"In Princeton every Sunday he would walk
one and a half miles from his home to buy
the Sunday New York Times , and so,
according to his daughters, his church
denomination was pedestrian."
— "André Weil As I Knew Him," by Goro Shimura,
Notices of the American Mathematical Society ,
Vol. 46, No. 4, April 1999, page 430
The above passage was suggested by
a reported death from July 9, 2013, and by
a photo taken by Trish Mayo on July 6,
2013. See also Log24 on that date.
See also 11 February 2012 in this journal, as well as the link in
last evening's post to 2 March 2012, in the context of synchronicity.
You say goodbye, I say …
A YouTube video uploaded on March 2, 2012—
This journal on the date of the above video's uploading— March 2, 2012:
"…des carreaux mi-partis de deux couleurs par une ligne diagonale…."
See also Josefine Lyche in Vril Chick and Bowling in Diagon Alley.
From a Telegraph obituary about a death on July 8, 2013:
"The pilots’ tactic was to fly to within a certain distance of the target, and cut their engines. They would then glide in silently, release their bombs, then restart their engines and fly home. The Germans called them the 'Nachthexen' (the Night Witches) due to the whooshing sound they made— 'like a witch’s broomstick in the night'— as they flew past. There was, supposedly, a promise to award an Iron Cross to any Luftwaffe pilot who actually managed to bring down a Night Witch."
In memoriam:
"At some point in Greek history, it was noticed that the capital upsilon—Y—
looked like a path branching left and right. The comparison, like so much
traditional material, was ascribed to the Pythagoreans, in accordance with
the dualism just mentioned; our earliest source for it, however, is as late as
the Roman poet Persius (Satires, 3.56)."
— "The Garden of Forking Paths" in the weblog
Varieties of Unreligious Experience, Nov. 21, 2006
Amy Adams at the Lancia Café in Taormina, Sicily, on June 15, 2013.
Adams was in Taormina for the Italian premiere of her Superman film.
See also this journal on that date— June 15, 2013.
Posts related to the Garden of Forking Paths: Witch Ball (Jan. 24, 2013),
Sermon for Harvard (Sept. 19, 2010), and Amy Adams + Craft.
Related material from June 3, 2008 …
On Faith:
“God is the original conspiracy theory….
Among the varieties of Christian monotheism,
none is more totalitarian, none lodges more radical
claims for God’s omnipotence, than Calvinism—
and within America, the chief analogue of Calvinist
theology, Puritanism. According to Calvin every
particle of dust, every act, every thought, every
creature is governed by the will of God, and yields
clues to the divine plan.”
– Scott Sanders, “Pynchon’s Paranoid History“
Profile picture of "Jo Lyxe" (Josefine Lyche) at Vimeo—
Compare to an image of Vril muse Maria Orsitsch.
From the catalog of a current art exhibition
(25 May – 31 August, 2013) in Norway,
I DE LANGE NÆTTER —
|
Josefine Lyche
Keywords (to help place my artwork in the (See also the original catalog page.) |
Clearly most of this (the non-highlighted parts) was taken
from my webpage Diamond Theory. I suppose I should be
flattered, but I am not thrilled to be associated with the
(apparently fictional) Vril Society.
For some background, see (for instance)
Conspiracy Theories and Secret Societies for Dummies .
" 'So this is heaven!' A line that strikes dread into
a theater reviewer's heart."
— Dan Sullivan in the Los Angeles Times
“The most terrifying verse I know:
merrily merrily merrily life is but a dream.”
—Joan Didion, The Last Thing He Wanted
"Audiences never had any difficulty with his work,
which was instantly recognisable as the stuff of dreams…."
— Apology for the life of a British playwright
who died on July 3, 2013.
"I saw 'More Light' twice, for my sins, and wasn't surprised
that half of the second audience left at intermission."
— Dan Sullivan in the Los Angeles Times (continued)
Some light from this journal on the day of the above
playwright's death, the day before, and the day after—
For a more plausible heaven, see the posts of July first
and an LA Times obituary for a man who died on that date.
In memory of Douglas J. Dayton, who reportedly died last Friday—
The Studio of Gratifying Discourse.
See also Barry's Lexicon and (for The Blake School)…
Today is the 61st anniversary of the publication
of the book Mere Christianity , by C. S. Lewis.
In its honor, here is a link to "Hexagram 61"
in this journal.
See also "Moonshine and Lion."
From Andries Brouwer —
* Related material: Yesterday's evening post and The People's Cube.
(By the way, any 4×4 array is a tesseract .)
"Classical Geometry in Light of Galois Geometry"
is now available at independent.academia.edu.
Related commentary: Yesterday's post Vision
and a post of February 21, 2013: Galois Space.
"Then it came to him.
In a single stroke he had what might be called
a complete vision of the information age."
— "Douglas C. Engelbart, Inventor of the
Computer Mouse, Dies at 88," by John Markoff
in this afternoon's online New York Times
Related material:
The Pearly Gates of Cyberspace
in the Dec. 4, 2008, post OCODE.
My diamond theorem articles at PlanetMath and at
Encyclopedia of Mathematics have been updated
to clarify the relationship between the graphic square
patterns of the diamond theorem and the schematic
square patterns of the Curtis Miracle Octad Generator.
Continued from Sunday's post Book Award and last
midnight's post Holding the Frame—
The nineteenth-century German writer Rudolf Haym on
German romantic Hellenism—
"In the enjoyment of this fair picture-world, our nation must
needs delude itself a moment with the dream of Greek felicity
and Greek repose to awaken directly poorer and more restless
than before. To Poetry such a delusion was indeed natural, and
who would dispute it with her after she had offered to our
enjoyment what was sweetest and most perfect! But we see
now all at once Metaphysic seized with the same illusion.
Turning aside from the strait path of sober inquiry and from the
labour of deliverance through the most conscientious criticism,
Hegel begins to expand over our spiritual world his ideal that
was found in Hellas, that was strengthened by exhaustive
penetration into the ultimate grounds of all religion. A dreamed-of
and yearned-for future is treated as present. A system tricked
out with the entire dignity of the science of truth raises itself
beside our poetry, and with diamond net spins us into an idea
with which the want, the incompleteness, and the unbeauty of
our political and historical actuality is at every point in contradiction."
— Rudolf Haym, Hegel und seine Zeit (1857), 91-92, translated
and quoted in The Secret of Hegel , by James Hutchison Stirling
(1898 edition, p. 626)
Major Barbara (Gabriel Pascal, 1941) — "There are some performances
that bypass your critical faculties altogether, connecting not with your brain
but with your soul. They are desperately few, those characterisations of
such heightened sensitivity, such emotional resonance that the effect is
both exalting and suffocating. You might chance upon one every three or
four years, if you're lucky. I don't know why, or how, but every time Wendy
Hiller utters a line or holds the frame in Major Barbara , I am on the verge
of tears." — Rick Burin
|
"What on earth is
— Said to be an annotation |
In the spirit of the late Thomas Guinzburg…
See also "Concrete Universal" in this journal.
Related material— From a Bloomsday reply
to a Diamond Theory reader's comment, an excerpt—
The reader's comment suggests the following passages from
the book by Stirling quoted above—
Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow in 1974.
Continued from the previous post (June 27),
about the death of the founder of the
Future of Humanity Institute (FHI) at Oxford…
From Oxford Today , June 26, 2013—
(See also a June 11 Independent story on the same topic.)
Update of 6:42 PM ET June 29:
Any similarity between the FHI logo and Plato's diamond
is of course purely coincidental—
The body of James Martin, 79, founder of the Oxford Martin School,
was reportedly found floating in the sea near his private island
off Bermuda on Monday, June 24, 2013.
In his memory— A Log24 post from last December.
"These are death's own supremest images,
The pure perfections of parental space"
— Wallace Stevens,
"The Owl in the Sarcophagus"
From O Marks the Spot, Jill St. John's birthday, 2012:
"Row, row, row your boat…"
"A kind of liturgical singsong" — John Leonard on Didion
“I could a tale unfold whose lightest word
Would harrow up thy soul….“
— Hamlet’s Father’s Ghost
The results of a search in this journal for “a tale unfold” suggest
a review of the following passage from Donna Tartt’s Secret History…
A math weblog discussed this passage on January 24, 2013.
For related alliances, see this weblog on that same date.
Sunset in Manhattan today is at 8:31 PM.
Connoisseurs of ambiguity may consult the
date 8/31 in this journal.
Online biography of author Cormac McCarthy—
"… he left America on the liner Sylvania, intending to visit
the home of his Irish ancestors (a King Cormac McCarthy
built Blarney Castle)."
Two Years Ago:
Blarney in The Harvard Crimson—
Melissa C. Wong, illustration for "Atlas to the Text,"
by Nicholas T. Rinehart:
Thirty Years Ago:
Non-Blarney from a rural outpost—
Illustration for the generalized diamond theorem,
by Steven H. Cullinane:
"Maybe birthdays are dangerous. Like Christmas."
— Cormac McCarthy, The Sunset Limited
From the LA Times online obituaries today:
|
Michael Feran Baigent was born in Nelson, New Zealand,
From 1998 he lectured on and led tours of the temples and Elliott Reid Longtime film, TV actor with a comic touch
Elliott "Ted" Reid, 93, a longtime character actor in films |
From a post last Saturday, June 22, and the earlier
post last Friday, June 21, that preceded it:
|
The Eliade passage was quoted in a 1971 Ph.D. thesis Some context— Stevens's Rock in this journal. Friday, June 21, 2013
Lexicon
|
|
"… a fundamental language
"… the questions raised by R. Lowell |
See also, in this journal, Big Rock.
“For in that sleep of death what dreams may come
When we have shuffled off this mortal coil,
Must give us pause.” — Hamlet
Sleep well, Mr. Matheson.
Here is the link to an MIT Scratch project from the above comment.
See also a comment by a Random Norwegian Dude:
For related art, see
"4D AMBASSADOR (HYPERCUBE)" for Steven H. Cullinane
by the Norwegian artist Josefine Lyche.
From today's earlier post, Stevens and the Rock—
"Rock shows him something that transcends
the precariousness of his humanity:
an absolute mode of being.
Its strength, its motionlessness, its size
and its strange outlines
are none of them human;
they indicate the presence of something
that fascinates, terrifies, attracts and threatens,
all at once."
— Mircea Eliade, Patterns in Comparative Religion (1958)
An object with such an "absolute mode of being"
is the plot center of a new novel discussed here previously—
Max Barry's Lexicon . From a perceptive review:
I believe he’s hit on something special here.
It’s really no surprise that Matthew Vaughn
of Kick-Ass and X-Men: First Class fame
has bought the rights to maybe make the movie;
Lexicon certainly has the makings of a fine film.
Or graphic novel… Whatever.
Passage quoted in A Philosopher's Stone (April 4, 2013)—
This passage from Heidegger suggested the lexicon excerpt on
to hypokeimenon (the underlying) in yesterday's post Lexicon.
A related passage:
The Eliade passage was quoted in a 1971 Ph.D. thesis
on Wallace Stevens.
Some context— Stevens's Rock in this journal.
From the final pages of the new novel
Lexicon , by Max Barry:
|
"… a fundamental language
"… the questions raised by R. Lowell |
"… the clocks were striking thirteen." — 1984
The New York Times philosophy column "The Stone"
last evening had an essay on art by a sarcastic anarchist,
one Crispin Sartwell—
"… whole generations of art lovers have been
trained in modernist dogma, and arts institutions’
access to various forms of state or foundation
support depend on it completely. One goes to
the museum to gasp at stunning works of
incomparable, super-human genius by beings
who are infinitely more exalted and important
than the mere humans staring at their paintings.
That’s why ordinary people staring at a Picasso
(allegedly) experience a kind of transcendence
or re-articulation of their lives and world."
Cubism Re-Articulated:
Click image for some backstory.
(IMAGE: Walter Gropius and Froebel's Third Gift,
from a Google image search today)
Background: Cubism in this journal and
Pilate Goes to Kindergarten.
Related material: Chesterton + Thursday in this journal.
See Juneteenth in this journal.
For related meditations, see last October 27th.
"Da hats ein Eck" —
"you've/she's (etc.) got problems there"
St. Galluskirche:
St. Gallus's Day, 2012:
Click image for a St. Gallus's Day post.
A related problem:
Discuss the structure of the 4x4x4 "magic" cube
sent by Pierre de Fermat to Father Marin Mersenne
on April 1, 1640, in light of the above post.
This journal on May 14, 2013:
"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…
For those who prefer Trudeau's
"Story Theory" of truth to his "Diamond Theory"
Related material: Click images below for the original posts.
See as well the novel "Lexicon" at Amazon.com
and the word "lexicon" in this journal.
"Man of Steel is subversive mythology for atheists
that exalts a Superman who behaves the way they
think God should but doesn’t."
— Jeff Jensen, "Why the Superman of 'Man of Steel'
is the Jesus we wish Jesus would be,"
Entertainment Weekly this afternoon
"He's a bird, he's a plane… He's our savior?"
— Nicole Sperling, "'Man of Steel's' Christian link,"
Los Angeles Times this afternoon
Elsewhere on the Web today:
See also Baez in this journal.
"Everything's coming up Snow White."
For Charlize:
"Snow, Glass, Apples," by Neil Gaiman
* See Saturday's post At the Still Point
From a weblog post on June 11, 2013, by one Pete Trbovich:
|
Here again, I don't think Steven Cullinane is really unhinged per se. At the very least, his geometric study is fun to play with, particularly when you find this toy. And I'm not really sure that anything he says is wrong per se. But you might find yourself asking "So what?" or more to the point, "Why is this supposed to be the central theory to explaining life, the universe, and everything?" |
It isn't supposed to be such a theory.
I do not know why Trbovich thinks it is .
— Steven H. Cullinane
Update of 11 PM June 16:
For one such central theory of everything, see
the I Ching . Diamond theory is, unlike that
Chinese classic, pure mathematics, but the larger
of the binary-coordinate structures it is based on
are clearly isomorphic, simply as structures , to
the I Ching 's 64 hexagrams.
Make of this what you will.
(Continued from yesterday's posts, "Object of Beauty"
and "Amy's Shadow")
A winner of a Nobel Prize for X-ray crystallography stands
at the head of the New York Times obituary list today.
In memoriam —
|
X-Ray Vision "Crystal Engineering in Kindergarten," by Bart Kahr:
"If the reader is beginning to suspect that Froebel’s
Click images for some backstories. |
Some further background:
The Times follows yesterday's egregious religious error
with an egregious scientific error:
"The technique developed by Dr. Karle and Herbert A. Hauptman,
called X-ray crystallography, is now routinely used by scientists…."
Karle was reportedly born in 1918, Hauptman in 1917.
Wikipedia on the history of X-ray crystallography:
"The idea that crystals could be used as a
diffraction grating for X-rays arose in 1912…."
The Nobel Foundation:
"The Nobel Prize in Physics 1914 was awarded to
Max von Laue 'for his discovery of the diffraction of
X-rays by crystals.'"
"The Nobel Prize in Physics 1915 was awarded jointly to
Sir William Henry Bragg and William Lawrence Bragg
'for their services in the analysis of crystal structure
by means of X-rays.'"
Why knows what evil lurks…? — The Shadow
Backstory: "Amy Adams" + Shadow in this journal.
Related material —
Amy Adams as Lois Lane:
In the new Amy Adams version, Superman's Smallville mom
is played by Diane Lane.
Lane also played George Reeves's sugar mommy
in the 2006 film Hollywoodland .
Ben Affleck and Diane Lane at the 2006 Venice Film Festival
premiere of Hollywoodland :
See, too, today's previous post, and Amy Adams as Lacey Yeager
in the yet-to-be-made film version of An Object of Beauty .
This journal on July 5, 2007 —
“It is not clear why MySpace China will be successful."
— The Chinese magazine Caijing in 2007, quoted in
Asia Sentinel on July 12, 2011
This journal on that same date, July 12, 2011 —
See also the eightfold cube and kindergarten blocks
at finitegeometry.org/sc.
Friedrich Froebel, Froebel's Chief Writings on Education ,
Part II, "The Kindergarten," Ch. III, "The Third Play":
"The little ones, who always long for novelty and change,
love this simple plaything in its unvarying form and in its
constant number, even as they love their fairy tales with
the ever-recurring dwarfs…."
This journal, Group Actions, Nov. 14, 2012:
"Those who insist on vulgarizing their mathematics
may regard linear and affine group actions on the eight
cubes as the dance of Snow White (representing (0,0,0))
and the Seven Dwarfs—
."
.jpg)
"Art historians often speak of
the 'moving' or 'shifting' perspective
in Chinese paintings."
"Security issues are very tough to figure out."
See also Figurism at Wikipedia and June 8 here.
Meanwhile (update of 3:55 PM ET June 13)…
"Eight is a Gate." — Mnemonic rhyme
Today's previous post, Window, showed a version
of the Chinese character for "field"—
This suggests a related image—
The related image in turn suggests…
Unlike linear perspective, axonometry has no vanishing point,
and hence it does not assume a fixed position by the viewer.
This makes axonometry 'scrollable'. Art historians often speak of
the 'moving' or 'shifting' perspective in Chinese paintings.
Axonometry was introduced to Europe in the 17th century by
Jesuits returning from China.
As was the I Ching. A related structure:
From Jim Holt’s Aug. 29, 2008, review of
The Same Man:
George Orwell and Evelyn Waugh in Love and War
by David Lebedoff
“Orwell thought ‘good prose is like a window pane,’
forceful and direct. Waugh was an elaborate stylist
whose prose ranged from the dryly ironical to the
richly ornamented and rhetorical. Orwell was solitary
and fiercely earnest. Waugh was convivial and
brutally funny. And, perhaps most important, Orwell
was a secularist whose greatest fear was the
emergence of Big Brother in this world. Waugh was
a Roman Catholic convert whose greatest hope lay
with God in the next.”
The Orwell quote is from “Why I Write.”
A search for the original yields…
Detail:
Synchronicity:
See, too, in this journal the
Chinese character for “field”—
The eight parts of the semaphore circle
in the previous post suggest some context
for Fritz Leiber's eight-limb "spider" symbol:
See Mary Karr, Time on the Cross, and chuahaidong.org.
Yesterday's post The Belicic Problem suggests
a review of a Log24 post from October 29, 2007:
The extremely loose plot of Anthony Hopkins's
pet project "Slipstream" was in part inspired by
the events of 1956 in Santa Mira.
In keeping with Hopkins's strange plot logic, and
with the strange visual logic of the New York Times
editorial logo in yesterday's Santa Mira post,
here is a "diamond pivot bright"—
Click image for an explanation.
From the comments:
Click "Zaslavsky" above for some background from Binghamton.
For some background from Santa Mira, see…
The story takes place in the fictional Santa Mira, California
where Dr. Miles Bennell (Kevin McCarthy) is soon overrun
by several patients claiming that their loved ones are imposters.
Thus, a panic is set off as the doctor and his friend Jack Belicic
(King Donovan) try to find the answer to the issue at the hand.
What they discover is that somehow people have been replaced
by aliens, who are incubated in pea pods, from space.
Andrew Rosenthal on a government official
in "Taking Note," the New York Times editorial
page editor's blog, at 3:12 PM today:
"… we are going to have to parse his meanings
of complex words like 'yes' and 'no.'"
Parse this, Rosenthal:
For some help, do a Google image search on "semaphore."
University Diaries today has a meditation on
nothingness and the University of North Carolina.
She includes a picture by John Picacio that was done as a
cover illustration for the novel A Canticle for Leibowitz .
Related material:
A June 10 obituary for Msgr. Tim O'Connor, former rector
of Sacred Heart Cathedral in Raleigh, NC.
"To those who knew him, O’Connor’s aesthetic sense
was a defining quality. As rector at Sacred Heart Cathedral—
the seat of the bishop of Raleigh— he led a $500,000
renovation project in the late ’90s that refurbished the floors
and pews and installed art, such as painting the ceiling blue
with 14-karat gold leaf stars."
— Julian Spector — jspector@newsobserver.com
Some context:
Sermon in this journal last Sunday, June 9, which
was the reported date of Msgr. O'Connor's death.
Mary Chapin Carpenter in this journal on July 6, 2008:
Related art:
Ceiling of Raleigh's Sacred Heart Cathedral—
Some context for this art:
From "Spider Robinson: The SF Writer as Empath"
by Ben Bova —
When Analog magazine was housed over at Graybar Building
on Lexington Avenue, our offices were far from plush. In fact,
they were grimy. Years worth of Manhattan soot clung to the
walls. The windows were opaque with grime. (What has this
to do with Spider Robinson? Patience, friend.)
Many times young science fiction fans would come to Manhattan
and phone me from Grand Central Station, which connected
underground with the good old Graybar. "I've just come to New
York and I read every issue of Analog and I'd like to come up and
see what a science fiction magazine office looks like," they would
invariably say.
I'd tell them to come on up, but not to expect too much. My advice
was always ignored. The poor kid would come in and gape at the
piles of manuscripts, the battered old metal desks, and mountains
of magazines and stacks of artwork, the ramshackle filing cabinets
and bookshelves. His eyes would fill with tears. His mouth would
sag open.
He had, of course, expected whirring computers, telephones with
TV attachments, smoothly efficient robots humming away,
ultramodern furniture, and a general appearance reminiscent of a
NASA clean room. (Our present offices, in the spanking new Condé
Nast Building on Madison Avenue, are a little closer to that dream.)
The kid would shamble away, heartsick, the beautiful rainbow-hued
bubble of his imagination burst by the sharp prick of reality.
"Funny how annoying a little prick can be." — Garry Shandling as Senator Stern
Today's previous post on coordinate systems
suggests a look at the phrase "Galois coordinates."
A search shows that the phrase, though natural,
has apparently not been used before 2011* for solutions
to what Hermann Weyl called "the relativity problem."
A thorough historical essay on Galois coordinatization
in this sense would require more academic resources
than I have available. It would likely describe a number
of applications of Galois-field coordinates to square
(and perhaps to cubical) arrays that were studied before
1976, the date of my Diamond Theory monograph.
But such a survey might not find any such pre-1976
coordinatization of a 4×4 array by the 16 elements
of the vector 4-space over the Galois field with two
elements, GF(2).
Such coordinatizations are important because of their
close relationship to the Mathieu group M 24 .
See a preprint by Anne Taormina and Katrin Wendland,
"The overarching finite symmetry group of Kummer
surfaces in the Mathieu group M 24 ," with its remark
denying knowledge of any such coordinatization
prior to a 1989 paper by R. T. Curtis.
Related material:
Some images related to Galois coordinates, excerpted
from a Google search today (click to enlarge)—
* A rather abstract 2011 paper that uses the phrase
"Galois coordinates" may have some implications
for the naive form of the relativity problem
related to square and cubical arrays.
Part I
Part II
"I Am a Dancer" — NY Times, "The Stone," 9:07 PM ET
Sunday, June 9, 2012 (Tony night)
Part III
(Continued from Sept. 22, 2011)
See Taormina in this journal, and the following photo of "Anne Newton"—
Click photo for context.
Related material:
"Super Overarching" in this journal,
a group of order 322,560, and…
See also the MAA Spectrum program —
— and an excerpt from the above book:
For this, the dies natalis of poet Gerard Manley Hopkins,
it seems apt to cite a 1973 master's thesis on what the author
calls multiguity in Hopkins.
See also multispeech in this journal.
Related material:
See, too, the online front page of The New York Times
from 1:54 PM ET today, and, as an example of multispeech,
yesterday morning's post Rubric's Cuber.
Yesterday's noon post concerned a forthcoming novel
about poetry and intelligence services. Some related backstory:
A predecessor to the Max Barry novel Lexicon .
(The latter will be published on June 18.)
See, too, an MAA Spectrum book:
Click on images for details.
From Night of Lunacy (Sunday, May 5, 2013):
Related posts: Rubric, Cuber, and Pound Sign.
Click image for some background.
See also Story Theory and Princeton Apocalypse.
Latin Lesson
Details in an etymology linked to here Monday, June 3,
in a post titled The Deep End —
"… mid-15c., from Middle French pensée … from
fem. past participle of penser 'to think,' from
Latin pensare 'consider'…."
A remembrance of the late, great, Esther Williams,
who died early today:
After marrying Lamas, she retired from public life.
Williams explained in a 1984 interview, "A really terrific guy
comes along and says, 'I wish you'd stay home and be
my wife,' and that's the most logical thing in the world for a Latin.
And I loved being a Latin wife — you get treated very well.
There's a lot of attention in return for that sacrifice."
The Mathematical Association of America has a
submit-a-review form that apparently allows readers
to comment on previously reviewed books.
This morning I submitted the following comment on
Alexander Bogomolny's March 16, 2012, review of
Martin J. Erickson's Beautiful Mathematics :
In section 5.17, pages 106-108, "A Group of Operations,"
Erickson does not acknowledge any source. This section
is based on the Cullinane diamond theorem. See that
theorem (published in an AMS abstract in 1979) at
PlanetMath.org and EncyclopediaOfMath.org, and
elsewhere on the Web. Details of the proof given by
Erickson may be found in "Binary Coordinate Systems,"
a 1984 article on the Web at
http://finitegeometry.org/sc/gen/coord.html.
If and when the comment may be published, I do not know.
Update of about 6:45 PM ET June 7:
The above comment is now online at the MAA review site.
Update of about 7 PM ET July 29:
The MAA review site's web address was changed, and the
above comment was omitted from the page at the new address.
This has now been corrected.
"Philosophy is a battle against the bewitchment
of our intelligence by means of our language." — Wittgenstein
"You've got to pick up every stitch…
Must be the season of the witch."
— Donovan song at the end of Nicole Kidman's "To Die For"
Today's morning post, Rubric, suggests a check
of Alexander Bogomolny's tweets:
Clicking the hint leads to Bogomolny's Ambiguities in Plain Language:
See also, in this journal, alea (which appears within the derived word "aleatory").
From a mathematical review:
"The book ends with eye-opening explorations….
If pressed for an extra rubric, I would consider
a separate section on "Engaging Games," as
this is something that mathematicians are
preoccupied with— literally and metaphorically."
See in this journal Language Game, Nexus, and
posts of May 12, 2013.
A review of Beautiful Mathematics for 8 PM.
The corrected index the reviewer links to is here.
As a June 1 post shows, it is not corrected enough .
The review is dated March 16, 2012.
See this journal on that date.
See also Good Bye, Marty.
Wikipedia:
The Chinese name of the gate, Tiānānmén 天安門 …
is made up of the Chinese characters for "heaven,"
"peace" and "gate" respectively, which is why the
name is conventionally translated as "The Gate of
Heavenly Peace". However, this translation is
somewhat misleading, since the Chinese name is
derived from the much longer phrase "receiving the
mandate from heaven, and stabilizing the dynasty."
Another anniversary today:
See also some related philosophy and mathematics.
The Daily Princetonian today:
A different cover act, discussed here Saturday:
See also, in this journal, the Galois tesseract and the Crosswicks Curse.
"There is such a thing as a tesseract." — Crosswicks saying
New Yorker editor David Remnick at Princeton today
(from a copy of his prepared remarks):
"Finally, speaking of fabric design…."
I prefer Tom and Harold:
Tom Wolfe in The Painted Word —
"I am willing (now that so much has been revealed!)
to predict that in the year 2000, when the Metropolitan
or the Museum of Modern Art puts on the great
retrospective exhibition of American Art 1945-75,
the three artists who will be featured, the three seminal
figures of the era, will be not Pollock, de Kooning, and
Johns-but Greenberg, Rosenberg, and Steinberg.
Up on the walls will be huge copy blocks, eight and a half
by eleven feet each, presenting the protean passages of
the period … a little 'fuliginous flatness' here … a little
'action painting' there … and some of that 'all great art
is about art' just beyond. Beside them will be small
reproductions of the work of leading illustrators of
the Word from that period…."
Harold Rosenberg in The New Yorker —
Tom's book seems to be repeating, in 1975, what Harold said better in 1969.
"Finally, speaking of fabric design…."
Note "fabric design" in Rosenberg's words on philistine views of the art of Noland.
Triple Threat
"'Mr. Remnick's work is smart, funny and insightful —
a triple threat Class Day speaker!' said Class Day
co-chair Lily Alberts." — News at Princeton
Related material: David Remnick on Miss Gould.
See also Remnick and Miss Gould in this journal.
From "The Genre Artist," by Carlo Rotella, in The New York Times ,
published online on July 15, 2009 —
"Dan Simmons, the best-selling writer of horror and fantasy,
described discovering Vance as 'a revelation for me, like
coming to Proust or Henry James. Suddenly you’re in the
deep end of the pool.'"
Another approach to the deep end:
This journal on the above date— July 15, 2009—
and also on Sunday, May 26, 2013, the date of Vance's death —
"This nothing's more than matter." —Laertes in Hamlet
Midrash for theologians:
Rotella's article was published in print a few days later in
The New York Times Magazine of Sunday, July 19, 2009.
See this journal on that date for "Finite Jest," with some
remarks by Pascal related to the above quote from Hamlet .
"There is pansies, that's for thoughts." —Ophelia
See the Klein correspondence at SymOmega today and in this journal.
"The casual passerby may wonder about the name SymOmega.
This comes from the notation Sym(Ω) referring to the symmetric group
of all permutations of a set Ω, which is something all of us have
both written and read many times over."
"What we do may be small, but it has
a certain character of permanence."
— G. H. Hardy, A Mathematician's Apology
The diamond theorem group, published without acknowledgment
of its source by the Mathematical Association of America in 2011—
"When it comes down to it,
I think we all just want
to love and be loved."
— Ellen Page in Vanity Fair online this afternoon
See also lyrics to a tune by Dvořák and eden ahbez.
A meditation on this morning's New York Times obituaries:
Happy birthday to jazz pianist Clint Eastwood.
Related material: Skylark in this journal and Return to Paradise.
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.
(Why the above Google Books description of the quotation's
source is in Danish, I do not know. A search for
Bohr + Chinese in this journal may be relevant, as may
also be Faust in Copenhagen.)
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
Galois-tesseract model.
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:
Confidential report lists U.S. weapons system designs
compromised by Chinese cyberspies
Related entertainment:
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
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 .
These stories suggest a meditation by Kierkegaard
and some related remarks from July 2, 2009.
"The final ingredient of the design conception
was its most important and its most dangerous…."
— The Cambridge Companion to Grand Opera
Starring Michael Douglas:
Related material:
Happy Birthday, Mary Shelley (August 30, 2003)
… from yesterday— Bling Ring and Church Logic.
Related narratives— Get Quotes (source of image below)
as well as Helprin's Doors and Trickster.
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.
Related material: Diamond Girl and the following ad
for Eliza Doolittle Day:
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:
See, too, in the Conway-Sloane book, the Galois tesseract …
and, in this journal, Geometry for Jews and The Deceivers , by Bester.
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."
[Cur89] reference:
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
Curtis article.
|
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).
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).
Backstory: The two previous Log24 posts
Raiders of the Lost Aleph (May 14) and
The Crying of Bucharest (May 15).
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":
Related material:
All Souls' Day at the Still Point (Nov. 2, 2003) and
Frodo and the Oxford Murders (Oct. 13, 2011).
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 —
FADE IN:
A rim of swirling light appears, circling helplessly into a
gigantic BLACK HOLE. It spirals inward…
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—
See Quaternions in an Affine Galois Plane
and Group Actions, 1984-2009.
See, too, the Mathematics and Narrative post
from April 28, 2013, and last night's
For Indiana Spielberg.
(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—
Symmetry and Hierarchy and the above VINCI Genius commercial.
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…
(Click image for some background.)
For a pundit of pugilism: Plan 9 continues.
"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
* A language game for Hofstadter: click on "Seeing As"
in today's noon post.
"On Seeing A's and Seeing As" — Hofstadter
"Man redet dann vom Kern der Dinge." — Heidegger
"So we moved, and they, in a formal pattern"
— Four Quartets
See also yesterday's "Multi-Levels to Keep All Happy"
and past posts that mention Multispeech.
Western Washington University in Bellingham maintains a
website to benefit secondary-school math: MathNEXUS.
The MathNEXUS "website of the week" on April 14, 2013,
was the Diamond 16 Puzzle and its related webpages.
Click on the above image for the April 14 webpage.
The above images are from a prequel (March 29, 2013)
to 'Nauts (March 26, 2006.)
See also Spider Mother, Gamer Post, and Spider Tale.
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…."
— Song sung on NBC's Smash tonight
Fulsere vere candidi mihi soles….
— 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 .
Rubik core:
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 ."
— Page 29 of "A twist in the M24 moonshine story,"
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
Book Description
"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
A page with the above title has been created at
the Encyclopedia of Mathematics.
How long it will stay there remains to be seen.
"Why history?
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:FROM Christoph Waltz"Currently in post-production": The Zero Theorem. For Christoph WaltzRaiders of the Lost Tesseract continues… SOCRATES: Is he not better off in knowing his ignorance? |
See also today's previous post.
Click a course description below for some related material.
See also Strike That Pose and Gone to China.
From February 24, 2005:
The above three-part image may be viewed as a tribute to
Jerusalem Day (today), to Saul Bass, or to Spider Jerusalem.
(See related posts and Damnation Morning.)
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."
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