"When it comes down to it,
I think we all just want
to love and be loved."
Friday, May 31, 2013
"When it comes down to it,
A meditation on this morning's New York Times obituaries:
Happy birthday to jazz pianist Clint Eastwood.
Thursday, May 30, 2013
Yesterday, May 29, was JFK's birthday.
The above is a belated quotation for that occasion.
Click on the quotation for truth instead of rhetoric.
Tuesday, May 28, 2013
The hypercube model of the 4-space over the 2-element Galois field GF(2):
The phrase Galois tesseract may be used to denote a different model
of the above 4-space: the 4×4 square.
MacWilliams and Sloane discussed the Miracle Octad Generator
(MOG) of R. T. Curtis further on in their book (see below), but did not
seem to realize in 1977 that the 4×4 structures within the MOG are
based on the Galois-tesseract model of the 4-space over GF(2).
The thirty-five 4×4 structures within the MOG:
Curtis himself first described these 35 square MOG patterns
combinatorially, (as his title indicated) rather than
algebraically or geometrically:
A later book co-authored by Sloane, first published in 1988,
did recognize the 4×4 MOG patterns as based on the 4×4
Between the 1977 and 1988 Sloane books came the diamond theorem.
Update of May 29, 2013:
The Galois tesseract appeared in an early form in the journal
Computer Graphics and Art , Vol. 2, No. 1, February 1977
(the year the above MacWilliams-Sloane book was first published):
A May 27, 2013, Washington Post story by Ellen Nakashima:
From Ayn Sof (January 7, 2011):
"You're gonna need a bigger boat." — Roy Scheider in Jaws
"We're gonna need more holy water." — Season of the Witch
Liam Neeson (right) and Taylor Kitsch
Sunday, May 26, 2013
A phrase in the news recently,
"la métaphysique de l'illimité ,"
suggests a search for related material.
Found: The discussion of the metaphysics of the limitless
in Chapter Two, "The Quest: Philebus ," of Plato and the Good:
Illuminating the Darkling Vision , by Rosemary Desjardins.
See, too, the Log24 post Ayn Sof of January 7, 2011,
and A Document in Madness :
* The title is from the 2011 film version of
the 2001 novel The Dark Fields .
Thursday, May 23, 2013
These stories suggest a meditation by Kierkegaard
and some related remarks from July 2, 2009.
Wednesday, May 22, 2013
"The final ingredient of the design conception
was its most important and its most dangerous…."
Starring Michael Douglas:
Happy Birthday, Mary Shelley (August 30, 2003)
Tuesday, May 21, 2013
Related narratives— Get Quotes (source of image below)
Monday, May 20, 2013
This post is continued from "Church Narrative," a Log24 post of November 17, 2010.
In memory of Ray Manzarek, remarks from a different weblog on that same date:
Click images for details.
Seth and Stefon, eat your hearts out.
Sunday, May 19, 2013
Best vs. Bester
The previous post ended with a reference mentioning Rosenhain.
For a recent application of Rosenhain's work, see
Desargues via Rosenhain (April 1, 2013).
From the next day, April 2, 2013:
"The proof of Desargues' theorem of projective geometry
comes as close as a proof can to the Zen ideal.
It can be summarized in two words: 'I see!' "
– Gian-Carlo Rota in Indiscrete Thoughts (1997)
Also in that book, originally from a review in Advances in Mathematics ,
Vol. 84, Number 1, Nov. 1990, p. 136:
From an arXiv preprint submitted July 18, 2011,
and last revised on March 11, 2013 (version 4):
"By our construction, this vector space is the dual
of our hypercube F24 built on I \ O9. The vector space
structure of the latter, to our knowledge, is first
mentioned by Curtis in [Cur89]. Hence altogether
our proposition 2.3.4 gives a novel geometric
meaning in terms of Kummer geometry to the known
vector space structure on I \ O9."
R. T. Curtis, "Further elementary techniques using
the miracle octad generator," Proc. Edinburgh
Math. Soc. 32 (1989), 345-353 (received on
July 20, 1987).
— Anne Taormina and Katrin Wendland,
"The overarching finite symmetry group of Kummer
surfaces in the Mathieu group M 24 ,"
arXiv.org > hep-th > arXiv:1107.3834
"First mentioned by Curtis…."
No. I claim that to the best of my knowledge, the
vector space structure was first mentioned by me,
Steven H. Cullinane, in an AMS abstract submitted
in October 1978, some nine years before the
Update of the above paragraph on July 6, 2013—
No. The vector space structure was described by
The vector space structure as it occurs in a 4×4 array
See Notes on Finite Geometry for some background.
See in particular The Galois Tesseract.
For the relationship of the 1978 abstract to Kummer
geometry, see Rosenhain and Göpel Tetrads in PG(3,2).
Saturday, May 18, 2013
A followup to last midnight's Black Hole Revisited .
See also Victor Turner on liminality, together with Paul Goodman
on public squares, in a post of May 8, 2007.
Related material: Midnight in Dostoevsky (St. Andrew's Day, 2009).
The following sequence of images was suggested by
Peter Woit's May 16 post "One Ring to Rule Them All."
Also from Devil's Night 2008:
From the May 16 Nobel Symposium talk discussed in
Woit's "One Ring to Rule Them All":
All Souls' Day at the Still Point (Nov. 2, 2003) and
Frodo and the Oxford Murders (Oct. 13, 2011).
Wednesday, May 15, 2013
From a reported interview with Terry Gilliam:
Question: "You said in an interview that The Zero Theorem
was very influenced by Bucharest. In what way?"
Some related material from Log24:
See also a Google search from this evening—
— and the beginning of the Zero Theorem screenplay —
A rim of swirling light appears, circling helplessly into a
gigantic BLACK HOLE. It spirals inward…
Tuesday, May 14, 2013
See Coxeter + Aleph in this journal.
Epigraph to "The Aleph," a 1945 story by Borges:
"O God! I could be bounded in a nutshell,
and count myself a King of infinite space…"
– Hamlet, II, 2
Detail from the video in the previous post:
For other permutations of points in the
order-3 affine plane—
(Continued from December 30, 2012)
"And let us finally, then, observe the
parallel progress of the formations of thought
across the species of psychical onomatopoeia
of the primitives, and elementary symmetries
and contrasts, to the ideas of substances,
to metaphors, the faltering beginnings of logic,
formalisms, entities, metaphysical existences."
— Paul Valéry, Introduction to the Method of
Leonardo da Vinci
But first, a word from our sponsor…
Brought to you by two uploads, each from Sept. 11, 2012—
Monday, May 13, 2013
For the late Bob Stewart:
"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'"
Translation Studies Continued:
See Cameron's Kernel and…
"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'*
These appearances had a fitting symmetry:
It was as a game-show contestant that Dr. Brothers
had received her first television exposure."
— Margalit Fox in this evening's online New York Times
"So we moved, and they, in a formal pattern"
— Four Quartets
Sunday, May 12, 2013
Click on the above image for the April 14 webpage.
Saturday, May 11, 2013
The title is from today's noon post, Core.
It also appears, quoted from Popovič, in Susan Bassnett's
Translation Studies (third edition, Routledge, 2002)—
"It is an established fact in Translation Studies that if a dozen
translators tackle the same poem, they will produce a dozen
different versions. And yet somewhere in those dozen versions there
will be what Popovič calls the ‘invariant core’ of the original poem.
This invariant core, he claims, is represented by stable, basic and
constant semantic elements in the text, whose existence can be
proved by experimental semantic condensation. Transformations, or
variants, are those changes which do not modify the core of meaning
but influence the expressive form. In short, the invariant can be
defined as that which exists in common between all existing
translations of a single work. So the invariant is part of a dynamic
relationship and should not be confused with speculative arguments
about the ‘nature’, the ‘spirit’ or ‘soul’ of the text; the ‘indefinable
quality’ that translators are rarely supposed to be able to capture."
"A writer hopes to leave behind a work no one forgets…."
— André Weil, The Apprenticeship of a Mathematician
nam unguentum dabo, quod meae puellae
donarunt Veneres Cupidinesque….
— Catullus, quoted in Bassnett's Translation Studies
Promotional description of a new book:
"Like Gödel, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking."
"Like Gödel, Escher, Bach before it…."
Or like Metamagical Themas .
Non- Rubik cores:
Of the odd nxnxn cube:
Of the even nxnxn cube:
Related material: The Eightfold Cube and…
"A core component in the construction
is a 3-dimensional vector space V over F2 ."
"Publication Date: April 23, 2013
James Blish called him the “finest conscious artist
science fiction ever produced.” Kurt Vonnegut based
the famous character Kilgore Trout on him. And
such luminaries as Harlan Ellison, Stephen King, and
Octavia Butler have hailed him as a mentor.
Theodore Sturgeon was both a popular favorite and
a writer’s writer…."
A writers' writer's writer:
"A writer's writer, Mrs. Le Guin
brings reality itself to the proving ground."
* Shakespeare's birthday, April 23
Friday, May 10, 2013
How long it will stay there remains to be seen.
Thursday, May 9, 2013
Well, the essence of history is story ,
and a good story is an end in itself."
— Barry Mazur, "History of Mathematics as a tool,"
February 17, 2013
This journal on February 17, 2013:
See also today's previous post.
Click a course description below for some related material.
Wednesday, May 8, 2013
From February 24, 2005:
Tuesday, May 7, 2013
Or: Ready When You Are, C. B.
Dennis McLellan, Special to The Los Angeles Times , May 7, 2013:
Born in Los Angeles on June 29, 1920, Harryhausen was 13
when he saw "King Kong" during its run at Grauman's Chinese
Theater in Hollywood.
"I haven't been the same since," he is repeatedly quoted
as saying over the years.
"I came out of the theater awestruck," Harryhausen elaborated
in a 1999 interview with the Chicago Tribune. "It was such a
totally different, unusual film. The story line led you from the
mundane world into the most outrageous fantasy that's ever
been put on the screen."
For Jerusalem Day
"There are interesting correspondences between
Jewish Kabbala, Torah, and Talmud, and
Chinese Buddhism and Taoism…."
See also Chinese Checkers in this journal.
Sunday, May 5, 2013
Structure vs. Character continued…
* The title is from Heidegger.
Saturday, May 4, 2013
From yesterday’s post “Structure“—
A meditation on today’s New York Times obituaries:
“… Reality is not a given whole. An understanding of this,
a respect for the contingent, is essential to imagination
as opposed to fantasy. Our sense of form, which is an
aspect of our desire for consolation, can be a danger to
our sense of reality as a rich receding background.
Against the consolations of form, the clean crystalline
work, the simplified fantasy-myth, we must pit the
destructive power of the now so unfashionable naturalistic
idea of character.
Real people are destructive of myth, contingency is
destructive of fantasy and opens the way for imagination.
Think of the Russians, those great masters of the contingent.
Too much contingency of course may turn art into journalism.
But since reality is incomplete, art must not be too much
afraid of incompleteness. Literature must always represent a
battle between real people and images; and what it requires
now is a much stronger and more complex conception of the
— Iris Murdoch, January 1961, “Against Dryness”
Friday, May 3, 2013
For the Church of St. Frank:
Thursday, May 2, 2013
For the Church of St. Frank:
Now that Frank Kermode is gone, perhaps the phrase suits Frank Langella.
Some related reflections on character:
Wednesday, May 1, 2013
"Winfrey will speak on May 30 during Commencement day’s
Afternoon Exercises, which serve as the annual meeting of
the Harvard Alumni Association. The exercises will take place
in the Tercentenary Theatre of Harvard Yard,
between Memorial Church and Widener Library."
On the 1977 Octavia Butler novel Mind of My Mind :
"The first chapter in a history that Butler has already taken up
at a much later stage in Patternmaster (1976).
Mind of My Mind begins with Doro, a ruthless mutant
as old as the pyramids who has spent the last 4,000 years
trying to breed a race in his own image. The culminating
experiment is his daughter Mary. But, to Doro's astonishment,
Mary's first instinct on attaining her full powers is to begin
building a mental community— a Pattern— out of the
wretched thousands of Doro's half-telepathic failures
and partial successes. Despite some ragged moments,
Butler is clearly on to a promising vein— something like
Zenna Henderson's 'People' stories without their
saccharine silliness. There's a lot of intrinsic energy in the
Pattern idea, and one wants to see where this erratic, gifted
storyteller will pick it up next."
— Kirkus Reviews , Vol. XLV, No. 8 (1977), p. 453.
Those who prefer Eastern approaches to religion may consult
Robert Thurman and his daughter Uma.
"Oprah, Uma. Uma, Oprah." — David Letterman