"I am a town." — Mary Chapin Carpenter
"A town, huh?" — Sydney Prosser
Related material — "Put on your red dress, baby."
"I am a town." — Mary Chapin Carpenter
"A town, huh?" — Sydney Prosser
Related material — "Put on your red dress, baby."
Continued from December 25—
A link from Sunday afternoon to Nov. 26, 2012,
suggests a review of one of the above structures.
The Dreaming Jewels cover at left is taken from a review
by Jo Walton at Tor.com—
"This is a book that it’s clearly been difficult
for publishers to market. The covers have been
generally pretty awful, and also very different.
I own a 1975 Corgi SF Collectors Library
paperback that I bought new for 40p in the later
seventies. It’s purple, and it has a slightly grainy
cover, and it matches my editions of The Menace
From Earth and A Canticle for Leibowitz .
(Dear old Corgi SF Collectors Editions with their
very seventies fonts! How I imprinted on them at
an early age!) I mention this, however, because
the (uncredited) illustration actually represents and
illustrates the book much better than any of the other
cover pictures I’ve seen. It shows a hexagon with an
attempt at facets, a man, a woman, hands, a snake,
and stars, all in shades of green. It isn’t attractive,
but it wouldn’t put off people who’d enjoy what’s inside
either."
The "hexagon with an attempt at facets" is actually
an icosahedron, as the above diagram shows.
(The geometric part of the diagram is from a Euclid webpage.)
For Plato's dream about these jewels, see his Timaeus.
A link to a Nov. 22 post on Arcade Fire was added today
to yesterday's "Dating an OS" post.
That Nov. 22 post suggests a review related to a new film —
"If the spy wars of the later 20th century were fought
in 'a wilderness of mirrors,' beset by paradox and
moral uncertainty— evil done in the name of good—
then John le Carré, or, rather, the narrative voice that
went by the name John le Carré, was the perfect
choice to polish those mirrors. It was the voice of the
urbane, upper-class Englishman: courteous, opaque
and chilly, with a ruthless, penetrative intellect and
razor wit for the delivery of its insights."
— Alan Furst in The New York Times Sunday
Book Review on October 12, 2008
For other material on mirrors, see all posts tagged Arcade Fire.
Amy Adams in the new film “Her” —
“You’re dating an OS? What is that like?”
— Question quoted in a Hollywood Reporter
story on the film’s second trailer
From the same story, by Philiana Ng —
” The trailer is set to Arcade Fire’s
mid-tempo ballad ‘Supersymmetry.’ “
Parts of an answer for Amy —
Nov. 26, 2012, as well as
Dec. 24, 2013, and
The Hollywood Reporter story is from Dec. 3, 2013.
See also that date in this journal.
See also Pop Meets Hochkultur in a post of Dec. 18, 2013.
Some background for that post— July 19, 2008.
Many people enter the merry- go-round.
Here and there one catches a phrase —
"Room for one more on the hippo's back"….
— Adapted from the prologue to
Liliom , by Ferenc Molnár
Click Elysium for a related image.
For fans of Hunger Games and Elysium —
Roberta Smith in this evening's* online New York Times—
"Especially with the gap between the wealthiest
and everyone else so wide, it is dicey
for a major museum to celebrate the often frivolous
objects on which the rich spend their ever increasing
surplus income. Such a show must be beyond reproach
in every way: transparent in organization, impeccable
in exhibition design, illuminating in catalog and labeling
and, most of all, self-evidently excellent in the quality of
the objects on display."
Da capo: "I've heard of affairs that are strictly Platonic."
“Design is how it works.” — Steve Jobs
“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer (Ch. 14 (pp. 693-746),
Section 16 (p. 716) of Handbook of Combinatorics, Vol. I ,
MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel,
and László Lovász)
For some background on that Steiner system, see the footnote to
yesterday’s Christmas post.
“… her mind rotated the facts….”
Related material— hypercube rotation,* in the context
of rotational symmetries of the Platonic solids:
“I’ve heard of affairs that are strictly Platonic”
* Footnote added on Dec. 26, 2013 —
See Arnold Emch, “Triple and Multiple Systems, Their Geometric
Configurations and Groups,” Trans. Amer. Math. Soc. 31 (1929),
No. 1, 25–42.
On page 42, Emch describes the above method of rotating a
hypercube’s 8 facets (i.e., three-dimensional cubes) to count
rotational symmetries —
See also Diamond Theory in 1937.
Also on p. 42, Emch mentions work of Carmichael on a
Steiner system with the Mathieu group M11 as automorphism
group, and poses the problem of finding such systems and
groups that are larger. This may have inspired the 1931
discovery by Carmichael of the Steiner system S(5, 8, 24),
which has as automorphisms the Mathieu group M24 .
"She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test."
— Steve Martin, An Object of Beauty
"So you should not feel so all alone…"
— Adapted song lyric
Review of a book first published in 1989—
Reality's Mirror: Exploring the Mathematics of Symmetry —
"Here is a book that explains in laymen language
what symmetry is all about, from the lowliest snowflake
and flounder to the lofty group structures whose
astonishing applications to the Old One are winning
Nobel prizes. Bunch's book is a marvel of clear, witty
science writing, as delightful to read as it is informative
and up-to-date. The author is to be congratulated on
a job well done." — Martin Gardner
A completely different person whose name
mirrors that of the Mathematics of Symmetry author —
See also this journal on the date mentioned in the Princetonian .
"Always with a little humor." — Yen Lo
In memory of Mikhail Kalashnikov, who reportedly died today at 94:
Integrity, Craftsmanship, Tradition .
See also an SNL tracking shot—
From the Bacardi website—
"Hamilton, Bermuda, December 13, 2012 —
Bacardi Limited caps off the yearlong celebration
of its 150th anniversary with the creation of a
commemorative time capsule…."
See also this journal on that date.
From The Iceman Cometh (1946, set in 1912) —
HOPE— (calls effusively) Hey there, Larry! Come over
and get paralyzed! What the hell you doing, sitting there?
(Then as Larry doesn't reply he immediately forgets him
and turns to the party. They are all very drunk now, just a
few drinks ahead of the passing-out stage, and hilariously
happy about it.) Bejees, let's sing! Let's celebrate! It's my
birthday party! Bejees, I'm oreyeyed! I want to sing! (He
starts the chorus of "She's the Sunshine of Paradise Alley,"
and instantly they all burst into song. But not the same song.
Each starts the chorus of his or her choice….)
From Paradise Alley (1978, set in 1946) —
From a prequel to The Shining , by Stephen King—
You had to keep an eye on the boiler
because if you didn’t, she would creep on you.
What did that mean, anyway? Or was it just
one of those nonsensical things that sometimes
came to you in dreams, so much gibberish?
Of course there was undoubtedly a boiler
in the basement or somewhere to heat the place,
even summer resorts had to have heat sometimes,
didn’t they (if only to supply hot water)? But creep ?
Would a boiler creep ?
You had to keep an eye on the boiler.
It was like one of those crazy riddles,
why is a mouse when it runs,
when is a raven like a writing desk,
what is a creeping boiler?
See also Steam.
For one answer to the riddle, click here.
Meanwhile…
Log24 on Sunday, October 5, 2008— “In a game of chess, the knight’s move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a ‘knight’s move’ in intelligence.” Related material: Terence McKenna: “Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey ‘haunts time like a ghost.’” Anonymous author: “‘Knight’s move thinking’ is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia.” |
Related journalism—
"What's the 'S' stand for?" — Amy Adams
The title is taken from a book for ages 8-12 published
on Shakespeare's birthday, April 23, 2013.
Also from that date, a note for older readers—
… Half a dozen of the other —
For further context, see all posts for the cruelest month of this past year.
* Secrets : A sometimes dangerous word.
Headline on an avant-garde-theater piece in
The New York Times that was the subject of
a Log24 post on December 15 (Julie Taymor's birthday):
"To Thine Own Algorithm Be True"
Today is the feast of St. Peter Canisius.
Click on Canisius for material related to the Times
story, and on the feast for a more traditional tale.
"It's going to be accomplished in steps,
this establishment of the Talented
in the scheme of things."
— To Ride Pegasus ,
by Anne McCaffrey (Radcliffe '47),
quoted here on December 1, 2013
"Twenty-one days is enough time to build trust
and decimate it several times over, and long enough
for someone to drop their pretensions altogether.
So while 'Dude, You’re Screwed' is about a person
at war with himself, 'Naked and Afraid' is about
people at war with each other. The elements may
get you down, but hell is other people."
— Jon Caramanica in The New York Times
(page C1 of today's New York print edition)
The Miami-Dade County Public Schools math webpage
now has a link to the Diamond 16 Puzzle.
(On His Dies Natalis )…
This is asserted in an excerpt from…
"The smallest non-rank 3 strongly regular graphs
which satisfy the 4-vertex condition"
by Mikhail Klin, Mariusz Meszka, Sven Reichard, and Alex Rosa,
BAYREUTHER MATHEMATISCHE SCHRIFTEN 73 (2005), 152-212—
(Click for clearer image)
Note that Theorem 46 of Klin et al. describes the role
of the Galois tesseract in the Miracle Octad Generator
of R. T. Curtis (original 1976 version). The tesseract
(a 4×4 array) supplies the geometric part of the above
exceptional geometric-combinatorial isomorphism.
For Josefine Lyche, artist of High White Noon —
Thursday, October 10, 2013
|
(This morning's Text and Pretext, continued)
"… a reality that only my notes can provide."
— Kinbote in Nabokov's novel Pale Fire
Click the above remarks on screws for another perspective on reality.
The above image is a pre-text. For details, see the text .
A scene from the 2002 film Max—
(Click for a video on the film.)
Related material— This journal, posts of Sept. 8-9, 2013.
Some backstory— Outsider Art, and an obituary for Günther Förg
in tonight's online New York Times —
"Günther Förg, a German painter, sculptor and
photographer whose work exemplified, toyed with,
tweaked and commented on— sometimes all at
once— the broad artistic movement known as
modernism, died at his home in Freiburg, Germany,
on Dec. 5, his 61st birthday."
The Log24 posts of that date, Dec. 5, are not without relevance.
Microsoft in 2009 on its new search engine name—
"We like Bing because it sounds off in our heads
when we think about that moment of discovery
and decision making— when you resolve those
important tasks."
A search on Bing today —
A colorful tale —
"How about another hand for the band?
They work real hard for it.
The Cherokee Cowboys, ladies and gentlemen."
— Ray Price, video, "Danny Boy Mid 80's Live"
Other deathly hallows suggested by today's NY Times—
Click the above image for posts from December 14.
That image mentions a death on August 5, 2005, in
"entertainment Mecca" Branson, Missouri.
Another note from August 5, 2005, reposted here
on Monday—
Happy birthday, Keith Richards.
"Mr. Nissenson took years to create alternative worlds
in pursuing questions of faith in books like 'The Tree
of Life.'" — NY Times obituaries index this evening
"O fearful meditation!" — William Shakespeare
in this journal (see posts on Ray Price).
The above image is from Geometry of the 4×4 Square.
(The link "Visible Mathematics" in today's previous post, Quartet,
led to a post linked to that page, among others.)
Note that the seventh square above, at top right of the array of 35,
is the same as the image in Quartet.
Happy Beethoven's Birthday.
Related material: Abel 2005 and, more generally, Abel.
See also Visible Mathematics.
The New York Times this evening has a story
on "A Piece of Work," an avant-garde production
at Brooklyn Academy of Music (BAM) that is to open
Wednesday.
A background check on Annie Dorsen, the production's
author-director, yields the following remarks on a video
promoting a show titled "Magical"—
"This video is sent us by the company for promotion
of their show in Bergen the 15. and 16. of April 2011.
Excerpt from the program:
Do magic and feminism go together? Anne Juren, the
French choreographer living in Vienna, and Annie
Dorsen, the New York based director, attempt to prove
that it can: it’s alchemical, it’s political and it works."
Related material: This journal eight years ago today, and
the Log24 posts from the dates, April 15-16, 2011, of the
"Magical" production in Bergen, Norway.
Happy birthday, Julie Taymor.
Odin's Jewel
Jim Holt, the author of remarks in yesterday's
Saturday evening post—
"It turns out that the Kyoto school of Buddhism
makes Heidegger seem like Rush Limbaugh—
it’s so rarified, I’ve never been able to
understand it at all. I’ve been knocking my head
against it for years."
— Vanity Fair Daily , July 16, 2012
Backstory: Odin + Jewel in this journal.
See also Odin on the Kyoto school —
For another version of Odin's jewel, see Log24
on the date— July 16, 2012— that Holt's Vanity Fair
remarks were published. Scroll to the bottom of the
"Mapping Problem continued" post for an instance of
the Galois tesseract —
The title, which I dislike, is taken from a 2011 publication
of the MAA, also sold by Cambridge University Press.
Some material relevant to the title adjective:
"For those who have learned something of higher mathematics, nothing could be more natural than to use the word 'beautiful' in connection with it. Mathematical beauty, like the beauty of, say, a late Beethoven quartet, arises from a combination of strangeness and inevitability. Simply defined abstractions disclose hidden quirks and complexities. Seemingly unrelated structures turn out to have mysterious correspondences. Uncanny patterns emerge, and they remain uncanny even after being underwritten by the rigor of logic."— Jim Holt, opening of a book review in the Dec. 5, 2013, issue of The New York Review of Books |
Some relevant links—
The above list was updated on Jan. 31, 2014, to include the
"Strangeness" and "Hidden quirks" links. See also a post of
Jan. 31, 2014.
Update of March 9, 2014 —
The link "Simply defined abstractions" is to the construction of the Steiner
system S(5, 8, 24) described by R. T. Curtis in his 1976 paper defining the
Miracle Octad Generator. It should be noted that this construction is due
to Richard J. Turyn, in a 1967 Sylvania research report. (See Emily Jennings's
talk of 1 Nov. 2012.) Compare the Curtis construction, written in 1974,
with the Turyn construction of 1967 as described in Sphere Packings, Lattices
and Groups , by J. H. Conway and N. J. A. Sloane (first published in 1988).
(Continued from yesterday afternoon)
From yesterday's online New York Times (5:59 PM ET)—
ART REVIEW What exactly are we looking at? Is it the real thing, or is it the promotion of a famous brand gussied up in spectacular, pseudo-sacramental style? Gold or fool’s gold? This sort of confusion pervades today’s art world, where, so often, the sales pitch comes in the form of quasi-religious rhetoric. It’s a big reason the tribal arts of Africa and other lands — as well as the putatively purely authentic creations of folk artists and so-called outsiders — are held in such high esteem.
— Ken Johnson, review of two exhibitions, |
"Tenser, said the tensor…"
"… Galois was a mathematical outsider…."
— Tony Mann, "head of the department of mathematical sciences,
University of Greenwich, and president, British Society for the
History of Mathematics," in a May 6, 2010, review of Duel at Dawn
in Times Higher Education.
Related art:
(Click for a larger image.)
For a less outside version of the central image
above, see Kunstkritikk on Oct. 15, 2013.
The late Colin Wilson appears at the head
of this afternoon's New York Times obituaries —
Margalit Fox's description this afternoon of
Wilson's first book, from 1956—
"The Outsider had an aim no less ambitious
than its scope: to delineate the meaning of
human existence."
This suggests a review of Log24 posts on "The Zero Theorem"
that yields—
See also Log24 on the date of Wilson's death.
Related material: Devil's Night, 2011.
See the Telegraph obituary of Jim Hall
and a post on Charlie Christian (and others).
The inclusion of D. H. Lawrence in that post
suggests a review of posts tagged Howl.
"The werewolves are here to save us."
— Simon in "The Mortal Instruments: City of Bones."
For the late Jim Hall—
Backstory: Icon, 1:44 PM ET today.
Update of 11 PM ET Dec. 10, 2013 —
For all the notes, see Da Capo (11 AM today)
and the Cullinane frequency matrix (12×12).
Matrix used to illustrate the well-tempered
scale. The integer frequency-ratio values
are only approximate in such a scale.
See also last night's "Pink Champagne on Ice" post.
The "ice" in that post's title refers to the white lines
forming a tesseract in the book cover's background—
"icy white and crystalline," as Johnny Mercer put it.
(A Tune for Josefine, Nov. 25.)
See also the tag Diamond Theory tesseract in this journal.
"Let’s love, and kill like 17 now."
— AFI song, soundtrack of "City of Bones"
See also Comic Strip Dead and
Llewyn Davis in this journal.
Related material —
* The title is a musical term…
The title refers to a post of April 26, 2009.
For Blancanieves, Elizabeth Taylor, and Lily Collins.
See also this journal on the above upload date— June 21, 2012.
Or: The Naked Blackboard Jungle
"…it would be quite a long walk
Swiftly Mrs. Who brought her hands… together.
"Now, you see," Mrs. Whatsit said,
– A Wrinkle in Time , |
Related material: Machete Math and…
Starring the late Eleanor Parker as Swiftly Mrs. Who.
An I Ching study quoted in Waiting for Ogdoad (St. Andrew's Day, 2013)—
(Click for clearer image.)
The author of the above I Ching study calls his lattice "Arising Heaven."
The following lattice might, therefore, be called "Heaven Descending."
Click for the source, mentioned in Anatomy of a Cube (Sept. 18, 2011).
Tonight was Honors Night at the Kennedy Center.
"For every kind of vampire,
there is a kind of cross." — Pynchon
From "Colin Wilson: The Persistence of Meaning" "At a literary conference at SUNY New Paltz three years ago, among people who I thought would be positively disposed to Wilson, my mentioning of his name resulted in any number of arched eyebrows and suavely disparaging remarks. Now this might itself be, not an affirmation of justified oblivion, as one could easily assume, but rather a kind of indirect evidence for intrinsic merit. I stress the academic character of the event and the self-assured oiliness of the dismissal. In context, the reference seemed to carry a distinctly un-PC valence so that the reaction to it, as I picture it in retrospect, resembled that of a patrician vampire to garlic."
— Thomas F. Bertonneau on Thursday, |
* The title refers to the film illustrated above, and also
(with a different meaning) to this morning's 11 AM post,
as well as to topics that may interest fans of the authors
in this afternoon's previous post.
Update of 2:02 PM ET:
From this journal on the day of Wilson's death—
"Danvers is a town in Essex County, Massachusetts, |
These two quotations, intended for Stephen King fans,
may also appeal to Colin Wilson fans.
… and Little Colva—
Two links on a Jewish approach to such matters:
Bee Season and, more generally, Kabbalah.
"So it's the laughter we will remember…." —Streisand
Speak for yourself, Barbra.
Wachs reportedly died on Monday, December 2, 2013.
"What's too painful to remember…" — Streisand
"So set 'em up, Joe…" — Sinatra
I've got a little story you oughta know .
A recent addition to Barry Mazur's home page—
"December 1, 2013: Here are rough notes for
a short talk entitled The Faces of Evidence
(in Mathematics) ([PDF]) to be given at the
Cambridge Scientific Club, Dec. 5 2013."
The PDF link does not work, but some earlier remarks by
Mazur on this topic have been published elsewhere:
Related material:
The Proof and the Lie (St. Andrew's Day, 2003), and
a recent repetition of the lie in Wikipedia:
"Around 1955, Japanese mathematicians Goro Shimura
and Yutaka Taniyama observed a possible link between
two apparently completely distinct, branches of mathematics,
elliptic curves and modular forms."
This statement, from the article on Algebraic number theory,
was added on Oct. 22, 2013 by one "Brirush," apparently a
Temple University postdoctoral researcher, in what he rightly
called a "terrible history summary."
Happy Feast of Saint Nicholas.
See the previous post, the remarks of Roger Kimball
on Frank Stella's lecture at Harvard on Oct. 12, 1983,
and "Study of O" in this journal, with my own images
of space from October 1983.
* The title refers to a 1996 film.
Happy birthday to Jeff Bridges.
Related remarks: yesterday's post at this hour.
Excerpt from a poem by Johanna Skibsrud
(Toronto Quarterly , April 2, 2011)—
No, I could not love a human being if they
Even if I was a bear
Even if you were a bear
But I am not a bear. And will not eat you. And you are not a bear. And will not eat me. And that is why I could not love you. |
Related material: Into the Bereshit.
See also the remarks on space in Skibsrud's
January 2012 doctoral thesis at the University
of Montreal—
" 'The nothing that is': An Ethics of Absence
Within the Poetry of Wallace Stevens."
— as well as Bull Run I and Bull Run II.
A new website illustrates its URL.
See DiamondSpace.net.
See my Google Sites page if you would like to
download a zipped copy (31 MB) of my
Finite-Geometry Notes site
(not zipped, at finitegeometry.org/sc/map.html).
Or you can of course use a website downloader.
(Suggested by a recent NY Times piece on
a company, Citia, that splits books into pieces
for easier electronic access. The large zipped
file referred to above is sort of a reverse of this
process.)
First edition, 1973, cover art by Gene Szafran
"It's going to be accomplished in steps,
this establishment of the Talented
in the scheme of things."
— To Ride Pegasus ,
by Anne McCaffrey (Radcliffe '47)
Click for clearer image.
From Willard Van Orman Quine Guest Book Volume 1—
"May 7, 1997 'McX and Wyman' — In his essay 'On What There Is', Willard Quine introduces two fictional philosophers who put forward certain ontological doctrines: McX and Wyman. It would be interesting to know whether Quine was thereby alluding to some real philosophers. My guess for McX would be Hugh MacColl, but I have no idea who Wyman might stand for. Thanks for considering the question! from Dr. Kai F. Wehmeier — Email: Kai.Wehmeier (at) math.uni-muenster.de Web Page: http://wwwmath.uni-muenster.de/math/users/wehmeier/"
"I spoke with Prof Quine last night regarding your question which he found interesting. He says his intention was to create some fictional philosophers ('X' and 'Y') to illustrate some of his concerns. There may also have been a 'Z' man. These fictional philosophers were not designed to represent any particular philosophers although their viewpoints may happen [to] reflect those of actual philosophers. – Doug” [Douglas Boynton Quine]
Related material:
The X-Men Tree (Nov. 12),
X-Men Tree continued (Nov. 17),
Waiting for Ogdoad (Oct. 30),
Interpenetrative Ogdoad (Oct. 31),
Waiting for Ogdoad continued (Nov. 30),
For Sean Connery on St. Andrew's Day (Nov. 30).
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