Heard Thursday evening in the dark fields of the republic —
"Rebel rebel, you've torn your dress
Rebel rebel, your face is a mess
Rebel rebel, how could they know?
Hot tramp, I love you so!"
Addendum — 10:30 AM ET on 5 Nov. 2022 —
Addendum — 5:45 PM ET on 4 Nov. 2022 —
The Triangle Club of Sadness
"If you can't dazzle 'em with brilliance,
baffle 'em with bullshit." — Folk saying
Brilliance —
Bullshit —
A New York Times book review on All Saints' Day 2002 —
"Like every villain, Sill has an origin story. This one involves
the murder of his father and the assassination of Martin Luther King Jr.
As vengeance, Sill resolves to destroy America using a weapon
called a 'complex projective plane orbiter.' What does that mean?
Don’t worry about it."
Related reading: The Aloha Grid .
"Rotate, Flip, and Stretch, Baby!"
"One way to evaluate an artist is to observe the quantity and quality
of misinterpretation his work begets. By this measure Everett ranks
very highly. 'Damn it, I don’t understand it, but I love it,' mutters one
of the characters, regarding Sill’s weapon of nothingness. Same.
Kitu has a colleague named Eigen Vector, which refers to …
something having to do with linear transformations?"
— Book review by Molly Young in The New York Times
on All Hallows' Day 2022
See as well Bik in The New Yorker on June 23, 2021.
"In a typical Booth cartoon, a lot happens at once."
Cartoonish news from yesterday . . .
New Yorker cartoon caption, not by Booth —
"What part of Noh don't you understand?"
Scholium —
The H — and …
(Title suggested by Google News today
and by a Percival Everett short story.}
"Principal photography has begun in Croatia
on the action thriller Canary Black , starring Kate Beckinsale
and Rupert Friend (Anatomy of a Scandal )."
"The film’s plot follows a top CIA operative, Avery Graves
(Beckinsale)…. Cut off from her team, she turns to her
underworld contacts to survive and help locate the
coveted intelligence that the kidnappers want."
[Croatia , underworld , and coveted intelligence links added.}
From other Log24 posts tagged "The Phantom Date" —
“… her mouth is red and large, with Disney overtones. But it is her eyes,
a pale green of surprising intensity, that hold me.”
— Violet Henderson in Vogue , 30 August 2017
The above title is that of a Log24 post on St. Cecilia's Day in 2017
that quoted some earlier All Souls' Day remarks from Berlin.
From that post —
Exercise: Explain why the lead article in the November issue of
Notices of the American Mathematical Society misquotes Weyl
and gives the misleading impression that the example above,
the eightfold cube , might be part of the mathematical pursuit
known as geometric group theory .
Background: Earlier instances here of the phrase "geometric group theory."
The New York Times today reported a death on October 18th,
the Feast of St. Luke.
See also Luke in this journal. Some will prefer Cool Hand Luke to
the alleged gospel author.
From Log24 posts tagged Boole vs. Galois —
Kauffman‘s fixation on the work of Spencer-Brown is perhaps in part
due to Kauffman’s familiarity with Boolean algebra and his ignorance of
Galois geometry. See other posts now tagged Boole vs. Galois.
See also “A Four-Color Epic” (April 16, 2020).
See also "hell of a band" in this journal.
From an Oct. 26 elegy in the form of a book review …
From a search in this journal for "deploy" —
Related art —
As for "Miracles and Visionaries," I prefer the literature associated
with the 1974 Miracle Octad Generator of R. T. Curtis.
A reference to neoliberalism in today's news suggests a look at
a British journalist's remarks from April 2016 . . .
"Like communism, neoliberalism is
the God that failed. But the zombie doctrine
staggers on . . . ."
Big Rock
"I'm going to hit this problem
with a big rock."
– Mathematical saying, quoted here
on St. Peter's Day 2008
"I see a red door and I want it painted black" — The Rolling Stones
"… Évariste was born on October 25, 1811."
— Eric Temple Bell, Men of Mathematics
Related material —
But seriously . . .
For Pekonen in this journal, see
From the Finland Station (25 April 2022).
See as well an obituary from Finland.
Related material —
CLIPPED FROM The Californian , Salinas, California,
28 July 2001, Saturday • Page 25 —
The above 2001 article on Cruz Saddlery in Salinas is about the family
of "Sacheen Littlefeather," whose real name was reportedly Maria Louise Cruz.
For more about Maria/Sacheen, see yesterday's San Francisco Chronicle :
"Sacheen Littlefeather was a Native American icon.
Her sisters say she was an ethnic fraud."
From that article —
Also on October 3rd . . . The Concrete of Destiny .
See also . . .
Illustration . . .
Metadata —
Continuing the "Design Awards" series of posts . . .
See as well, from a search in this journal for Caprica . . .
Meanwhile, in this journal on the above date of death —
The above image of an 18 Sept. post commemorates a Sept. 18 death.
Related material: Kiss of the Spider Woman and Dramarama.
See as well remarks here from 23 Dec. 2014
on the Greek word "stoicheia."
… "and moss grows fat on a rolling stone."
The previous post suggests A Scholium for St. Bridget . . .
The author of the above Math Academy story is one Jay Mathews:
As a model for accelerated learning, I prefer Kate Demianova.
"Boron atoms and metal atoms can form a configuration . . . ."
See as well other posts now tagged Death Valley Days.
See as well "Sunset Boulevard" in this journal.
Fake News headline from the previous post —
"Treasure Seeker Trapped in Burial Vault"
Illustration —
A link in memory of a Princeton-educated mathematics professor who
reportedly died on June 22, 2022 . . . Some non-Princeton triangles.
A routine check for the accuracy of Watson's quotation yields the source
of Didion's remarks — a 1975 UC Riverside commencement address.
A search for background on the previous post's Eliot Weinberger yields,
from Berlin . . .
"In 2000 he was the first US writer to be honoured with
the Order of the Aztec Eagle from the Mexican government."
— "2000 zeichnete ihn die mexikanische Regierung als ersten
US-amerikanischen Autor mit dem Order of the Aztec Eagle aus."
The Aztec Eagle with a serpent in its beak, landing on a prickly pear,
is pictured on the flag of Mexico.
See also Weinberger's work at Prickly Paradigm Press.
Related material: Other Log24 posts tagged Prickly.
"Think about anything often enough, from enough angles,
and it’s bound to splinter and refract. Our minds are like
kaleidoscopes, packed with mirrors we twist to see the
world anew. Sometimes we’re twisting consciously,
sometimes unconsciously. But no matter what, we end up
seeing patterns that are more a product of the tool in hand
than of the world on its other end."
— Henry M. Cowles in The Los Angeles Review of Books ,
October 11, 2022
Cowles on the book under review —
"… Patrick House’s Nineteen Ways of Looking at Consciousness ,
a new book on neuroscience and its limits. Lest readers jump to
the wrong conclusion: The referent in House’s title, though also
poetic, is not Stevens but rather Nineteen Ways of Looking at
Wang Wei , an anthology of attempts to translate a four-line poem
from the Tang Dynasty."
"The referent" anthology is, according to Google Books,
"a close reading of different translations of a single poem."
The close reader is Eliot Weinberger, who appeared here in 2011 …
The "my own" link above is to "Pilate Goes to Kindergarten."
See also a Log24 search for "The Path."
Related material from a similar search
for "Nanavira Thera" —
"I am glad you have discovered that the situation is comical:
ever since studying Kummer I have been, with some difficulty,
refraining from making that remark."
— Nanavira Thera, Seeking the Path [Early Letters, 17 July 1958].
The following note from Oct. 10, 1985, was not included
in my finitegeometry.org/sc pages.
See some related group actions on the cuboctahedron at right above.
"For Marker, memory isn’t passive; it’s an act of resistance—
the edge that cuts a path into the future—and the effective work
of memory is the very definition of art."
— July 30, 2012 in The New Yorker… Richard Brody on the late
film editor Chris Marker.
("Raiders of the Lost Spell" continues.)
The above flashback to a 2002 post was suggested by a search in
this journal for "Firebird" that yielded, as the only result . . .
http://www.amazon.com/
Witch-Seldom-Firebird-Nancy-Springer/dp/0142302201/.
That URL connects to The Hex Witch of Seldom at Amazon.com.
That book was reportedly published by Firebird on September 16, 2002,
the date of the above Log24 post.
Log24 art (colored Unicode symbols) from the above date of death:
"Click the red symbol, and …"
— Adapted from "The Matrix."
The phrase "cultural correlations" from the previous post suggests . . .
From this journal on Bloomsday 2008 —
The holy image
denoting belief and revelation
may be interpreted as
a black hole or as a
symbol by James Joyce :
|
When? Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler. Where?
— Ulysses , conclusion of Chapter 17. |
See the previous post as well as posts now tagged Soul and Spirit.
|
Soul
|
Spirit
|
The mirror has two faces (at least).
[Klein, 1983] S. Klein.
"Analogy and Mysticism and the Structure of Culture
(and Comments & Reply)"
Current Anthropology , 24 (2):151–180, 1983.
The citation above is from a 2017 paper —
"Analogy-preserving Functions:
A Way to Extend Boolean Samples,"
by M. Couceiro, N. Hug, H. Prade, G, Richard.
26th International Joint Conference on Artificial Intelligence
(IJCAI 2017), Aug. 2017, Melbourne, Australia. pp.1-7, ff.
That 2017 paper discusses Boolean functions .
Some more-recent remarks on these functions
as pure mathematics —
"On the Number of Affine Equivalence Classes
of Boolean Functions," by Xiang-dong Hou,
arXiv:2007.12308v2 [math.CO]. Rev. Aug. 18, 2021.
See also other posts now tagged Analogy and Mysticism.
"Battles argues that 'the experience of the physicality
of the book is strongest in large libraries,' and stand
among the glass cube at the center of the British Library,
the stacks upon stacks in Harvard’s Widener Library, or
the domed portico of the Library of Congress and tell me
any differently."
— Ed Simon, Binding the Ghost: Theology, Mystery, and
the Transcendence of Literature. Hardcover – April 19, 2022.
… And back to cube:
Related meditation: Beer Summit.
In memory of a mathematics professor who
reportedly died on May 21, 2022 —
"… mouses over to a file …." Or a folder.
The above art by Steven H. Cullinane is not unrelated to
art by Josefine Lyche. Her work includes sculpted replicas
of the above abstract Platonic solids, as well as replicas of
my own work related to properties of the 4×6 rectangle above.
Symmetries of both the solids and the rectangle may be
viewed as permutations of parts — In the Platonic solids,
the parts are permuted by continuous rotations of space itself.
In the rectangle, the parts are permuted by non-continuous
transformations, as in the I Ching . . . i.e., by concrete illustrations
of change.
Also on the above Berlin date —
Wednesday, November 6, 2013
|
"… a hyper-intellectual fable that riddles you into a house
of mirrors from which you wonder if you’ll ever emerge.
(Imagine packaging the universe’s most existential questions
as Abbott and Costello’s 'Who’s on First?' routine.)"
— Book review by Michael Callahan in The New York Times
on September 19, 2022.
The exercise posted here on Sept. 11, 2022, suggests a
more precisely stated problem . . .
The 24 coordinate-positions of the 4096 length-24 words of the
extended binary Golay code G24 can be arranged in a 4×6 array
in, of course, 24! ways.
Some of these ways are more geometrically natural than others.
See, for instance, the Miracle Octad Generator of R. T. Curtis.
What is the size of the largest subcode C of G24 that can be
arranged in a 4×6 array in such a way that the set of words of C
is invariant under the symmetry group of the rectangle itself, i.e. the
four-group of the identity along with horizontal and vertical reflections
and 180-degree rotation.
Recent Log24 posts tagged Bitspace describe the structure of
an 8-dimensional (256-word) code in a 4×6 array that has such
symmetry, but it is not yet clear whether that "cube-motif" code
is a Golay subcode. (Its octads are Golay, but possibly not all its
dodecads; the octads do not quite generate the entire code.)
Magma may have an answer, but I have had little experience in
its use.
* Footnote of 30 September 2022. The 4×6 problem is a
special case of a more general symmetric embedding problem.
Given a linear code C and a mapping of C to parts of a geometric
object A with symmetry group G, what is the largest subcode of C
invariant under G? What is the largest such subcode under all
such mappings from C to A?
Update of 5:20 AM ET on Sept. 29. 2022 —
The octads of the [24, 8, 8] cube-motif code
can be transformed by the permutation below
into octads recognizable, thanks to the Miracle
Octad Generator (MOG) of R. T. Curtis, as
belonging to the Golay code.
The title is by Henry James.*
For examples, see the Sept. 19 webpage below . . .
… and, in this journal, posts from that same date now tagged Cube Codes.
*
For connoisseurs of bullshit, from The New Yorker yesterday —
“A Trip to Infinity” and the Delicate Art
|
"Remember, remember
the eighth of September."
Update of 6 AM Sept. 27:
A search for related material
on The Eighth of September
yields a Pablo Neruda poem
and a Barbara Stevens Sullivan
novel, both with that title.
Also by Sullivan . . .
See as well a Log24 post from 2016, "The Mystery of O,"
on June 29, the Feast of Saints Peter and Paul.
"The actor Nick Offerman, himself an accomplished woodworker
and a member of Ms. Hiller’s legion of admirers, called her an
'Obi-Wan Kenobi level master.'"
— The New York Times this evening, obituary by Clay Risen
for Nancy Hiller.
Related woodwork note —
Click the above to search this journal for "Dead End."
In memory of historical novelist Hilary Mantel, who reportedly
died yesterday, two images dealing with this year's Sept. 11 —
The image from Rome was suggested by yesterday's Dürer post and
by the year 1514 in the life of Thomas Cromwell, Mantel's main topic.
Jung’s four-diamond figure from
Aion — a symbol of the self –
For those who prefer the Ed Wood approach —
The previous post's image illustrating the
ancient Lo Shu square as an affine transformation
suggests a similar view of Dürer's square.
That view illustrates the structural principle
underlying the diamond theorem —
See as well . . .
Three-color patterns from 1964,
rendered as shades of grey —
A rather different approach —
The above image is from a tweet dated Jan. 11, 2018.
Related material from this journal — That date, in posts
now tagged In the Bag. Those posts are followups to
a remark by Nabokov:
The previous post's Data Meets Meta tale continues —
There's a world where I can go
Tell my secrets to
In my room
In my room (in my room)…
— Beach Boys, 1963
"A good public narrative can, at the best of times,
transform an art theft into a lucky break for the gallery."
From a search in this journal for Goya —
From "Raiders of the Lost Space," Sept. 11, 2022 —
A related technique appears in a 1989 paper by Cheng and Sloane
that I saw for the first time today:
A linear code of length 24, dimension 8, and minimum weight 8
(a "[24, 8, 8] code") that was discussed in recent posts tagged
Bitspace might, viewed as a vector space, be called "motif space."
Yesterday evening's post "From a Literature Search for Binary [24, 8, 8] Codes"
has been updated. A reference from that update —
Computer Science > Information Theory
|
| Comments: | To appear in IEEE Trans. on Information Theory Vol. 24 No. 8 |
| Subjects: | Information Theory (cs.IT) |
| Cite as: | arXiv:cs/0607074 [cs.IT] |
From Peng and Farrell, 2006 —
For one example of a binary [24, 8, 8] code, see other bitspace posts.
It is not clear whether that example is a subcode of the Golay code.
See also
http://www.codetables.de/BKLC/
Tables.php?q=2&n0=1&n1=256&k0=1&k1=256
and
http://www.codetables.de/BKLC/BKLC.php?q=2&n=12&k=8 .
Update of 3:22 AM ET on 20 September 2022 —
Update of 3:44 AM ET 20 September 2022 —
Another relevant document:
"The kaleidoscope of peoples, parties and religions…."
— Description of Vienna in the early 20th century from
"Black Gold and Yellow Star" by Jerome Segal (PDF, 16 pp.)
See as well Mosaic and Kaleidoscope in this journal.
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