of Truth,” Columbus Day, 2013

For Women’s History Month

Filed under: General — Tags: — m759 @ 4:30 AM

“…what he was trying to get across was not that he was the Soldier of a Power that was fighting across all of time to change history, but simply that we men were creatures with imaginations and it was our highest duty to try to tell what it was really like to live in other times and places and bodies. Once he said to me, ‘The growth of consciousness is everything… the seed of awareness sending its roots across space and time. But it can grow in so many ways, spinning its web from mind to mind like the spider or burrowing into the unconscious darkness like the snake. The biggest wars are the wars of thought.'”

— Fritz Leiber, “The Oldest Soldier” (1960)

“And that’s the snake.” — Jill Clayburgh in “It’s My Turn” (1980)

Backstory — “For Daedalus,” May 26, 2009.

For a more up-to-date look at Burroway, see a
Chicago Tribune  story of March 21, 2014.

Sunday, March 30, 2014

Brightness at Noon

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


Princeton’s Sermon

Filed under: General — Tags: — m759 @ 11:00 AM

IMAGE- Sermon topic 'One Thing Do I Know'

Click image for the backstory.

The sermon itself is not yet on line.

Perhaps the following will help.

IMAGE- Search for 'One thing do I know'

Josefine’s Sunday School

Filed under: General — m759 @ 9:30 AM

Two timely images for Oslo artist Josefine Lyche —

Backstory:  Searches for “Blazing World” and for “Josefine + Lyche + Pink
in this journal.

The image above is by a man, Brian Stauffer. Related material:

An image from today’s NY Times Sunday Book Review —

This  image is by a non-man, Kelsey Dake.

The first image above, since it combines Lyche’s enthusiasm for the color
pink and (apparently) for fishnet stockings, seems to me the better picture,
despite its prurient nature.

(Updated through 10 AM ET)

Saturday, March 29, 2014

Sequence (continued)

Filed under: General — m759 @ 11:29 PM

Click the above for further details.

An elegy adapted from “Sequence,” by Theodore Roethke —

“She listened when light sang.”

Perhaps such a song was sung
on Shakespeare’s (and Nabokov’s) birthday, 2009.

Butcher’s Clay

Filed under: General — m759 @ 9:14 PM

Friday evening’s post Musement dealt with Iris Murdoch’s
phrase “the clean crystalline work.”

For dirty bloody work see the life of Don Reitz, who
reportedly died at 84 on March 19.

Five Ninths

Filed under: General — m759 @ 4:48 PM

“For every kind of vampire, there is a kind of cross.” — Gravity’s Rainbow

“I don’t write exclusively on Jewish themes or about Jewish characters.
My collection of short stories, Strange Attractors , contained nine pieces,
five of which were, to some degree, Jewish, and this ratio has provided me
with a precise mathematical answer (for me, still the best kind of answer)
to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer.”

— Rebecca Goldstein, “Against Logic

Related material:  The cross of five ninths, from Epiphany 2006.

Friday, March 28, 2014


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

(The title is from a work by Charles Sanders Peirce.)

For LYNX 760 —

IMAGE- Image search for 'the clean crystalline work'

For more beauty and strangeness, see Strange McEntire.

Chinese Rune

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

"The Geometry of the I Ching introduces something called the Cullinane sequence
for the hexagrams, and uses a notation based on the four sides and two diagonals
in a square to indicate the yin and yang lines. The resulting rune-like symbols
are intriguing…."

— Andreas Schöter's  I Ching  home page

Actually, the geometry is a bit deeper than the rune-like symbols.

" 'Harriet Burden has been really great to me,'
Rune says in an interview, 'not only as a collector
of my work but as a true supporter. And I think of her
as a muse for the project … ' "

— In The Blazing World , the artist known as Rune


Filed under: General — Tags: — m759 @ 11:16 AM

"Constructed as a Nabokovian cat’s cradle, the novel
purports to be the work of a professor of aesthetics…."

— Fernanda Eberstadt in a book review now online

Blazing Thule

Filed under: General — Tags: — m759 @ 10:20 AM

The title is suggested by a new novel (see cover below),
and by an unwritten book by Nabokov —

Siri Hustvedt, 'The Blazing World'.

Related material:

Art School Confidential

Filed under: General — Tags: — m759 @ 4:01 AM

For Reba McEntire on her birthday:
Complex Reflection and Naturalized Epistemology.


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

For Josefine Lyche, by fellow artist  Nuno Borges:

Related material:

Recent remarks by Lyche and
a recurring image from this journal.

Thursday, March 27, 2014

Symbol Game

Filed under: General — m759 @ 10:00 PM

The following is from a web page by
Andreas Schöter, developer of  The Symbol Game.

Building the Narrative

The game can simply be played as a competitive board game,
simply trying to accumulate the most points. However,
to play this way is to miss the main purpose of the Symbol Game.

The author’s page on the game itself —

(This post was suggested by this afternoon’s post  Diamond Space.)


Filed under: General — m759 @ 3:27 PM

Diamond Space

Filed under: General,Geometry — Tags: , , — m759 @ 2:28 PM


Definition:  A diamond space  — informal phrase denoting
a subspace of AG(6, 2), the six-dimensional affine space
over the two-element Galois field.

The reason for the name:

IMAGE - The Diamond Theorem, including the 4x4x4 'Solomon's Cube' case

Click to enlarge.

Wednesday, March 26, 2014


Filed under: General — m759 @ 3:48 PM


The front page of The New York Times Book Review 
for next Sunday (March 30, 2014) is devoted to a
review of Siri Hustvedt’s new novel  The Blazing World .
See two posts from St. Patrick’s day:  Her and Narratives.

The review’s author is Fernanda Eberstadt.

The review is titled “Outsider Art.”
See also that phrase in this journal.

Sinai Prize

Filed under: General — m759 @ 1:00 PM

Yakov G. Sinai today won the 2014 Abel Prize.
Earlier, he won the Wolf Prize.

Wolf Foundation press release quoted in the March 1997
Notices of the American Mathematical Society —

On Sinai —

“He is generally recognized as the world leader
in the mathematics of statistical physics.”

This afternoon’s New York Lottery:  813 and 1857.

Unrelated remarks:  813 and  1857.

Abel Prize 2014

Filed under: General — m759 @ 12:12 PM

IMAGE- AMS news, March 26, 2014


Filed under: General — m759 @ 12:00 PM

For some context, see Holy Field
and Krauss Grid.

Tuesday, March 25, 2014

Narrative and Mathematics

Filed under: General — Tags: — m759 @ 1:01 AM


"Richard Hughes’s celebrated short novel is
a masterpiece of concentrated narrative."

New York Review of Books  on
     A High Wind in Jamaica

As perhaps were, in their way, parts of the life
of the late Patrice Wymore Flynn, who reportedly
died at 87 on Saturday.

Deep backstory:  See Colony of Santiago (Jamaica).

For the "mathematics" part of this post's title, see
Saturday's Log24 post on Kummer-surface terms
and a post of September 23, 2012.

Sunday, March 23, 2014

Memorial Word

Filed under: General — m759 @ 10:30 PM

In memory of a Spanish statesman
who died today at 81… Santiago.

Saturday, March 22, 2014

Two Types of Symmetry

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


IMAGE- Weber hexads in 'Kummer's Quartic Surface'

IMAGE- Ohashi on the 192 Weber hexads

Literary (also from May 18, 2010)

IMAGE- Heraclitus, 'Immortals mortal, mortals immortal'- 'athanatoi thnetoi, thnetoi athanatoi'

Friday, March 21, 2014

Three Constructions of the Miracle Octad Generator

Filed under: General,Geometry — Tags: , , — m759 @ 12:24 PM

IMAGE- Two constructions, by Turyn/Curtis, and by Conway, of the Miracle Octad Generator

See also a Log24 post on this subject from Dec. 14, 2013,
especially (scroll down) the update of March 9, 2014.

Related material on the Turyn-Curtis construction
from the University of Cambridge —

— Slide by “Dr. Parker” — Apparently Richard A. Parker —
Lecture 4, “Discovering M24,” in slides for lectures 1-8 from lectures
at Cambridge in 2010-2011 on “Sporadic and Related Groups.”
See also the Parker lectures of 2012-2013 on the same topic.

A third construction of Curtis’s 35  4×6  1976 MOG arrays would use
Cullinane’s analysis of the 4×4 subarrays’ affine and projective structure,
and point out the fact that Conwell’s 1910 correspondence of the 35
4+4-partitions of an 8-set with the 35 lines of the projective 3-space
over the 2-element field, PG(3, 2), is essentially the same correspondence
as that constituting Curtis’s 1976 MOG.

See The Diamond Theorem,  Finite RelativityGalois Space,
Generating the Octad Generator, and The Klein Correspondence.

Update of March 22-March 23 —

Adding together as (0,1)-matrices over GF(2) the black parts (black
squares as 1’s, all other squares as 0’s) of the 35  4×6 arrays of the 1976
Curtis MOG would then reveal*  the symmetric role played in octads
by what Curtis called the heavy brick , and so reveal also the action of
S3 on the three Curtis bricks that leaves invariant the set of all 759
octads of the S(5, 8, 24) constructed from the 35  MOG arrays.  For more
details of this “by-hand” construction, see Geometry of the 4×4 Square.
For the mathematical properties of the S(5, 8, 24), it is convenient to
have a separate construction,  not  by hand (such as Turyn’s), of the
extended binary Golay code. See the Brouwer preprint quoted above.

* “Then a miracle occurs,” as in the classic 1977 Sidney Harris cartoon.

Illustration of array addition from March 23 —

IMAGE- Discovery of the S_3 action on bricks in the Conwell-Cullinane 'by-hand' approach to octad-building

Thursday, March 20, 2014

Classical Galois

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

IMAGE- The large Desargues configuration and Desargues's theorem in light of Galois geometry

Click image for more details.

To enlarge image, click here.

Wednesday, March 19, 2014

Plato Thanks the Academy

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


IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

“Click on fanciful .”

To Gather Stones Together

Filed under: General — Tags: — m759 @ 12:20 PM

Robert Stone’s Heaven —

“Behold the handmaid of the Lord.”

Sharon Stone’s Heaven —

“I’m  alive.”

“No. You’re dead, this is heaven,
and I’m the Virgin Mary.”

(Costume design by L’Wren Scott)

Tuesday, March 18, 2014

Class of 64 continues…

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

Mathematician Norbert Wiener reportedly died on this date in 1964.

"Mathematics is too arduous and uninviting a field to appeal to those to whom it does not give great rewards. These rewards are of exactly the same character as those of the artist. To see a difficult uncompromising material take living shape and meaning is to be Pygmalion, whether the material is stone or hard, stonelike logic. To see meaning and understanding come where there has been no meaning and no understanding is to share the work of a demiurge. No amount of technical correctness and no amount of labour can replace this creative moment, whether in the life of a mathematician or of a painter or musician. Bound up with it is a judgment of values, quite parallel to the judgment of values that belongs to the painter or the musician. Neither the artist nor the mathematician may be able to tell you what constitutes the difference between a significant piece of work and an inflated trifle; but if he is not able to recognise this in his own heart, he is no artist and no mathematician."

— Wiener, Ex-Prodigy

Oye Como Va

Filed under: General — m759 @ 12:00 AM

Steve Winwood Leads Carlos Santana Tribute
at Kennedy Center Honors —

Monday, March 17, 2014


Filed under: General — Tags: — m759 @ 10:09 PM

"It is a very fun happy collection
and I think it is
classic and timeless and elegant."

The late L'Wren Scott,
Vanity Fair , Nov. 20, 2013

Update of 10:30 PM ET —

"I don't want  Santana Abraxas!"

Mellon Posts

Filed under: General — Tags: — m759 @ 3:33 PM

IMAGE- Rachel Mellon, Heiress Known for Garden Designs, Is Dead at 103

Related material: Posts tagged Mellon in this journal, which include
remarks by Jim Holt on "The Devil's Bible" and "Big-Bang Theology."

See as well the New York Times  front page from 1:01 PM ET today.


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

Or: The Confessions of Nat Tate

“A convincing lie is, in its own way, a tiny, perfect narrative.”
— William Boyd, “A Short History of the Short Story” (2006)

“A novel written in the first-person singular has certain powerful
narrative advantages, especially when it takes the form of a ‘confession.'”
— William Boyd, “Memoir of a Plagiarist” (1994)

IMAGE- 'Siri Hustvedt Interview: Fakes and Fiction'

IMAGE- 'Siri Hustvedt Interview: Fakes and Fiction'

From a Log24 post yesterday —

For Little Man Tate —

IMAGE- Wechsler block-design cubes and related WAIS-R manual

Related material — Wechsler in this journal and an earlier Siri Hustvedt
art novel, from 2003 —

Mark and Lucille, Bill and Violet, Al and Regina, etc., etc., etc. —

IMAGE- Siri Hustvedt on the name 'Wechsler' in 'What I Loved'


Filed under: General — m759 @ 12:00 AM

IMAGE- Siri, the Apple personal assistant, as defined at Wikipedia

The name Siri is Norwegian, meaning
‘beautiful woman who leads you to victory.'”

I prefer Josefine.

Sunday, March 16, 2014

Old Jew

Filed under: General — m759 @ 2:25 PM

See also Blockheads (esp. today’s 2 PM post) and
That old Jew gave me this here.”

IMAGE- 'A Flag for Sunrise,' by Robert Stone, p. 373

Blockheads continues

Filed under: General — m759 @ 2:00 PM

For Little Man Tate —

Related material — Wechsler in this journal.

Red to Green continues

Filed under: General — m759 @ 1:00 PM

The New Yorker  of March 17 on
a New York literary family—

“First they were Communists, then liberals
(he was questioned by the House Committee
on Un-American Activities);
always they were avid party-givers.”

“Gatsby believed in the green light… ”
— F. Scott Fitzgerald

“Why did the Pole spend all night outside the whorehouse?
He was waiting for the red light to turn green.”
— Blanche Knott, Truly Tasteless Jokes

Mira Sorvino in a  TV version of  The Great Gatsby 

“Are you my one o’clock?” — Adapted from Mighty Aphrodite

See as well Green Hunt.

Saturday, March 15, 2014

Red to Green

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

Part I:  The New Yorker

Passages from The New Yorker  issue dated March 17, 2014—

"Both autism and psychopathy entail a lack of empathy. Psychologists, though, distinguish between the 'cognitive empathy' deficits of autism (difficulty understanding what emotions are, trouble interpreting other people’s nonverbal signs) and the 'emotional empathy' deficits of psychopathy (lack of concern about hurting other people, an inability to share their feelings). The subgroup of people with neither kind of empathy appears to be small, but such people may act out their malice in ways that can feel both guileless and brutal."  — "The Reckoning," by Andrew Solomon

"The question of what constitutes a story is troublesome." — "Long Story Short," by Dana Goodyear

Part II: The New York Times

Part III:  Log24

Language Game,
Red to Green

Language Game

Filed under: General — Tags: — m759 @ 3:00 PM

Cullinane = Cullinan + e

Greene = Green + e

Greene on Mathematics

Filed under: General,Geometry — Tags: , , — m759 @ 1:20 AM

A reply in the March 8 LA Times  to the opinion piece by Edward Frenkel discussed here yesterday

"It is completely wrong to imply that Euclidean geometry is somehow not interesting because it is old. Actually, Euclidean geometry appeals not only in its intrinsic mathematical nature but also in its power to explain what one sees around one spatially.

If this subject is taught badly, like any other subject it can seem tedious. If it is taught well, it arouses the sense of the intellectual power and attractiveness of mathematical thought as well as or better than anything else that can be presented to a beginner.

One of the points of mathematics educationally is to introduce students to a subject in which precise thought exists. They are surrounded by a world of baloney versions of science. Mathematics is where they find out that really precise thought exists. The last thing they need is to be given the impression that mathematics is another subject in which learning a few buzzwords is the whole show.

Modern mathematics can exist only because older mathematics has existed.

Robert E. Greene

Pacific Palisades

The writer is a professor of mathematics at UCLA."

And several other things too.

Obiter Dicta

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

"I am haunted by humans."
(Search for the source at Google.)

"Art worldlings are one thing, Hollywood another."
(Search for the source at Log24.)

These quotations were suggested by two obits this morning:

Friday, March 14, 2014

Whitewashing Picasso

Filed under: General,Geometry — Tags: , , — m759 @ 4:30 PM

A search today for Edward Frenkel's phrase
"portals into the magic world of modern math"
leads to a reprint of his March 2 LA Times  opinion piece
in The Salem News —

IMAGE- Edward Frenkel in The Salem News

To hell with Picasso, I'll take Tom Sawyer.

The Search for Charles Wallace

Filed under: General — Tags: , — m759 @ 2:19 PM

The search in the previous post for the source of a quotation from Poincaré yielded, as a serendipitous benefit, information on an interesting psychoanalyst named Wilfred Bion (see the Poincaré  quotation at a webpage on Bion). This in turn suggested a search for the source of the name of author Madeleine L'Engle's son Bion, who may have partly inspired L'Engle's fictional character Charles Wallace.  Cynthia Zarin wrote about Bion in The New Yorker  of April 12, 2004 that

"According to the family, he is the person for whom L’Engle’s insistence on blurring fiction and reality had the most disastrous consequences."

Also from that article, material related to the name Bion and to what this journal has called "the Crosswicks Curse"*—

"Madeleine L’Engle Camp was born in 1918 in New York City, the only child of Madeleine Hall Barnett, of Jacksonville, Florida, and Charles Wadsworth Camp, a Princeton man and First World War veteran, whose family had a big country place in New Jersey, called Crosswicks. In Jacksonville society, the Barnett family was legendary: Madeleine’s grandfather, Bion Barnett, the chairman of the board of Jacksonville’s Barnett Bank, had run off with a woman to the South of France, leaving behind a note on the mantel. Her grandmother, Caroline Hallows L’Engle, never recovered from the blow. ….

… The summer after Hugh and Madeleine were married, they bought a dilapidated farmhouse in Goshen, in northwest Connecticut. Josephine, born in 1947, was three years old when they moved permanently to the house, which they called Crosswicks. Bion was born just over a year later."

* "There is  such a thing as a tesseract."


Filed under: General — Tags: , — m759 @ 1:09 PM

Edward Frenkel in a vulgar and stupid
LA Times  opinion piece, March 2, 2014 —

"In the words of the great mathematician Henri Poincare, mathematics is valuable because 'in binding together elements long-known but heretofore scattered and appearing unrelated to one another, it suddenly brings order where there reigned apparent chaos.' "

My attempts to find the source of these alleged words of Poincaré were fruitless.* Others may have better luck.

The search for Poincaré's words did, however, yield the following passage —


If a new result is to have any value, it must unite elements long since known, but till then scattered and seemingly foreign to each other, and suddenly introduce order where the appearance of disorder reigned. Then it enables us to see at a glance each of these elements in the place it occupies in the whole. Not only is the new fact valuable on its own account, but it alone gives a value to the old facts it unites. Our mind is frail as our senses are; it would lose itself in the complexity of the world if that complexity were not harmonious; like the short-sighted, it would only see the details, and would be obliged to forget each of these details before examining the next, because it would- be incapable of taking in the whole. The only facts worthy of our attention are those which introduce order into this complexity and so make it accessible to us.

Mathematicians attach a great importance to the elegance of their methods and of their results, and this is not mere dilettantism. What is it that gives us the feeling of elegance in a solution or a demonstration? It is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. But that is also precisely what causes it to give a large return; and in fact the more we see this whole clearly and at a single glance, the better we shall perceive the analogies with other neighbouring objects, and consequently the better chance we shall have of guessing the possible generalizations. Elegance may result from the feeling of surprise caused by the unlooked-for occurrence together of objects not habitually associated. In this, again, it is fruitful, since it thus discloses relations till then unrecognized. It is also fruitful even when it only results from the contrast between the simplicity of the means and the complexity of the problem presented, for it then causes us to reflect on the reason for this contrast, and generally shows us that this reason is not chance, but is to be found in some unsuspected law. ….


Si un résultat nouveau a du prix, c'est quand en reliant des éléments connus depuis longtemps, mais jusque-là épars et paraissant étrangers les uns aux autres, il introduit subitement l'ordre là où régnait l'apparence du désordre. Il nous permet alors de voir d'un coup d'œil chacun de ces éléments et la place qu'il occupe dans l'ensemble. Ce fait nouveau non-seulement est précieux par lui-même, mais lui seul donne leur valeur à tous les faits anciens qu'il relie. Notre esprit est infirme comme le sont nos sens; il se perdrait dans la complexité du monde si cette complexité n'était harmonieuse, il n'en verrait que les détails à la façon d'un myope et il serait forcé d'oublier chacun de ces détails avant d'examiner le suivant, parce qu'il serait incapable de tout embrasser. Les seuls faits dignes de notre attention sont ceux qui introduisent de l'ordre dans cette complexité et la rendent ainsi accessible.

Les mathématiciens attachent une grande importance à l'élégance de leurs mé-thodes et de leurs résultats; ce n'est pas là du pur dilettantisme. Qu'est ce qui nous donne en effet dans une solution, dans une démonstration, le sentiment de l'élégance? C'est l'harmonie des diverses parties, leur symétrie, leur heureux balancement; c'est en un mot tout ce qui y met de l'ordre, tout ce qui leur donne de l'unité, ce qui nous permet par conséquent d'y voir clair et d'en comprendre l'ensemble en même temps que les détails. Mais précisément, c'est là en même temps ce qui lui donne un grand rendement ; en effet, plus nous verrons cet ensemble clairement et d'un seul coup d'œil, mieux nous apercevrons ses analogies avec d'autres objets voisins, plus par conséquent nous aurons de chances de deviner les généralisations possibles. L'élé-gance peut provenir du sentiment de l'imprévu par la rencontre inattendue d'objets qu'on n'est pas accoutumé à rapprocher; là encore elle est féconde, puisqu'elle nous dévoile ainsi des parentés jusque-là méconnues; elle est féconde même quand elle ne résulte que du contraste entre la simplicité des moyens et la complexité du problème posé ; elle nous fait alors réfléchir à la raison de ce contraste et le plus souvent elle nous fait voir que cette raison n'est pas le hasard et qu'elle se trouve dans quelque loi insoupçonnée. ….

* Update of 1:44 PM ET March 14 — A further search, for "it suddenly brings order," brought order. Words very close to Frenkel's quotation appear in a version of Poincaré's "Future of Mathematics" from a 1909 Smithsonian report

"If a new result has value it is when, by binding together long-known elements, until now scattered and appearing unrelated to each other, it suddenly brings order where there reigned apparent disorder."

Thursday, March 13, 2014

Entartete Kunst

Filed under: General,Geometry — m759 @ 10:00 PM

The title refers to a New York Times  story about
an art exhibition that opened today.

This evening’s NY Lottery numbers:  016 and 2858.

Pictures from these links:

016  (Blackboard Jungle , 1955) —

IMAGE- Blackboard from 'Blackboard Jungle'

 (number of a Log24 post, 2007) —


Filed under: General — m759 @ 12:00 PM

A Presbyterian meditation —

A scene from the film of the above book —

“Looking carefully at Golay’s code is like staring into the sun.”

Richard Evan Schwartz

For more of the story, see Golay in this journal.

Completing the Supersquare

Filed under: General — m759 @ 10:00 AM

Presbyterian elder Reubin Askew was called “Jesus Christ Supersquare”
after completing his first year as governor of Florida—

IMAGE- Reubin Askew was called 'Jesus Christ Supersquare' after completing his first year as governor of Florida.

Now Askew has completed his life.

See also other instances of “Super” in this journal.

Update of 10:30 AM March 13 —

For those who like puzzles, here is yet another
instance of “Super,” this one related to the pattern
in last evening’s post Obiter Dictum —

IMAGE- Rubik 'Supercube' with nine triangular half-squares on each face

Wednesday, March 12, 2014

Obiter Dictum

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

The title is both a legal phrase and a phrase
used by Tom Wolfe in his writings on art.

See, too, the pattern of nine triangular half-squares
arranged in a 3×3 square used in the logo of  the
Jean Stephen art galleries in Minneapolis…

IMAGE - Former location of Jean Stephen art galleries

… and in a print at the Tate in London  (click to enlarge)—

See as well an obit of the print’s artist, Justin Knowles, who reportedly died
on Feb. 24, 2004.

Some instances of that date in this journal are related to Knowles’s aesthetics.

Art Wars

Filed under: General — m759 @ 7:00 PM

Frederick Hart’s 1982 sculpture “Ex Nihilo” for Washington’s National Cathedral—

Related material — Tom Wolfe on Frederick Hart, said to have been
published in The New York Times Magazine  of Sunday, Jan. 2, 2000—

In 1982, Ex Nihilo  was unveiled in a dedication ceremony. The next day, Hart scanned the newspapers for reviews… The Washington PostThe New York Times… nothing… nothing the next day, either… nor the next week… nor the week after that. The one mention of any sort was an obiter dictum in The Post ‘s Style (read: Women’s) section indicating that the west facade of the cathedral now had some new but earnestly traditional (read: old-fashioned) decoration. So Hart started monitoring the art magazines. Months went by… nothing. It reached the point that he began yearning for a single paragraph by an art critic who would say how much he loathed Ex Nihilo… anything, anything at all!… to prove there was someone out there in the art world who in some way, however slightly or rudely, cared.

The truth was, no one did, not in the least. Ex Nihilo  never got ex nihilo  simply because art worldlings refused to see it.

Art worldings are one thing, Hollywood another.

Al Pacino’s moving wall sculpture in “The Devil’s Advocate” (1997)—

“After the film’s initial release, sculptor Frederick Hart sued Warner Bros.
claiming that a large sculpture prominently featured in the film
(on the wall of Al Pacino’s penthouse apartment) is an unauthorized copy
of his work ‘Ex Nihilo,’ displayed at the entrance of Washington’s Episcopal
National Cathedral.” — IMDb

Tuesday, March 11, 2014

Dark Fields of the Republic

Filed under: General,Geometry — Tags: , — m759 @ 10:00 PM

This post was suggested by today's previous post, Depth,
by Plato's Diamond, and by Rebecca Newberger Goldstein's
recent fanciful fiction about Plato.

Plato, Republic , Book II, Paul Shorey translation at Perseus

“Consider,” [382a] said I; “would a god wish to deceive, or lie, by presenting in either word or action what is only appearance?” “I don’t know,” said he. “Don’t you know,” said I, “that the veritable lie, if the expression is permissible, is a thing that all gods and men abhor?” “What do you mean?” he said. “This,” said I, “that falsehood in the most vital part of themselves, and about their most vital concerns, is something that no one willingly accepts, but it is there above all that everyone fears it.” “I don’t understand yet either.” “That is because you suspect me of some grand meaning,” [382b] I said; “but what I mean is, that deception in the soul about realities, to have been deceived and to be blindly ignorant and to have and hold the falsehood there, is what all men would least of all accept, and it is in that case that they loathe it most of all.” “Quite so,” he said.

Related material —

A meditation from the Feast of St. Francis, 2012 —

A post from Sept. 30, 2012, the reported date of  death
for British children's author Helen Nicoll —

The New Criterion  on the death of Hilton Kramer —

This uncredited translation of Plato is, Google Books tells us,
by "Francis MacDonald Cornfield."  The name is an error,
but the error is illuminating —

Signs Movie Stills: Mel Gibson, Joaquin Phoenix, Patricia Kalember, M. Night Shyamalan


Filed under: General,Geometry — Tags: , — m759 @ 11:16 AM

"… this notion of ‘depth’ is an elusive one
even for a mathematician who can recognize it…."

— G. H. Hardy,  A Mathematician's Apology

Part I:  An Inch Deep

IMAGE- Catch-phrase 'a mile wide and an inch deep' in mathematics education

Part II:  An Inch Wide

See a search for "square inch space" in this journal.

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison


See also recent posts with the tag depth.

Monday, March 10, 2014

Strategic Hamlets

Filed under: General,Geometry — m759 @ 10:00 PM

From an obituary for a Kennedy advisor
who reportedly died at 94 on February 23, 2014*—

“He favored withdrawing rural civilians
into what he called ‘strategic hamlets’
and spraying defoliants to cut off
the enemy’s food supply.”

Other rhetoric:  Hamlet and Infinite Space  in this journal,
as well as King of Infinite Space , Part I and Part II.

These “King” links, to remarks on Coxeter  and  Saniga ,
are about two human beings to whom Hamlet’s
phrase “king of infinite space” has been applied.

The phrase would, of course, be more accurately
applied to God.

* The date of the ‘God’s Architecture’ sermon
at Princeton discussed in this afternoon’s post.

God’s Architecture

Filed under: General — m759 @ 1:19 PM

Part I:

The sermon, “God’s Architecture,” at Nassau Presbyterian
Church in Princeton on Sunday, Feb. 23, 2014.  (This is the
“sermon” link in last Sunday’s 11 AM ET Log24 post.)

An excerpt:

“I wonder what God sees when God looks at our church.
Bear with me here because I’d like to do a little architectural
redesign. I look up at our sanctuary ceiling and I see buttons.
In those large round lights, I see buttons. I wonder what would
happen if we unbutton the ceiling, Then I wonder if we were to
unzip the ceiling, pull back the rooftop, and God were to look in
from above – What does God see? What pattern, what design,
what shape takes place?” — Rev. Lauren J. McFeaters

Related material —  All About Eve: 

A. The Adam and Eve sketch from the March 8 “Saturday Night Live”

B. “Katniss, get away from that tree!” —

C. Deconstructing God in last evening’s online New York Times .

Part II:

Heavensbee!” in the above video, as well as Cartier’s Groundhog Day
and Say It With Flowers.

Part III:

Humans’  architecture, as described (for instance) by architecture
theorist Anne Tyng, who reportedly died at 91 on Dec. 27, 2011.
See as well Past Tense and a post from the date of Tyng’s death.

Sunday, March 9, 2014

The Story Creeps Up

Filed under: General,Geometry — Tags: — m759 @ 11:01 PM

For Women’s History Month —

Conclusion of “The Storyteller,” a story
by Cynthia Zarin about author Madeleine L’Engle—

See also the exercise on the Miracle Octad Generator (MOG) at the end of
the previous post, and remarks on the MOG by Emily Jennings (non -fiction)
on All Saints’ Day, 2012 (the date the L’Engle quote was posted here).

Hesse’s Table

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

From “Quartic Curves and Their Bitangents,” by
Daniel Plaumann, Bernd Sturmfels, and Cynthia Vinzant,
arXiv:1008.4104v2  [math.AG] 10 Jan 2011 —

The table mentioned (from 1855) is…

Exercise: Discuss the relationship, if any, to
the Miracle Octad Generator of R. T. Curtis.

At Play in the Fields of Brazil

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

From Facebook, a photo from the Feast of St. Francis, 2013:

Neantro Saavedra-Rivano, author of the 1976 paper  “Finite
Geometries in the Theory of Theta Characteristics,”  in Brasilia—

On the same date, art from Inception  and from Diamonds Studio
in Brazil —


Filed under: General,Geometry — Tags: , — m759 @ 11:00 AM

On Theta Characteristics
IMAGE- Saavedra-Rivano, 'Finite Geometries in the Theory of Theta Characteristics' (1976)

— From Zentralblatt-math.org.  8 PM ET update:  See also a related search.

IMAGE- Saavedra-Rivano, Ph.D. U. de Paris 1972, advisor Grothendieck

Some may prefer a more politically correct— and simpler— sermon.

Background for the simpler sermon: Quilt Geometry.

Saturday, March 8, 2014

Women’s History Month

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

For the Princeton Class of 1905 —

Joyce Carol Oates Meets Emily Dickinson.

Oates —

"It is an afternoon in autumn, near dusk.
The western sky is a spider’s web of translucent gold.
I am being brought by carriage—two horses—
muted thunder of their hooves—
along narrow country roads between hilly fields
touched with the sun’s slanted rays,
to the village of Princeton, New Jersey.
The urgent pace of the horses has a dreamlike air,
like the rocking motion of the carriage;
and whoever is driving the horses
his face I cannot see, only his back—
stiff, straight, in a tight-fitting dark coat."

Dickinson —

"Because I could not stop for Death—
He kindly stopped for me—
The Carriage held but just Ourselves—
And Immortality."

Conwell Heptads in Eastern Europe

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

“Charting the Real Four-Qubit Pauli Group
via Ovoids of a Hyperbolic Quadric of PG(7,2),”
by Metod Saniga, Péter Lévay and Petr Pracna,
arXiv:1202.2973v2 [math-ph] 26 Jun 2012 —

P. 4— “It was found that +(5,2) (the Klein quadric)
has, up to isomorphism, a unique  one — also known,
after its discoverer, as a Conwell heptad  [18].
The set of 28 points lying off +(5,2) comprises
eight such heptads, any two having exactly one
point in common.”

P. 11— “This split reminds us of a similar split of
63 points of PG(5,2) into 35/28 points lying on/off
a Klein quadric +(5,2).”

[18] G. M. Conwell, Ann. Math. 11 (1910) 60–76

A similar split occurs in yesterday’s Kummer Varieties post.
See the 63 = 28 + 35 vectors of R8 discussed there.

For more about Conwell heptads, see The Klein Correspondence,
Penrose Space-Time, and a Finite Model

For my own remarks on the date of the above arXiv paper
by Saniga et. al., click on the image below —

Walter Gropius

Friday, March 7, 2014

Field Dream

Filed under: General — m759 @ 7:11 PM

A field in China —

IMAGE- Chinese field from opening of TV series 'Resurrection'

The following link was suggested by today’s previous post
and by the ABC TV series “Resurrection” scheduled to start
at 9 PM ET Sunday, March 9, 2014 —

Field Dream

Kummer Varieties

Filed under: General,Geometry — Tags: , , — m759 @ 11:20 AM

The Dream of the Expanded Field continues

Image-- The Dream of the Expanded Field

From Klein's 1893 Lectures on Mathematics —

"The varieties introduced by Wirtinger may be called Kummer varieties…."
E. Spanier, 1956

From this journal on March 10, 2013 —

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
"The Universal Kummer Threefold," by
Qingchun Ren, Steven V Sam, Gus Schrader, and Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Update of 10 PM ET March 7, 2014 —

The following slides by one of the "Kummer Threefold" authors give
some background related to the above 64-point vector space and
to the Weyl group of type E7(E7):

The Cayley reference is to "Algorithm for the characteristics of the
triple ϑ-functions," Journal für die Reine und Angewandte
Mathematik  87 (1879): 165-169. <http://eudml.org/doc/148412>.
To read this in the context of Cayley's other work, see pp. 441-445
of Volume 10 of his Collected Mathematical Papers .

Thursday, March 6, 2014

ART WARS (continued)

Filed under: General — m759 @ 7:04 PM

See “But is it Art?,” linked to here and here

The Old Well*

Filed under: General — m759 @ 12:00 PM

See posts tagged The Well.

Related material:  Artist Joseph Kosuth, who pictured
the dictionary definition of “nothing” shown in the index of
today’s LA Times  obituaries, and a Chinese film director,
one of those portrayed in that index.

Also mentioned on the obituaries index page —

IMAGE- Leonard Knight, Salvation Mountain, Niland, CA

See as well  The Church of the Holy Hubcap.

* Film title, translation of Chinese: 老井; pinyin: lǎo jǐng.

Wednesday, March 5, 2014

Rosenhain and Göpel Again

Filed under: General — Tags: , — m759 @ 8:25 PM

IMAGE- Rosenhain, Göpel, and hyperelliptic curves

See also Rosenhain and Göpel in the Wikipedia
article Kummer surface, and in this journal.

Related material: user @hyperelliptic on Twitter.

The Good Earth

Filed under: General — m759 @ 2:00 PM

In Beijing, it is now 3 AM on March 6,
the dies natalis  of St. Pearl Buck.

(Click to enlarge.)

IMAGE- Chiang Yee on the ninefold square and Chinese calligraphy

Holy Hub Caps

Filed under: General — m759 @ 12:00 PM

Review of Joseph Campbell's The Inner Reaches of Outer Space

The reviewer compares Campbell to "one of those guys who
builds his own church out of hub caps."

A simple hub cap — see ninefold  in this journal.

Tuesday, March 4, 2014


Filed under: General — m759 @ 6:00 PM


“Alles wird viel einfacher, wenn man zuerst von der
Unendlichkeit der Theilbarkeit abstrahirt und bloss
Discrete Grössen betrachtet.”

Carl Friedrich Gauss in 1825

(Quoted here in the July 16, 2013, post Child Buyers.)

This Just In

Filed under: General — m759 @ 3:31 PM

The Ten

Filed under: General — m759 @ 10:00 AM

Marissa Mayer Says Cheese.

Related material:  The previous post and  Cheesy Consolation Prize .

The Crimson Passion…

Filed under: General — m759 @ 9:00 AM


Amy Adams as…

The $146 Million Domestic


Filed under: General — m759 @ 8:00 AM

"Mr. Kaplan, you are quite the performer."


Filed under: General — m759 @ 12:00 AM

"… in Speedtalk it was… difficult not  to be logical."

— Robert A. Heinlein in Gulf 

Related material: ABC TV at 9 PM ET
on Sunday, March 9, 2014… 3/09.

See also page  309 in the previous post, Outside the Box.

Shades of Plan 9.

Monday, March 3, 2014

Outside the Box

Filed under: General — m759 @ 10:00 PM

IMAGE- Page 309 in 'Studies in the Logic of Charles Sanders Peirce'

Click for related material.

Language Game

Filed under: General — m759 @ 9:00 PM

Mystic Pizza:  See Ellen and Pizza.

Blackboard Jungle Revisited

Filed under: General,Geometry — m759 @ 10:00 AM

IMAGE- Blackboard from 'Blackboard Jungle'

Blackboard Jungle , 1955

"We are going to keep doing this
until we get it right." — June 15, 2007

"Her wall is filled with pictures,
she gets 'em one by one" — Chuck Berry

See too a more advanced geometry lesson
that also uses the diagram pictured above.

Sunday, March 2, 2014

Square Dance

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

From The Telegraph  today

And no fact of Alain Resnais’s life seemed to strike a stranger note than his assertion that the films which first inspired his ambition to become a film director were those in which Fred Astaire and Ginger Rogers danced. Or was it Dick Powell and Ruby Keeler? He could never be sure. “I wondered if I could find the equivalent of that exhilaration,” he recalled.

If he never did it was perhaps because of his highly cultivated attitude to serious cinema. His character and temperament were more attuned to the theory of film and a kind of intellectual square dance* which was far harder to bring to the screen with “exhilaration” than the art of Astaire and Rogers.

*See today's 11 AM ET Sermon.

"Heaven, I'm in Heaven!"

Happy Oscar Day

Filed under: General — Tags: — m759 @ 12:18 PM

Plato Thanks the Academy…

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


… With a trip to yesteryear suggested by
the Feb. 28 New York Times  article 
"Casting Shadows on a Fanciful World"

("Wes Anderson Evokes Nostalgia in 
'The Grand Budapest Hotel' ").


Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

Raiders of the Lost  (Continued)

"Socrates: They say that the soul of man is immortal…."

From August 16, 2012

In the geometry of Plato illustrated below,
"the figure of eight [square] feet" is not ,  at this point
in the dialogue, the diamond in Jowett's picture.

An 1892 figure by Jowett illustrating Plato's Meno

A more correct version, from hermes-press.com —

Socrates: He only guesses that because the square is double, the line is double.Meno: True.


Socrates: Observe him while he recalls the steps in regular order. (To the Boy.) Tell me, boy, do you assert that a double space comes from a double line? Remember that I am not speaking of an oblong, but of a figure equal every way, and twice the size of this-that is to say of eight feet; and I want to know whether you still say that a double square comes from double line?

[Boy] Yes.

Socrates: But does not this line (AB) become doubled if we add another such line here (BJ is added)?

[Boy] Certainly.

Socrates: And four such lines [AJ, JK, KL, LA] will make a space containing eight feet?

[Boy] Yes.

Socrates: Let us draw such a figure: (adding DL, LK, and JK). Would you not say that this is the figure of eight feet?

[Boy] Yes.

Socrates: And are there not these four squares in the figure, each of which is equal to the figure of four feet? (Socrates draws in CM and CN)

[Boy] True.

Socrates: And is not that four times four?

[Boy] Certainly.

Socrates: And four times is not double?

[Boy] No, indeed.

Socrates: But how much?

[Boy] Four times as much.

Socrates: Therefore the double line, boy, has given a space, not twice, but four times as much.

[Boy] True.

Socrates: Four times four are sixteen— are they not?

[Boy] Yes.

As noted in the 2012 post, the diagram of greater interest is
Jowett's incorrect  version rather than the more correct version
shown above. This is because the 1892 version inadvertently
illustrates a tesseract:

A 4×4 square version, by Coxeter in 1950, of  a tesseract

This square version we may call the Galois  tesseract.

Saturday, March 1, 2014


Filed under: General,Geometry — m759 @ 10:30 PM

IMAGE- Josefine Lyche changes her Facebook cover photo to a form of the Tetragrammaton.

From New World Encyclopedia —

See also Tetragrammaton in this journal.

For further context, see Solomon's Cube and Oct. 16, 2013.

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