Geometer H. S. M. Coxeter died on this date in 2003.
Monday, March 31, 2014
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.
Part I: The Burden of Proof —
Part II: The Story of Noam —
* See The Fountain in “The Story Theory of Truth,” Columbus Day, 2013
“…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
Click image for the backstory.
The sermon itself is not yet on line.
Perhaps the following will help.
Two timely images for Oslo artist Josefine Lyche —
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.
(Updated through 10 AM ET)
Saturday, March 29, 2014
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.
“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
For LYNX 760 —
For more beauty and strangeness, see Strange McEntire.
“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
— Andreas Schöter’s I Ching home page
” ‘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
“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
The title is suggested by a new novel (see cover below),
and by an unwritten book by Nabokov —
- An artists’ book scheduled to be released on March 21, 2014
- A piece by Josefine Lyche in the artists’ book
- The original by Borges on which Lyche’s piece was based
- A solar image from a March 13 post echoing
that on the Blazing World cover above
- A Tune for Josefine
- The circular blazing image from last midnight’s post Symbol
- From March 21, the scheduled date of the Oslo
artists’ book release, some remarks on the mathematics of the
Golay code, “Three Constructions of the Miracle Octad Generator“
- Backstory: Duelle in this journal.
Thursday, March 27, 2014
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.)
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:
Click to enlarge.
Wednesday, March 26, 2014
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.
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.
Tuesday, March 25, 2014
“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).
Sunday, March 23, 2014
Saturday, March 22, 2014
Friday, March 21, 2014
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.
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 —
Thursday, March 20, 2014
Wednesday, March 19, 2014
“Behold the handmaid of the Lord.”
“No. You’re dead, this is heaven,
and I’m the Virgin Mary.”
(Costume design by L’Wren Scott)
Tuesday, March 18, 2014
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
Steve Winwood Leads Carlos Santana Tribute
at Kennedy Center Honors —
Monday, March 17, 2014
“It is a very fun happy collection
and I think it is
classic and timeless and elegant.”
Update of 10:30 PM ET —
“I don’t want Santana Abraxas!”
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.
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)
From a Log24 post yesterday —
For Little Man Tate —
Mark and Lucille, Bill and Violet, Al and Regina, etc., etc., etc. —
“The name Siri is Norwegian, meaning
‘beautiful woman who leads you to victory.'”
I prefer Josefine.
Sunday, March 16, 2014
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
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
“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
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."
Thursday, March 13, 2014
Pictures from these links:
016 (Blackboard Jungle , 1955) —
2858 (number of a Log24 post, 2007) —
A Presbyterian meditation —
A scene from the film of the above book —
“Looking carefully at Golay’s code is like staring into the sun.”
For more of the story, see Golay in this journal.
Presbyterian elder 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 —
Wednesday, March 12, 2014
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…
… 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.
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 Post… The 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
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 —
The New Criterion on the death of Hilton Kramer —
"… 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
Part II: An Inch Wide
See a search for "square inch space" in this journal.
See also recent posts with the tag depth.
Monday, March 10, 2014
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.”
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.
“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”
C. Deconstructing God in last evening’s online New York Times .
Sunday, March 9, 2014
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).
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.
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 Theta Characteristics
Some may prefer a more politically correct— and simpler— sermon.
Background for the simpler sermon: Quilt Geometry.
Saturday, March 8, 2014
“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.”
“Because I could not stop for Death—
He kindly stopped for me—
The Carriage held but just Ourselves—
“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 Q +(5,2) (the Klein quadric)
has, up to isomorphism, a unique one — also known,
after its discoverer, as a Conwell heptad .
The set of 28 points lying off Q +(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 Q +(5,2).”
 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 —
Friday, March 7, 2014
A field in China —
The Dream of the Expanded Field continues…
From Klein’s 1893 Lectures on Mathematics —
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 —
Two such considerations —
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, W (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
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 —
See as well The Church of the Holy Hubcap.
* Film title, translation of Chinese: 老井; pinyin: lǎo jǐng.
Wednesday, March 5, 2014
Related material: user @hyperelliptic on Twitter.
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
“Alles wird viel einfacher, wenn man zuerst von der
Unendlichkeit der Theilbarkeit abstrahirt und bloss
Discrete Grössen betrachtet.”
(Quoted here in the July 16, 2013, post Child Buyers.)
"… 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
Blackboard Jungle , 1955
"We are going to keep doing this
until we get it right." — June 15, 2007
See too a more advanced geometry lesson
that also uses the diagram pictured above.
Sunday, March 2, 2014
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.
("Wes Anderson Evokes Nostalgia in
'The Grand Budapest Hotel' ").
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.
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?
Socrates: But does not this line (AB) become doubled if we add another such line here (BJ is added)?
Socrates: And four such lines [AJ, JK, KL, LA] will make a space containing eight feet?
Socrates: Let us draw such a figure: (adding DL, LK, and JK). Would you not say that this is the figure of eight feet?
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)
Socrates: And is not that four times four?
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.
Socrates: Four times four are sixteen— are they not?
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:
This square version we may call the Galois tesseract.